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<!doctype html><html lang=en-us><head><meta charset=utf-8><meta http-equiv=X-UA-Compatible content="IE=edge"><meta name=viewport content="width=device-width,initial-scale=1,shrink-to-fit=no"><title>w8 - lavafroth</title><meta name=description content="GRPA 1
def findOccOf(arr, x):
lo = 0
hi = len(arr) - 1
loval = None
while lo <= hi:
mid = (lo + hi) // 2
c = arr[mid]
if x < c:
hi = mid - 1
elif x > c:
lo = mid + 1
elif x == c:
loval = loval or mid
loval = min(loval, mid)
hi = mid - 1
lo = 0
hi = len(arr) - 1
hival = None
while lo <= hi:
mid = (lo + hi) // 2
c = arr[mid]
if x < c:
hi = mid - 1
elif x > c:
lo = mid + 1
elif x == c:
hival = hival or mid
hival = max(hival, mid)
lo = mid + 1
return loval, hival
GRPA 2
def merge_inversion(left, right):
merged = []
count = 0
i, j = 0, 0
m = len(left)
n = len(right)
while i + j < m + n:
if j == n or (i != m and left[i] < right[j]):
merged.append(left[i])
i += 1
continue
merged.append(right[j])
j += 1
count += m - i
return merged, count
def sort_and_count(arr):
n = len(arr)
if n == 1:
return arr, 0
left = arr[: n // 2]
right = arr[n // 2 :]
left, count_left = sort_and_count(left)
right, count_right = sort_and_count(right)
merged, count_both = merge_inversion(left, right)
return (merged, count_left + count_right + count_both)
def countIntersection(a, b):
tuples = sorted(zip(a, b))
b = [t[1] for t in tuples]
return sort_and_count(b)[1]
GRPA 3
dist = lambda a, b: ((a[0]-b[0])**2 + (a[1]-b[1])**2)**.5
def closest_pair(Px, Py):
n = len(Px)
if n <= 3:
min_d = float('inf')
for i in range(n):
for j in range(i + 1, n):
min_d = min(min_d, dist(Px[i], Px[j]))
return min_d
mid = n // 2
Qx = Px[:mid]
Rx = Px[mid:]
mid_point = Qx[-1][0]
Qy = []
Ry = []
for p in Py:
if p[0] <= mid_point:
Qy.append(p)
else:
Ry.append(p)
min_d = min(closest_pair(Qx, Qy), closest_pair(Rx, Ry))
Sy = [p for p in Py if mid_point - min_d <= p[0] <= mid_point + min_d]
for i in range(len(Sy)):
for j in range(i + 1, len(Sy)):
if Sy[j][1] - Sy[i][1] >= min_d:
break
min_d = min(min_d, dist(Sy[i], Sy[j]))
return min_d
def minDistance(points):
Px = sorted(points, key=lambda p: p[0])
Py = sorted(points, key=lambda p: p[1])
return round(closest_pair(Px, Py), 2)
GRPA 4
def mid(a):
if len(a) <= 7:
return sorted(a)[len(a)//2]
m = []
for i in range(0,len(a), 7):
m.append(mid(a[i:i+7]))
return mid(m)
def MoM7Pos(arr):
m = mid(arr)
pos = 0
for x in arr:
if x < m:
pos += 1
return pos
"><meta name=author content><link rel="preload stylesheet" as=style href=https://lavafroth.is-a.dev/app.min.css><link rel=preload as=image href=../header.svg><link as=font href=https://lavafroth.is-a.dev/latinmodern-math.otf><link rel=preload as=image href=https://lavafroth.is-a.dev/github.svg><link rel=preload as=image href=https://lavafroth.is-a.dev/about.svg><link rel=preload as=image href=https://lavafroth.is-a.dev/art.svg><link rel=preload as=image href=https://lavafroth.is-a.dev/rss.svg><link rel=icon href=https://lavafroth.is-a.dev/favicon.png><link rel=blog-icon href=https://lavafroth.is-a.dev/icon.png></head><body><header><a class=site-name href=https://lavafroth.is-a.dev/><svg viewBox="0 0 8790 2080"><path d="M80 1935V465h216v1270h286v2e2zm853 0 222-1470h264l222 1470h-210l-40-3e2h-208l-40 3e2zm280-528h148l-62-494-6-78h-12l-6 78zm1025 528L2014 465h210l108 868 8 142h12l8-142 108-868h210l-224 1470zm813 0 222-1470h264l222 1470h-210l-40-3e2h-208l-40 3e2zm280-528h148l-62-494-6-78h-12l-6 78zm851 528V465h514v222h-298v386h2e2v222h-2e2v640zm910 0V465h216q194 0 286 108 92 107 92 316 0 124-43 215-44 90-106 132l147 699h-216l-122-620h-38v620zm216-820q60 0 95-26 35-27 50-76t15-116q0-105-34-161-35-57-126-57zm1084 836q-90 0-154-42-65-42-99-114-35-72-35-162V767q0-91 35-162 34-72 99-114 64-42 154-42t155 42q64 42 99 114 34 72 34 162v866q0 90-34 162-35 72-99 114-65 42-155 42zm0-210q40 0 56-33 16-34 16-75V767q0-41-17-74-17-34-55-34-37 0-54 34-18 33-18 74v866q0 41 17 75 17 33 55 33zm890 194V687h-204V465h624v222h-204v1248zm828 0V465h216v608h168V465h216v1470h-216v-640h-168v640z"/></svg></a><nav><a style=--url:url(./github.svg) href=https://github.com/lavafroth aria-label=github target=_blank></a><a href=../about/ aria-label=about style=--url:url(./about.svg)></a><a href=../art/ aria-label=art style=--url:url(./art.svg)></a><a href=../index.xml aria-label=rss style=--url:url(./rss.svg)></a><nav></header><main><hgroup data-pagefind-body><p data-pagefind-ignore><time>Oct 3, 2025 | 3 minutes read</time></p><h1 data-pagefind-meta=title>w8</h1></hgroup><section class=post-content data-pagefind-body><h2 id=grpa-1>GRPA 1</h2><div class=highlight><pre tabindex=0 style=color:#f8f8f2;background-color:#272822;-moz-tab-size:4;-o-tab-size:4;tab-size:4><code class=language-python data-lang=python><span style=display:flex><span><span style=color:#66d9ef>def</span> <span style=color:#a6e22e>findOccOf</span>(arr, x):
</span></span><span style=display:flex><span> lo <span style=color:#f92672>=</span> <span style=color:#ae81ff>0</span>
</span></span><span style=display:flex><span> hi <span style=color:#f92672>=</span> len(arr) <span style=color:#f92672>-</span> <span style=color:#ae81ff>1</span>
</span></span><span style=display:flex><span>
</span></span><span style=display:flex><span> loval <span style=color:#f92672>=</span> <span style=color:#66d9ef>None</span>
</span></span><span style=display:flex><span> <span style=color:#66d9ef>while</span> lo <span style=color:#f92672>&lt;=</span> hi:
