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Commit 3ae41e70 authored by Brady James Garvin's avatar Brady James Garvin
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Recorded work from Monday.

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......@@ -104,24 +104,39 @@ Problem: Find the median of an odd-length list in average-case Θ(n) time. Use
```
In: [8, 7, 6, 9, 5], k = 2
In: […], k = 2
In: […], k = 2
Split: […], …, […]
Out: …
*
i
j
In: [8, 7, 6, 5, 9], k = 2
*
i
j (crossed)
i
In: [5, 7, 6, 8, 9], k = 2
Split: [5, 7, 6], 8, [9]
Out: 7
|
|
|
In: […], k = …
In: […], k = …
Split: […], …, […]
Out: …
In: [5, 7, 6], k = 2
*
i
j (crossed)
i
In: [5, 7, 6], k = 2
Split: [], 5, [7, 6]
Out: 7
|
|
|
In: […], k = …
In: […], k = …
Split: […], …, […]
Out: …
In: [7, 6], k = 1
*
i
j (crossed)
i
In: [6, 7], k = 1
Split: [6], 7, []
Out: 7
```
## Analysis
......@@ -129,9 +144,13 @@ Problem: Find the median of an odd-length list in average-case Θ(n) time. Use
* Uneven split:
T(n) = T(n - 1) + Θ(n) for n ≫ 0
T(n) = Θ()
T(n) = Θ()
* Even split:
T(n) ≈ T(n/2) + Θ(n) for n ≫ 0
T(n) = Θ(⋯)
T(n) = "about" Θ(1) + Θ(n) = Θ(n)
* Land on the pivot:
T(n) = 0 + Θ(n) = Θ(n)
......@@ -31,5 +31,15 @@ export function kthSmallest(sequence, k) {
k >= 0 && k < sequence.length,
'Tried to find the kth smallest element when k is out of bounds.',
);
return sequence[0]; // TODO: stub
if (sequence.length < 2) {
return sequence[0];
}
const [left, pivot, right] = partition(sequence);
if (k === left.length) {
return pivot;
}
if (k < left.length) {
return kthSmallest(left, k);
}
return kthSmallest(right, k - left.length - 1);
}
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