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$ curl repovive.com/roadmaps/fundamental-algorithms/sorting-algorithms/count-smaller-numbers-implementation

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$ curl repovive.com/roadmaps/fundamental-algorithms/sorting-algorithms/count-smaller-numbers-implementation

Repovive

Count Smaller Numbers - Implementation - Sorting Algorithms | Fundamental Algorithms | Repovive

Repovive.

Fundamental Algorithms8 sections · 294 units2h total

Open in Course

Count Smaller Numbers - Implementation

Here is the implementation using merge sort:

function countSmaller(nums):
    n = nums.length
    counts = array of n zeros
    indices = [0, 1, 2, ..., n-1]

    mergeSort(nums, indices, counts, 0, n - 1)
    return counts

function merge(nums, indices, counts, left, mid, right):
    temp = []
    i = left, j = mid + 1
    rightCount = 0

    while i <= mid and j <= right:
        if nums[indices[j]] < nums[indices[i]]:
            temp.append(indices[j])
            rightCount += 1
            j += 1
        else:
            counts[indices[i]] += rightCount
            temp.append(indices[i])
            i += 1

This runs in $O(n \log n)$ time and $O(n)$ space.