</span></span><span style=display:flex><span> mid <span style=color:#f92672>=</span> (lo <span style=color:#f92672>+</span> hi) <span style=color:#f92672>//</span> <span style=color:#ae81ff>2</span>
</span></span><span style=display:flex><span> c <span style=color:#f92672>=</span> arr[mid]
</span></span><span style=display:flex><span> <span style=color:#66d9ef>if</span> x <span style=color:#f92672>&lt;</span> c:
</span></span><span style=display:flex><span> hi <span style=color:#f92672>=</span> mid <span style=color:#f92672>-</span> <span style=color:#ae81ff>1</span>
</span></span><span style=display:flex><span> <span style=color:#66d9ef>elif</span> x <span style=color:#f92672>&gt;</span> c:
</span></span><span style=display:flex><span> lo <span style=color:#f92672>=</span> mid <span style=color:#f92672>+</span> <span style=color:#ae81ff>1</span>
</span></span><span style=display:flex><span> <span style=color:#66d9ef>elif</span> x <span style=color:#f92672>==</span> c:
</span></span><span style=display:flex><span> loval <span style=color:#f92672>=</span> loval <span style=color:#f92672>or</span> mid
</span></span><span style=display:flex><span> loval <span style=color:#f92672>=</span> min(loval, mid)
</span></span><span style=display:flex><span> hi <span style=color:#f92672>=</span> mid <span style=color:#f92672>-</span> <span style=color:#ae81ff>1</span>
</span></span><span style=display:flex><span>
</span></span><span style=display:flex><span> lo <span style=color:#f92672>=</span> <span style=color:#ae81ff>0</span>
</span></span><span style=display:flex><span> hi <span style=color:#f92672>=</span> len(arr) <span style=color:#f92672>-</span> <span style=color:#ae81ff>1</span>
</span></span><span style=display:flex><span> hival <span style=color:#f92672>=</span> <span style=color:#66d9ef>None</span>
</span></span><span style=display:flex><span> <span style=color:#66d9ef>while</span> lo <span style=color:#f92672>&lt;=</span> hi:
</span></span><span style=display:flex><span> mid <span style=color:#f92672>=</span> (lo <span style=color:#f92672>+</span> hi) <span style=color:#f92672>//</span> <span style=color:#ae81ff>2</span>
</span></span><span style=display:flex><span> c <span style=color:#f92672>=</span> arr[mid]
</span></span><span style=display:flex><span> <span style=color:#66d9ef>if</span> x <span style=color:#f92672>&lt;</span> c:
</span></span><span style=display:flex><span> hi <span style=color:#f92672>=</span> mid <span style=color:#f92672>-</span> <span style=color:#ae81ff>1</span>
</span></span><span style=display:flex><span> <span style=color:#66d9ef>elif</span> x <span style=color:#f92672>&gt;</span> c:
</span></span><span style=display:flex><span> lo <span style=color:#f92672>=</span> mid <span style=color:#f92672>+</span> <span style=color:#ae81ff>1</span>
</span></span><span style=display:flex><span> <span style=color:#66d9ef>elif</span> x <span style=color:#f92672>==</span> c:
</span></span><span style=display:flex><span> hival <span style=color:#f92672>=</span> hival <span style=color:#f92672>or</span> mid
</span></span><span style=display:flex><span> hival <span style=color:#f92672>=</span> max(hival, mid)
</span></span><span style=display:flex><span> lo <span style=color:#f92672>=</span> mid <span style=color:#f92672>+</span> <span style=color:#ae81ff>1</span>
</span></span><span style=display:flex><span>
</span></span><span style=display:flex><span>
</span></span><span style=display:flex><span> <span style=color:#66d9ef>return</span> loval, hival
</span></span></code></pre></div><h2 id=grpa-2>GRPA 2</h2><div class=highlight><pre tabindex=0 style=color:#f8f8f2;background-color:#272822;-moz-tab-size:4;-o-tab-size:4;tab-size:4><code class=language-python data-lang=python><span style=display:flex><span><span style=color:#66d9ef>def</span> <span style=color:#a6e22e>merge_inversion</span>(left, right):
</span></span><span style=display:flex><span> merged <span style=color:#f92672>=</span> []
</span></span><span style=display:flex><span> count <span style=color:#f92672>=</span> <span style=color:#ae81ff>0</span>
</span></span><span style=display:flex><span>
</span></span><span style=display:flex><span> i, j <span style=color:#f92672>=</span> <span style=color:#ae81ff>0</span>, <span style=color:#ae81ff>0</span>
</span></span><span style=display:flex><span>
</span></span><span style=display:flex><span> m <span style=color:#f92672>=</span> len(left)
</span></span><span style=display:flex><span> n <span style=color:#f92672>=</span> len(right)
</span></span><span style=display:flex><span> <span style=color:#66d9ef>while</span> i <span style=color:#f92672>+</span> j <span style=color:#f92672>&lt;</span> m <span style=color:#f92672>+</span> n:
</span></span><span style=display:flex><span> <span style=color:#66d9ef>if</span> j <span style=color:#f92672>==</span> n <span style=color:#f92672>or</span> (i <span style=color:#f92672>!=</span> m <span style=color:#f92672>and</span> left[i] <span style=color:#f92672>&lt;</span> right[j]):
</span></span><span style=display:flex><span> merged<span style=color:#f92672>.</span>append(left[i])
</span></span><span style=display:flex><span> i <span style=color:#f92672>+=</span> <span style=color:#ae81ff>1</span>
</span></span><span style=display:flex><span> <span style=color:#66d9ef>continue</span>
</span></span><span style=display:flex><span>
</span></span><span style=display:flex><span> merged<span style=color:#f92672>.</span>append(right[j])
