Problem List

Maximum Count Of Positive Integer And Negative Integer

June 01, 2025 • Go • binary search • easy

Problem

Given an array nums sorted in non-decreasing order, return the maximum between the number of positive integers and the number of negative integers.

Approach

1. Binary search until I found a zero
2. Do a search backwards and forwards recursively until I found the first and last zero
3. This gives a range of where the zeros are
4. Negative numbers end at the first zero index. So the number of zeros = index of first zero
5. Positive numbers run from the last index in the array to the last index of zero. Hence the formula
6. positiveCount = len(nums) - 1 - indexOfLastZero

Edge Cases

All zeros, return 0
All positive numbers
All negative numbers

Reflections

I may have slightly over engineered this problem. Got carried away when I saw can you do it in O(log n). Ironically my solution is O(n) if the array is all zeros, otherwise it is O(log n).

Go Solution

func maximumCount(nums []int) int {
    target := 0

    l, r := 0, len(nums) - 1
    for l <= r {
        mid := l + (r - l) / 2

        if nums[mid] == target {
            negativeNumCount := getZerosBack(mid, nums)
            startOfPositive := getZeros(mid, nums)
            positiveNumCount := len(nums) - 1 - startOfPositive
           
            return max(positiveNumCount, negativeNumCount)
        } else if nums[mid] < target {
            l = mid + 1
        } else if nums[mid] > target {
            r = mid - 1       
        }
    }

    neg := l
    pos := len(nums) - neg
    

    return max(pos, neg)
}

func getZeros(count int, nums []int) int {
    if count == len(nums) - 1 {
        return count
    }

    if nums[count+1] != 0 {
        return count
    }

    return getZeros(count+1,nums)
}

func getZerosBack(count int, nums []int) int {
    if count == 0 {
        return count
    }

    if nums[count-1] != 0 {
        return count
    }

    return getZerosBack(count-1,nums)
}

func max(a, b int) int {
    if a > b {
        return a
    }

    return b
}

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