Number of Ways to Split Array

Number of Ways to Split Array - Problem

You are given a 0-indexed integer array nums of length n.

nums contains a valid split at index i if the following are true:

The sum of the first i + 1 elements is greater than or equal to the sum of the last n - i - 1 elements.
There is at least one element to the right of i. That is, 0 <= i < n - 1.

Return the number of valid splits in nums.

Input & Output

Example 1 — Basic Array

$ Input: nums = [10,4,-8,7]

› Output: 2

💡 Note: Split at index 0: [10] vs [4,-8,7] → 10 >= 3 ✓. Split at index 1: [10,4] vs [-8,7] → 14 >= -1 ✓. Split at index 2: [10,4,-8] vs [7] → 6 < 7 ✗. Total: 2 valid splits.

Example 2 — All Positive

$ Input: nums = [2,3,1,0]

› Output: 2

💡 Note: Split at index 0: [2] vs [3,1,0] → 2 < 4 ✗. Split at index 1: [2,3] vs [1,0] → 5 >= 1 ✓. Split at index 2: [2,3,1] vs [0] → 6 >= 0 ✓. Total: 2 valid splits.

Example 3 — Minimum Size

$ Input: nums = [1,1]

› Output: 1

💡 Note: Only one possible split at index 0: [1] vs [1] → 1 >= 1 ✓. Total: 1 valid split.

Constraints

2 ≤ nums.length ≤ 10⁵
-10⁵ ≤ nums[i] ≤ 10⁵

Visualization

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Asked in

M Microsoft 15 G Google 12 a Amazon 8

The key insight is to avoid recalculating sums by using prefix sum technique. Instead of computing left and right sums from scratch for each split, calculate the total sum once, then maintain a running left sum and derive the right sum as total_sum - left_sum. Best approach is Prefix Sum with Time: O(n), Space: O(1).

Common Approaches

✓ Brute Force - Calculate Sums for Each Split

⏱️ Time: O(n²) Space: O(1)

Iterate through each valid split index (0 to n-2) and for each position, calculate the sum of left elements and sum of right elements, then compare them.

Prefix Sum - Single Pass Optimization

⏱️ Time: O(n) Space: O(1)

Calculate the total sum first, then iterate through the array maintaining a running left sum. The right sum can be calculated as total_sum - left_sum.

Brute Force - Calculate Sums for Each Split — Algorithm Steps

Step 1: For each index i from 0 to n-2
Step 2: Calculate sum of elements from 0 to i (left side)
Step 3: Calculate sum of elements from i+1 to n-1 (right side)
Step 4: If left_sum >= right_sum, increment count

Visualization

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Step-by-Step Walkthrough

Split at index 0

Left: [10], Right: [4,-8,7] → 10 >= 3 ✓

Split at index 1

Left: [10,4], Right: [-8,7] → 14 >= -1 ✓

Split at index 2

Left: [10,4,-8], Right: [7] → 6 < 7 ✗

Code -

solution.c — C

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

int solution(int* nums, int numsSize) {
    int count = 0;
    
    for (int i = 0; i < numsSize - 1; i++) {
        long long leftSum = 0;
        long long rightSum = 0;
        
        // Calculate left sum
        for (int j = 0; j <= i; j++) {
            leftSum += nums[j];
        }
        
        // Calculate right sum
        for (int j = i + 1; j < numsSize; j++) {
            rightSum += nums[j];
        }
        
        if (leftSum >= rightSum) {
            count++;
        }
    }
    
    return count;
}

void parseArray(const char* str, int* arr, int* size) {
    *size = 0;
    const char* p = str;
    while (*p && *p != '[') p++;
    if (*p == '[') p++;
    while (*p && *p != ']') {
        while (*p == ' ' || *p == ',') p++;
        if (*p == ']' || *p == '\0') break;
        arr[(*size)++] = (int)strtol(p, (char**)&p, 10);
    }
}

int main() {
    char line[100000];
    fgets(line, sizeof(line), stdin);
    
    // Simple parsing for array
    int nums[10000];
    int size = 0;
    char* token = strtok(line, "[,]");
    
    while (token != NULL) {
        if (strlen(token) > 0 && token[0] != '\n' && token[0] != ']') {
            nums[size++] = atoi(token);
        }
        token = strtok(NULL, "[,]");
    }
    
    int result = solution(nums, size);
    printf("%d\n", result);
    
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n²)

Outer loop runs n-1 times, inner sum calculations take O(n) each

⚠ Quadratic Growth

Space Complexity

O(1)

Only uses a few variables for counting and sum calculations

✓ Linear Space

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Input & Output

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Related Problems

Common Approaches

Brute Force - Calculate Sums for Each Split — Algorithm Steps

Visualization

Code -

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