</span></span><span style=display:flex><span> j <span style=color:#f92672>+=</span> <span style=color:#ae81ff>1</span>
</span></span><span style=display:flex><span> count <span style=color:#f92672>+=</span> m <span style=color:#f92672>-</span> i
</span></span><span style=display:flex><span>
</span></span><span style=display:flex><span> <span style=color:#66d9ef>return</span> merged, count
</span></span><span style=display:flex><span>
</span></span><span style=display:flex><span>
</span></span><span style=display:flex><span><span style=color:#66d9ef>def</span> <span style=color:#a6e22e>sort_and_count</span>(arr):
</span></span><span style=display:flex><span> n <span style=color:#f92672>=</span> len(arr)
</span></span><span style=display:flex><span> <span style=color:#66d9ef>if</span> n <span style=color:#f92672>==</span> <span style=color:#ae81ff>1</span>:
</span></span><span style=display:flex><span> <span style=color:#66d9ef>return</span> arr, <span style=color:#ae81ff>0</span>
</span></span><span style=display:flex><span> left <span style=color:#f92672>=</span> arr[: n <span style=color:#f92672>//</span> <span style=color:#ae81ff>2</span>]
</span></span><span style=display:flex><span> right <span style=color:#f92672>=</span> arr[n <span style=color:#f92672>//</span> <span style=color:#ae81ff>2</span> :]
</span></span><span style=display:flex><span>
</span></span><span style=display:flex><span> left, count_left <span style=color:#f92672>=</span> sort_and_count(left)
</span></span><span style=display:flex><span> right, count_right <span style=color:#f92672>=</span> sort_and_count(right)
</span></span><span style=display:flex><span> merged, count_both <span style=color:#f92672>=</span> merge_inversion(left, right)
</span></span><span style=display:flex><span>
</span></span><span style=display:flex><span> <span style=color:#66d9ef>return</span> (merged, count_left <span style=color:#f92672>+</span> count_right <span style=color:#f92672>+</span> count_both)
</span></span><span style=display:flex><span>
</span></span><span style=display:flex><span><span style=color:#66d9ef>def</span> <span style=color:#a6e22e>countIntersection</span>(a, b):
</span></span><span style=display:flex><span> tuples <span style=color:#f92672>=</span> sorted(zip(a, b))
</span></span><span style=display:flex><span> b <span style=color:#f92672>=</span> [t[<span style=color:#ae81ff>1</span>] <span style=color:#66d9ef>for</span> t <span style=color:#f92672>in</span> tuples]
</span></span><span style=display:flex><span> <span style=color:#66d9ef>return</span> sort_and_count(b)[<span style=color:#ae81ff>1</span>]
</span></span></code></pre></div><h2 id=grpa-3>GRPA 3</h2><div class=highlight><pre tabindex=0 style=color:#f8f8f2;background-color:#272822;-moz-tab-size:4;-o-tab-size:4;tab-size:4><code class=language-python data-lang=python><span style=display:flex><span>dist <span style=color:#f92672>=</span> <span style=color:#66d9ef>lambda</span> a, b: ((a[<span style=color:#ae81ff>0</span>]<span style=color:#f92672>-</span>b[<span style=color:#ae81ff>0</span>])<span style=color:#f92672>**</span><span style=color:#ae81ff>2</span> <span style=color:#f92672>+</span> (a[<span style=color:#ae81ff>1</span>]<span style=color:#f92672>-</span>b[<span style=color:#ae81ff>1</span>])<span style=color:#f92672>**</span><span style=color:#ae81ff>2</span>)<span style=color:#f92672>**</span><span style=color:#ae81ff>.5</span>
</span></span><span style=display:flex><span>
</span></span><span style=display:flex><span><span style=color:#66d9ef>def</span> <span style=color:#a6e22e>closest_pair</span>(Px, Py):
</span></span><span style=display:flex><span> n <span style=color:#f92672>=</span> len(Px)
</span></span><span style=display:flex><span> <span style=color:#66d9ef>if</span> n <span style=color:#f92672>&lt;=</span> <span style=color:#ae81ff>3</span>:
</span></span><span style=display:flex><span> min_d <span style=color:#f92672>=</span> float(<span style=color:#e6db74>&#39;inf&#39;</span>)
</span></span><span style=display:flex><span> <span style=color:#66d9ef>for</span> i <span style=color:#f92672>in</span> range(n):
</span></span><span style=display:flex><span> <span style=color:#66d9ef>for</span> j <span style=color:#f92672>in</span> range(i <span style=color:#f92672>+</span> <span style=color:#ae81ff>1</span>, n):
</span></span><span style=display:flex><span> min_d <span style=color:#f92672>=</span> min(min_d, dist(Px[i], Px[j]))
</span></span><span style=display:flex><span> <span style=color:#66d9ef>return</span> min_d
</span></span><span style=display:flex><span>
</span></span><span style=display:flex><span> mid <span style=color:#f92672>=</span> n <span style=color:#f92672>//</span> <span style=color:#ae81ff>2</span>
</span></span><span style=display:flex><span> Qx <span style=color:#f92672>=</span> Px[:mid]
</span></span><span style=display:flex><span> Rx <span style=color:#f92672>=</span> Px[mid:]
</span></span><span style=display:flex><span> mid_point <span style=color:#f92672>=</span> Qx[<span style=color:#f92672>-</span><span style=color:#ae81ff>1</span>][<span style=color:#ae81ff>0</span>]
</span></span><span style=display:flex><span>
</span></span><span style=display:flex><span> Qy <span style=color:#f92672>=</span> []
</span></span><span style=display:flex><span> Ry <span style=color:#f92672>=</span> []
</span></span><span style=display:flex><span> <span style=color:#66d9ef>for</span> p <span style=color:#f92672>in</span> Py:
