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$ curl repovive.com/roadmaps/fundamental-algorithms/divide-and-conquer/quickselect

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$ curl repovive.com/roadmaps/fundamental-algorithms/divide-and-conquer/quickselect

Repovive

QuickSelect - Divide and Conquer | Fundamental Algorithms | Repovive

Repovive.

Fundamental Algorithms8 sections · 294 units2h total

Open in Course

QuickSelect

Find the k-th smallest element in O(n) average.

Problem: Find $k$ -th smallest without fully sorting.

Approach: Partition like quicksort, recurse only one side.

function quickSelect(arr, left, right, k):
    if left == right: return arr[left]
    pivotIdx = partition(arr, left, right)
    if k == pivotIdx: return arr[k]
    else if k < pivotIdx:
        return quickSelect(arr, left, pivotIdx - 1, k)
    else:
        return quickSelect(arr, pivotIdx + 1, right, k)

Expected: $O(n)$ . Worst: $O(n^2)$ . Use median-of-medians for $O(n)$ guaranteed.