Minimum Equal Sum of Two Arrays After Replacing Zeros - Problem

Array Greedy Medium

You are given two arrays nums1 and nums2 consisting of positive integers. You have to replace all the 0's in both arrays with strictly positive integers such that the sum of elements of both arrays becomes equal.

Return the minimum equal sum you can obtain, or -1 if it is impossible.

Input & Output

Example 1 — Basic Case with Zeros

$ Input: nums1 = [3,2,0,1,0], nums2 = [6,5,0]

› Output: 12

💡 Note: Replace zeros with 1: nums1 = [3,2,1,1,1] (sum=8), nums2 = [6,5,1] (sum=12). Since both arrays have zeros, we can make nums1's zeros larger to match nums2's sum. The minimum equal sum is max(8,12) = 12.

Example 2 — Impossible Case

$ Input: nums1 = [1,2], nums2 = [3,4]

› Output: -1

💡 Note: No zeros in either array. nums1 sum = 3, nums2 sum = 7. Since we can't change any values, it's impossible to make them equal.

Example 3 — One Array Without Zeros

$ Input: nums1 = [1,1,1,1], nums2 = [0,0,0,0]

› Output: 4

💡 Note: nums1 sum = 4 (no zeros), nums2 can be [1,1,1,1] with sum = 4. Both sums can be equal at 4.

Constraints

1 ≤ nums1.length, nums2.length ≤ 10⁵
0 ≤ nums1[i], nums2[i] ≤ 10⁶

Visualization

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Asked in

M Microsoft 15 a Amazon 12

The key insight is to replace all zeros with 1 (minimum positive value) and check if we can balance the sums. If one array has no zeros but a smaller sum, it's impossible. Otherwise, take the maximum of the two minimum sums. Best approach is greedy. Time: O(n+m), Space: O(1)

Common Approaches

✓ Brute Force - Try All Combinations

⏱️ Time: O(∞) Space: O(1)

For each zero in both arrays, try all possible positive integer values and find the minimum equal sum. This approach explores all combinations but is extremely inefficient.

Greedy Approach

⏱️ Time: O(n + m) Space: O(1)

Replace all zeros with the minimum positive value (1) to get the minimum possible sum for each array. Then check if we can balance the sums by increasing some zeros to larger values.

Brute Force - Try All Combinations — Algorithm Steps

Generate all combinations of positive integers for zeros
Calculate sum for each combination
Find minimum equal sum across all valid combinations

Visualization

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Step-by-Step Walkthrough

Find Zeros

Identify all zero positions in both arrays

Try Values

For each zero, try values 1, 2, 3, ...

Check Equal

Find minimum equal sum across all combinations

Code -

solution.c — C

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

long long solution(int* nums1, int size1, int* nums2, int size2) {
    long long sum1 = 0, sum2 = 0;
    int zeros1 = 0, zeros2 = 0;
    
    for (int i = 0; i < size1; i++) {
        if (nums1[i] == 0) {
            zeros1++;
            sum1 += 1;
        } else {
            sum1 += nums1[i];
        }
    }
    
    for (int i = 0; i < size2; i++) {
        if (nums2[i] == 0) {
            zeros2++;
            sum2 += 1;
        } else {
            sum2 += nums2[i];
        }
    }
    
    if (zeros1 == 0 && zeros2 == 0) {
        return sum1 == sum2 ? sum1 : -1;
    }
    if (zeros1 == 0 && sum1 < sum2) {
        return -1;
    }
    if (zeros2 == 0 && sum2 < sum1) {
        return -1;
    }
    
    return sum1 > sum2 ? sum1 : sum2;
}

int main() {
    char line[10000];
    fgets(line, sizeof(line), stdin);
    
    int nums1[1000], size1 = 0;
    char* token = strtok(line, "[,]");
    while (token != NULL) {
        if (strcmp(token, "\n") != 0) {
            nums1[size1++] = atoi(token);
        }
        token = strtok(NULL, "[,]");
    }
    
    fgets(line, sizeof(line), stdin);
    int nums2[1000], size2 = 0;
    token = strtok(line, "[,]");
    while (token != NULL) {
        if (strcmp(token, "\n") != 0) {
            nums2[size2++] = atoi(token);
        }
        token = strtok(NULL, "[,]");
    }
    
    printf("%lld\n", solution(nums1, size1, nums2, size2));
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(∞)

Infinite combinations of positive integers for each zero position

✓ Linear Growth

Space Complexity

O(1)

Only using constant extra space for calculations

✓ Linear Space

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Minimum Equal Sum of Two Arrays After Replacing Zeros - Problem

Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Brute Force - Try All Combinations — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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