</span></span><span style=display:flex><span> <span style=color:#66d9ef>if</span> p[<span style=color:#ae81ff>0</span>] <span style=color:#f92672>&lt;=</span> mid_point:
</span></span><span style=display:flex><span> Qy<span style=color:#f92672>.</span>append(p)
</span></span><span style=display:flex><span> <span style=color:#66d9ef>else</span>:
</span></span><span style=display:flex><span> Ry<span style=color:#f92672>.</span>append(p)
</span></span><span style=display:flex><span>
</span></span><span style=display:flex><span> min_d <span style=color:#f92672>=</span> min(closest_pair(Qx, Qy), closest_pair(Rx, Ry))
</span></span><span style=display:flex><span>
</span></span><span style=display:flex><span> Sy <span style=color:#f92672>=</span> [p <span style=color:#66d9ef>for</span> p <span style=color:#f92672>in</span> Py <span style=color:#66d9ef>if</span> mid_point <span style=color:#f92672>-</span> min_d <span style=color:#f92672>&lt;=</span> p[<span style=color:#ae81ff>0</span>] <span style=color:#f92672>&lt;=</span> mid_point <span style=color:#f92672>+</span> min_d]
</span></span><span style=display:flex><span> <span style=color:#66d9ef>for</span> i <span style=color:#f92672>in</span> range(len(Sy)):
</span></span><span style=display:flex><span> <span style=color:#66d9ef>for</span> j <span style=color:#f92672>in</span> range(i <span style=color:#f92672>+</span> <span style=color:#ae81ff>1</span>, len(Sy)):
</span></span><span style=display:flex><span> <span style=color:#66d9ef>if</span> Sy[j][<span style=color:#ae81ff>1</span>] <span style=color:#f92672>-</span> Sy[i][<span style=color:#ae81ff>1</span>] <span style=color:#f92672>&gt;=</span> min_d:
</span></span><span style=display:flex><span> <span style=color:#66d9ef>break</span>
</span></span><span style=display:flex><span> min_d <span style=color:#f92672>=</span> min(min_d, dist(Sy[i], Sy[j]))
</span></span><span style=display:flex><span>
</span></span><span style=display:flex><span> <span style=color:#66d9ef>return</span> min_d
</span></span><span style=display:flex><span>
</span></span><span style=display:flex><span>
</span></span><span style=display:flex><span><span style=color:#66d9ef>def</span> <span style=color:#a6e22e>minDistance</span>(points):
</span></span><span style=display:flex><span> Px <span style=color:#f92672>=</span> sorted(points, key<span style=color:#f92672>=</span><span style=color:#66d9ef>lambda</span> p: p[<span style=color:#ae81ff>0</span>])
</span></span><span style=display:flex><span> Py <span style=color:#f92672>=</span> sorted(points, key<span style=color:#f92672>=</span><span style=color:#66d9ef>lambda</span> p: p[<span style=color:#ae81ff>1</span>])
</span></span><span style=display:flex><span> <span style=color:#66d9ef>return</span> round(closest_pair(Px, Py), <span style=color:#ae81ff>2</span>)
</span></span></code></pre></div><h2 id=grpa-4>GRPA 4</h2><div class=highlight><pre tabindex=0 style=color:#f8f8f2;background-color:#272822;-moz-tab-size:4;-o-tab-size:4;tab-size:4><code class=language-python data-lang=python><span style=display:flex><span><span style=color:#66d9ef>def</span> <span style=color:#a6e22e>mid</span>(a):
</span></span><span style=display:flex><span> <span style=color:#66d9ef>if</span> len(a) <span style=color:#f92672>&lt;=</span> <span style=color:#ae81ff>7</span>:
</span></span><span style=display:flex><span> <span style=color:#66d9ef>return</span> sorted(a)[len(a)<span style=color:#f92672>//</span><span style=color:#ae81ff>2</span>]
</span></span><span style=display:flex><span>
</span></span><span style=display:flex><span> m <span style=color:#f92672>=</span> []
</span></span><span style=display:flex><span> <span style=color:#66d9ef>for</span> i <span style=color:#f92672>in</span> range(<span style=color:#ae81ff>0</span>,len(a), <span style=color:#ae81ff>7</span>):
</span></span><span style=display:flex><span> m<span style=color:#f92672>.</span>append(mid(a[i:i<span style=color:#f92672>+</span><span style=color:#ae81ff>7</span>]))
</span></span><span style=display:flex><span>
</span></span><span style=display:flex><span> <span style=color:#66d9ef>return</span> mid(m)
</span></span><span style=display:flex><span>
</span></span><span style=display:flex><span><span style=color:#66d9ef>def</span> <span style=color:#a6e22e>MoM7Pos</span>(arr):
</span></span><span style=display:flex><span> m <span style=color:#f92672>=</span> mid(arr)
</span></span><span style=display:flex><span> pos <span style=color:#f92672>=</span> <span style=color:#ae81ff>0</span>
</span></span><span style=display:flex><span> <span style=color:#66d9ef>for</span> x <span style=color:#f92672>in</span> arr:
</span></span><span style=display:flex><span> <span style=color:#66d9ef>if</span> x <span style=color:#f92672>&lt;</span> m:
</span></span><span style=display:flex><span> pos <span style=color:#f92672>+=</span> <span style=color:#ae81ff>1</span>
</span></span><span style=display:flex><span> <span style=color:#66d9ef>return</span> pos
</span></span></code></pre></div></section><footer class=post-tags data-pagefind-meta=tags></footer></main><footer class=footer><p>&copy; 2025 <a href=https://lavafroth.is-a.dev/>lavafroth</a></p><p><a href=https://github.com/lavafroth/lavafroth.github.io/issues/new/choose>Report an issue</a></p><p><a href=https://github.com/lavafroth/lavafroth.github.io/discussions/>Discuss</a></p><p><a href=https://lavafroth.is-a.dev/privacy>Privacy</a></p><p><a href=https://creativecommons.org/licenses/by-sa/4.0/legalcode>License</a></p></footer></body></html>

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@@ -89,7 +89,140 @@ I am also fallible to mistakes.&lt;/p&gt;
&lt;/ol&gt;
&lt;h1 id="aq23"&gt;AQ2.3&lt;/h1&gt;
&lt;blockquote&gt;
&lt;p&gt;Selection sort always makes n(n-1)/2 comparisons which is of order &lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt; O(n^2) &lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/p&gt;</description></item><item><title>NixOS Notes to Self</title><link>https://lavafroth.is-a.dev/post/nixos-notes-to-self/</link><pubDate>Sun, 14 Sep 2025 18:31:52 +0530</pubDate><guid>https://lavafroth.is-a.dev/post/nixos-notes-to-self/</guid><description>&lt;p&gt;A dedicated post collecting solutions to minor NixOS headaches.&lt;/p&gt;
&lt;p&gt;Selection sort always makes n(n-1)/2 comparisons which is of order &lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt; O(n^2) &lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/p&gt;</description></item><item><title>w8</title><link>https://lavafroth.is-a.dev/divmqbyvl9y/</link><pubDate>Fri, 03 Oct 2025 16:04:18 +0530</pubDate><guid>https://lavafroth.is-a.dev/divmqbyvl9y/</guid><description>&lt;h2 id="grpa-1"&gt;GRPA 1&lt;/h2&gt;
&lt;div class="highlight"&gt;&lt;pre tabindex="0" style="color:#f8f8f2;background-color:#272822;-moz-tab-size:4;-o-tab-size:4;tab-size:4;"&gt;&lt;code class="language-python" data-lang="python"&gt;&lt;span style="display:flex;"&gt;&lt;span&gt;&lt;span style="color:#66d9ef"&gt;def&lt;/span&gt; &lt;span style="color:#a6e22e"&gt;findOccOf&lt;/span&gt;(arr, x):
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; lo &lt;span style="color:#f92672"&gt;=&lt;/span&gt; &lt;span style="color:#ae81ff"&gt;0&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; hi &lt;span style="color:#f92672"&gt;=&lt;/span&gt; len(arr) &lt;span style="color:#f92672"&gt;-&lt;/span&gt; &lt;span style="color:#ae81ff"&gt;1&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; loval &lt;span style="color:#f92672"&gt;=&lt;/span&gt; &lt;span style="color:#66d9ef"&gt;None&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; &lt;span style="color:#66d9ef"&gt;while&lt;/span&gt; lo &lt;span style="color:#f92672"&gt;&amp;lt;=&lt;/span&gt; hi:
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; mid &lt;span style="color:#f92672"&gt;=&lt;/span&gt; (lo &lt;span style="color:#f92672"&gt;+&lt;/span&gt; hi) &lt;span style="color:#f92672"&gt;//&lt;/span&gt; &lt;span style="color:#ae81ff"&gt;2&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; c &lt;span style="color:#f92672"&gt;=&lt;/span&gt; arr[mid]
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; &lt;span style="color:#66d9ef"&gt;if&lt;/span&gt; x &lt;span style="color:#f92672"&gt;&amp;lt;&lt;/span&gt; c:
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; hi &lt;span style="color:#f92672"&gt;=&lt;/span&gt; mid &lt;span style="color:#f92672"&gt;-&lt;/span&gt; &lt;span style="color:#ae81ff"&gt;1&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; &lt;span style="color:#66d9ef"&gt;elif&lt;/span&gt; x &lt;span style="color:#f92672"&gt;&amp;gt;&lt;/span&gt; c:
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; lo &lt;span style="color:#f92672"&gt;=&lt;/span&gt; mid &lt;span style="color:#f92672"&gt;+&lt;/span&gt; &lt;span style="color:#ae81ff"&gt;1&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; &lt;span style="color:#66d9ef"&gt;elif&lt;/span&gt; x &lt;span style="color:#f92672"&gt;==&lt;/span&gt; c:
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; loval &lt;span style="color:#f92672"&gt;=&lt;/span&gt; loval &lt;span style="color:#f92672"&gt;or&lt;/span&gt; mid
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; loval &lt;span style="color:#f92672"&gt;=&lt;/span&gt; min(loval, mid)
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; hi &lt;span style="color:#f92672"&gt;=&lt;/span&gt; mid &lt;span style="color:#f92672"&gt;-&lt;/span&gt; &lt;span style="color:#ae81ff"&gt;1&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; lo &lt;span style="color:#f92672"&gt;=&lt;/span&gt; &lt;span style="color:#ae81ff"&gt;0&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; hi &lt;span style="color:#f92672"&gt;=&lt;/span&gt; len(arr) &lt;span style="color:#f92672"&gt;-&lt;/span&gt; &lt;span style="color:#ae81ff"&gt;1&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; hival &lt;span style="color:#f92672"&gt;=&lt;/span&gt; &lt;span style="color:#66d9ef"&gt;None&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; &lt;span style="color:#66d9ef"&gt;while&lt;/span&gt; lo &lt;span style="color:#f92672"&gt;&amp;lt;=&lt;/span&gt; hi:
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; mid &lt;span style="color:#f92672"&gt;=&lt;/span&gt; (lo &lt;span style="color:#f92672"&gt;+&lt;/span&gt; hi) &lt;span style="color:#f92672"&gt;//&lt;/span&gt; &lt;span style="color:#ae81ff"&gt;2&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; c &lt;span style="color:#f92672"&gt;=&lt;/span&gt; arr[mid]
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; &lt;span style="color:#66d9ef"&gt;if&lt;/span&gt; x &lt;span style="color:#f92672"&gt;&amp;lt;&lt;/span&gt; c:
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; hi &lt;span style="color:#f92672"&gt;=&lt;/span&gt; mid &lt;span style="color:#f92672"&gt;-&lt;/span&gt; &lt;span style="color:#ae81ff"&gt;1&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; &lt;span style="color:#66d9ef"&gt;elif&lt;/span&gt; x &lt;span style="color:#f92672"&gt;&amp;gt;&lt;/span&gt; c:
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; lo &lt;span style="color:#f92672"&gt;=&lt;/span&gt; mid &lt;span style="color:#f92672"&gt;+&lt;/span&gt; &lt;span style="color:#ae81ff"&gt;1&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; &lt;span style="color:#66d9ef"&gt;elif&lt;/span&gt; x &lt;span style="color:#f92672"&gt;==&lt;/span&gt; c:
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; hival &lt;span style="color:#f92672"&gt;=&lt;/span&gt; hival &lt;span style="color:#f92672"&gt;or&lt;/span&gt; mid
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; hival &lt;span style="color:#f92672"&gt;=&lt;/span&gt; max(hival, mid)
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; lo &lt;span style="color:#f92672"&gt;=&lt;/span&gt; mid &lt;span style="color:#f92672"&gt;+&lt;/span&gt; &lt;span style="color:#ae81ff"&gt;1&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; &lt;span style="color:#66d9ef"&gt;return&lt;/span&gt; loval, hival
&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;h2 id="grpa-2"&gt;GRPA 2&lt;/h2&gt;
&lt;div class="highlight"&gt;&lt;pre tabindex="0" style="color:#f8f8f2;background-color:#272822;-moz-tab-size:4;-o-tab-size:4;tab-size:4;"&gt;&lt;code class="language-python" data-lang="python"&gt;&lt;span style="display:flex;"&gt;&lt;span&gt;&lt;span style="color:#66d9ef"&gt;def&lt;/span&gt; &lt;span style="color:#a6e22e"&gt;merge_inversion&lt;/span&gt;(left, right):
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; merged &lt;span style="color:#f92672"&gt;=&lt;/span&gt; []
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; count &lt;span style="color:#f92672"&gt;=&lt;/span&gt; &lt;span style="color:#ae81ff"&gt;0&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; i, j &lt;span style="color:#f92672"&gt;=&lt;/span&gt; &lt;span style="color:#ae81ff"&gt;0&lt;/span&gt;, &lt;span style="color:#ae81ff"&gt;0&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; m &lt;span style="color:#f92672"&gt;=&lt;/span&gt; len(left)
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; n &lt;span style="color:#f92672"&gt;=&lt;/span&gt; len(right)
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; &lt;span style="color:#66d9ef"&gt;while&lt;/span&gt; i &lt;span style="color:#f92672"&gt;+&lt;/span&gt; j &lt;span style="color:#f92672"&gt;&amp;lt;&lt;/span&gt; m &lt;span style="color:#f92672"&gt;+&lt;/span&gt; n:
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; &lt;span style="color:#66d9ef"&gt;if&lt;/span&gt; j &lt;span style="color:#f92672"&gt;==&lt;/span&gt; n &lt;span style="color:#f92672"&gt;or&lt;/span&gt; (i &lt;span style="color:#f92672"&gt;!=&lt;/span&gt; m &lt;span style="color:#f92672"&gt;and&lt;/span&gt; left[i] &lt;span style="color:#f92672"&gt;&amp;lt;&lt;/span&gt; right[j]):
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; merged&lt;span style="color:#f92672"&gt;.&lt;/span&gt;append(left[i])
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; i &lt;span style="color:#f92672"&gt;+=&lt;/span&gt; &lt;span style="color:#ae81ff"&gt;1&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; &lt;span style="color:#66d9ef"&gt;continue&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; merged&lt;span style="color:#f92672"&gt;.&lt;/span&gt;append(right[j])
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; j &lt;span style="color:#f92672"&gt;+=&lt;/span&gt; &lt;span style="color:#ae81ff"&gt;1&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; count &lt;span style="color:#f92672"&gt;+=&lt;/span&gt; m &lt;span style="color:#f92672"&gt;-&lt;/span&gt; i
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; &lt;span style="color:#66d9ef"&gt;return&lt;/span&gt; merged, count
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt;&lt;span style="color:#66d9ef"&gt;def&lt;/span&gt; &lt;span style="color:#a6e22e"&gt;sort_and_count&lt;/span&gt;(arr):
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; n &lt;span style="color:#f92672"&gt;=&lt;/span&gt; len(arr)
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; &lt;span style="color:#66d9ef"&gt;if&lt;/span&gt; n &lt;span style="color:#f92672"&gt;==&lt;/span&gt; &lt;span style="color:#ae81ff"&gt;1&lt;/span&gt;:
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; &lt;span style="color:#66d9ef"&gt;return&lt;/span&gt; arr, &lt;span style="color:#ae81ff"&gt;0&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; left &lt;span style="color:#f92672"&gt;=&lt;/span&gt; arr[: n &lt;span style="color:#f92672"&gt;//&lt;/span&gt; &lt;span style="color:#ae81ff"&gt;2&lt;/span&gt;]
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; right &lt;span style="color:#f92672"&gt;=&lt;/span&gt; arr[n &lt;span style="color:#f92672"&gt;//&lt;/span&gt; &lt;span style="color:#ae81ff"&gt;2&lt;/span&gt; :]
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; left, count_left &lt;span style="color:#f92672"&gt;=&lt;/span&gt; sort_and_count(left)
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; right, count_right &lt;span style="color:#f92672"&gt;=&lt;/span&gt; sort_and_count(right)
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; merged, count_both &lt;span style="color:#f92672"&gt;=&lt;/span&gt; merge_inversion(left, right)
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; &lt;span style="color:#66d9ef"&gt;return&lt;/span&gt; (merged, count_left &lt;span style="color:#f92672"&gt;+&lt;/span&gt; count_right &lt;span style="color:#f92672"&gt;+&lt;/span&gt; count_both)
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt;&lt;span style="color:#66d9ef"&gt;def&lt;/span&gt; &lt;span style="color:#a6e22e"&gt;countIntersection&lt;/span&gt;(a, b):
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; tuples &lt;span style="color:#f92672"&gt;=&lt;/span&gt; sorted(zip(a, b))
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; b &lt;span style="color:#f92672"&gt;=&lt;/span&gt; [t[&lt;span style="color:#ae81ff"&gt;1&lt;/span&gt;] &lt;span style="color:#66d9ef"&gt;for&lt;/span&gt; t &lt;span style="color:#f92672"&gt;in&lt;/span&gt; tuples]
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; &lt;span style="color:#66d9ef"&gt;return&lt;/span&gt; sort_and_count(b)[&lt;span style="color:#ae81ff"&gt;1&lt;/span&gt;]
&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;h2 id="grpa-3"&gt;GRPA 3&lt;/h2&gt;
&lt;div class="highlight"&gt;&lt;pre tabindex="0" style="color:#f8f8f2;background-color:#272822;-moz-tab-size:4;-o-tab-size:4;tab-size:4;"&gt;&lt;code class="language-python" data-lang="python"&gt;&lt;span style="display:flex;"&gt;&lt;span&gt;dist &lt;span style="color:#f92672"&gt;=&lt;/span&gt; &lt;span style="color:#66d9ef"&gt;lambda&lt;/span&gt; a, b: ((a[&lt;span style="color:#ae81ff"&gt;0&lt;/span&gt;]&lt;span style="color:#f92672"&gt;-&lt;/span&gt;b[&lt;span style="color:#ae81ff"&gt;0&lt;/span&gt;])&lt;span style="color:#f92672"&gt;**&lt;/span&gt;&lt;span style="color:#ae81ff"&gt;2&lt;/span&gt; &lt;span style="color:#f92672"&gt;+&lt;/span&gt; (a[&lt;span style="color:#ae81ff"&gt;1&lt;/span&gt;]&lt;span style="color:#f92672"&gt;-&lt;/span&gt;b[&lt;span style="color:#ae81ff"&gt;1&lt;/span&gt;])&lt;span style="color:#f92672"&gt;**&lt;/span&gt;&lt;span style="color:#ae81ff"&gt;2&lt;/span&gt;)&lt;span style="color:#f92672"&gt;**&lt;/span&gt;&lt;span style="color:#ae81ff"&gt;.5&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt;&lt;span style="color:#66d9ef"&gt;def&lt;/span&gt; &lt;span style="color:#a6e22e"&gt;closest_pair&lt;/span&gt;(Px, Py):
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; n &lt;span style="color:#f92672"&gt;=&lt;/span&gt; len(Px)
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; &lt;span style="color:#66d9ef"&gt;if&lt;/span&gt; n &lt;span style="color:#f92672"&gt;&amp;lt;=&lt;/span&gt; &lt;span style="color:#ae81ff"&gt;3&lt;/span&gt;:
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; min_d &lt;span style="color:#f92672"&gt;=&lt;/span&gt; float(&lt;span style="color:#e6db74"&gt;&amp;#39;inf&amp;#39;&lt;/span&gt;)
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; &lt;span style="color:#66d9ef"&gt;for&lt;/span&gt; i &lt;span style="color:#f92672"&gt;in&lt;/span&gt; range(n):
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; &lt;span style="color:#66d9ef"&gt;for&lt;/span&gt; j &lt;span style="color:#f92672"&gt;in&lt;/span&gt; range(i &lt;span style="color:#f92672"&gt;+&lt;/span&gt; &lt;span style="color:#ae81ff"&gt;1&lt;/span&gt;, n):
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; min_d &lt;span style="color:#f92672"&gt;=&lt;/span&gt; min(min_d, dist(Px[i], Px[j]))
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; &lt;span style="color:#66d9ef"&gt;return&lt;/span&gt; min_d
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; mid &lt;span style="color:#f92672"&gt;=&lt;/span&gt; n &lt;span style="color:#f92672"&gt;//&lt;/span&gt; &lt;span style="color:#ae81ff"&gt;2&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; Qx &lt;span style="color:#f92672"&gt;=&lt;/span&gt; Px[:mid]
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; Rx &lt;span style="color:#f92672"&gt;=&lt;/span&gt; Px[mid:]
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; mid_point &lt;span style="color:#f92672"&gt;=&lt;/span&gt; Qx[&lt;span style="color:#f92672"&gt;-&lt;/span&gt;&lt;span style="color:#ae81ff"&gt;1&lt;/span&gt;][&lt;span style="color:#ae81ff"&gt;0&lt;/span&gt;]
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; Qy &lt;span style="color:#f92672"&gt;=&lt;/span&gt; []
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; Ry &lt;span style="color:#f92672"&gt;=&lt;/span&gt; []
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; &lt;span style="color:#66d9ef"&gt;for&lt;/span&gt; p &lt;span style="color:#f92672"&gt;in&lt;/span&gt; Py:
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; &lt;span style="color:#66d9ef"&gt;if&lt;/span&gt; p[&lt;span style="color:#ae81ff"&gt;0&lt;/span&gt;] &lt;span style="color:#f92672"&gt;&amp;lt;=&lt;/span&gt; mid_point:
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; Qy&lt;span style="color:#f92672"&gt;.&lt;/span&gt;append(p)
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; &lt;span style="color:#66d9ef"&gt;else&lt;/span&gt;:
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; Ry&lt;span style="color:#f92672"&gt;.&lt;/span&gt;append(p)
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; min_d &lt;span style="color:#f92672"&gt;=&lt;/span&gt; min(closest_pair(Qx, Qy), closest_pair(Rx, Ry))
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; Sy &lt;span style="color:#f92672"&gt;=&lt;/span&gt; [p &lt;span style="color:#66d9ef"&gt;for&lt;/span&gt; p &lt;span style="color:#f92672"&gt;in&lt;/span&gt; Py &lt;span style="color:#66d9ef"&gt;if&lt;/span&gt; mid_point &lt;span style="color:#f92672"&gt;-&lt;/span&gt; min_d &lt;span style="color:#f92672"&gt;&amp;lt;=&lt;/span&gt; p[&lt;span style="color:#ae81ff"&gt;0&lt;/span&gt;] &lt;span style="color:#f92672"&gt;&amp;lt;=&lt;/span&gt; mid_point &lt;span style="color:#f92672"&gt;+&lt;/span&gt; min_d]
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; &lt;span style="color:#66d9ef"&gt;for&lt;/span&gt; i &lt;span style="color:#f92672"&gt;in&lt;/span&gt; range(len(Sy)):
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; &lt;span style="color:#66d9ef"&gt;for&lt;/span&gt; j &lt;span style="color:#f92672"&gt;in&lt;/span&gt; range(i &lt;span style="color:#f92672"&gt;+&lt;/span&gt; &lt;span style="color:#ae81ff"&gt;1&lt;/span&gt;, len(Sy)):
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; &lt;span style="color:#66d9ef"&gt;if&lt;/span&gt; Sy[j][&lt;span style="color:#ae81ff"&gt;1&lt;/span&gt;] &lt;span style="color:#f92672"&gt;-&lt;/span&gt; Sy[i][&lt;span style="color:#ae81ff"&gt;1&lt;/span&gt;] &lt;span style="color:#f92672"&gt;&amp;gt;=&lt;/span&gt; min_d:
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; &lt;span style="color:#66d9ef"&gt;break&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; min_d &lt;span style="color:#f92672"&gt;=&lt;/span&gt; min(min_d, dist(Sy[i], Sy[j]))
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; &lt;span style="color:#66d9ef"&gt;return&lt;/span&gt; min_d
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt;&lt;span style="color:#66d9ef"&gt;def&lt;/span&gt; &lt;span style="color:#a6e22e"&gt;minDistance&lt;/span&gt;(points):
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; Px &lt;span style="color:#f92672"&gt;=&lt;/span&gt; sorted(points, key&lt;span style="color:#f92672"&gt;=&lt;/span&gt;&lt;span style="color:#66d9ef"&gt;lambda&lt;/span&gt; p: p[&lt;span style="color:#ae81ff"&gt;0&lt;/span&gt;])
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; Py &lt;span style="color:#f92672"&gt;=&lt;/span&gt; sorted(points, key&lt;span style="color:#f92672"&gt;=&lt;/span&gt;&lt;span style="color:#66d9ef"&gt;lambda&lt;/span&gt; p: p[&lt;span style="color:#ae81ff"&gt;1&lt;/span&gt;])
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; &lt;span style="color:#66d9ef"&gt;return&lt;/span&gt; round(closest_pair(Px, Py), &lt;span style="color:#ae81ff"&gt;2&lt;/span&gt;)
&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;h2 id="grpa-4"&gt;GRPA 4&lt;/h2&gt;
&lt;div class="highlight"&gt;&lt;pre tabindex="0" style="color:#f8f8f2;background-color:#272822;-moz-tab-size:4;-o-tab-size:4;tab-size:4;"&gt;&lt;code class="language-python" data-lang="python"&gt;&lt;span style="display:flex;"&gt;&lt;span&gt;&lt;span style="color:#66d9ef"&gt;def&lt;/span&gt; &lt;span style="color:#a6e22e"&gt;mid&lt;/span&gt;(a):
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; &lt;span style="color:#66d9ef"&gt;if&lt;/span&gt; len(a) &lt;span style="color:#f92672"&gt;&amp;lt;=&lt;/span&gt; &lt;span style="color:#ae81ff"&gt;7&lt;/span&gt;:
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; &lt;span style="color:#66d9ef"&gt;return&lt;/span&gt; sorted(a)[len(a)&lt;span style="color:#f92672"&gt;//&lt;/span&gt;&lt;span style="color:#ae81ff"&gt;2&lt;/span&gt;]
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; m &lt;span style="color:#f92672"&gt;=&lt;/span&gt; []
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; &lt;span style="color:#66d9ef"&gt;for&lt;/span&gt; i &lt;span style="color:#f92672"&gt;in&lt;/span&gt; range(&lt;span style="color:#ae81ff"&gt;0&lt;/span&gt;,len(a), &lt;span style="color:#ae81ff"&gt;7&lt;/span&gt;):
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; m&lt;span style="color:#f92672"&gt;.&lt;/span&gt;append(mid(a[i:i&lt;span style="color:#f92672"&gt;+&lt;/span&gt;&lt;span style="color:#ae81ff"&gt;7&lt;/span&gt;]))
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; &lt;span style="color:#66d9ef"&gt;return&lt;/span&gt; mid(m)
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt;&lt;span style="color:#66d9ef"&gt;def&lt;/span&gt; &lt;span style="color:#a6e22e"&gt;MoM7Pos&lt;/span&gt;(arr):
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; m &lt;span style="color:#f92672"&gt;=&lt;/span&gt; mid(arr)
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; pos &lt;span style="color:#f92672"&gt;=&lt;/span&gt; &lt;span style="color:#ae81ff"&gt;0&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; &lt;span style="color:#66d9ef"&gt;for&lt;/span&gt; x &lt;span style="color:#f92672"&gt;in&lt;/span&gt; arr:
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; &lt;span style="color:#66d9ef"&gt;if&lt;/span&gt; x &lt;span style="color:#f92672"&gt;&amp;lt;&lt;/span&gt; m:
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; pos &lt;span style="color:#f92672"&gt;+=&lt;/span&gt; &lt;span style="color:#ae81ff"&gt;1&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span style="display:flex;"&gt;&lt;span&gt; &lt;span style="color:#66d9ef"&gt;return&lt;/span&gt; pos
&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;</description></item><item><title>NixOS Notes to Self</title><link>https://lavafroth.is-a.dev/post/nixos-notes-to-self/</link><pubDate>Sun, 14 Sep 2025 18:31:52 +0530</pubDate><guid>https://lavafroth.is-a.dev/post/nixos-notes-to-self/</guid><description>&lt;p&gt;A dedicated post collecting solutions to minor NixOS headaches.&lt;/p&gt;
&lt;h2 id="nixos-rebuild-shows-no-network-activity"&gt;&lt;code&gt;nixos-rebuild&lt;/code&gt; shows no network activity&lt;/h2&gt;
&lt;p&gt;On rare occasions, a system rebuild will get stuck while downloading a package from a source.
No network activity, no timeout, no writes to the nix store.&lt;/p&gt;

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