Maximum Number of Non-Overlapping Subarrays With Sum Equals Target

Maximum Number of Non-Overlapping Subarrays With Sum Equals Target - Problem

Given an array nums and an integer target, return the maximum number of non-empty non-overlapping subarrays such that the sum of values in each subarray is equal to target.

A subarray is a contiguous part of an array. Two subarrays are non-overlapping if they do not share any common elements.

Input & Output

Example 1 — Basic Case

$ Input: nums = [1,1,1,1,1], target = 2

› Output: 2

💡 Note: We can form 2 non-overlapping subarrays: [1,1] (sum=2) and [1,1] (sum=2). The last element [1] cannot form another subarray with sum=2.

Example 2 — Single Elements

$ Input: nums = [-1,1,5,1,1], target = 1

› Output: 3

💡 Note: We can form 3 non-overlapping subarrays: [1], [1], and [1]. Each single element equals the target.

Example 3 — Mixed Values

$ Input: nums = [-1,-1,1,1,1], target = 0

› Output: 1

💡 Note: We can form 1 subarray: [-1,1] (sum=0). The remaining elements [-1,1,1] could form [-1,1] but we already used one -1.

Constraints

1 ≤ nums.length ≤ 10⁵
-10⁴ ≤ nums[i] ≤ 10⁴
0 ≤ target ≤ 10⁶

Visualization

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Understanding the Visualization

Input

Array [1,1,1,1,1] with target sum 2

Process

Greedily find subarrays that sum to target

Output

Maximum count of non-overlapping subarrays

Key Takeaway

🎯 Key Insight: Use greedy strategy with prefix sums - take each valid subarray immediately to maximize the total count

Asked in

G Google 12 a Amazon 8 M Microsoft 6

The key insight is to use a greedy approach with prefix sums. As soon as we find a subarray with sum equal to target, we take it and reset our search. This maximizes the number of non-overlapping subarrays. Best approach uses prefix sum with hash set in O(n) time and O(n) space.

Common Approaches

Approach	Time	Space	Notes
✓ Greedy Approach with Prefix Sum	O(n)	O(n)	Use prefix sum and greedy strategy to find maximum count in one pass
Brute Force - Check All Subarrays	O(n² × 2ⁿ)	O(n)	Generate all possible subarrays and find maximum non-overlapping set

Greedy Approach with Prefix Sum — Algorithm Steps

Initialize prefix sum and hash set
For each element, update prefix sum
Check if current prefix sum or (prefix sum - target) creates valid subarray
When found, increment count and reset

Visualization

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Step-by-Step Walkthrough

Track Prefix Sum

Maintain running sum and seen prefix sums

Find Valid Subarray

When prefix_sum - target is seen, we found valid subarray

Reset and Continue

Count it, reset state, continue searching

Code -

solution.c — C

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

#define MAX_SIZE 10000

int solution(int* nums, int numsSize, int target) {
    int count = 0;
    int prefixSum = 0;
    int seen[MAX_SIZE * 2]; // Allow for negative sums
    int seenCount = 0;
    seen[seenCount++] = 0; // Include 0 to handle subarrays starting from index 0
    
    for (int i = 0; i < numsSize; i++) {
        prefixSum += nums[i];
        int needed = prefixSum - target;
        
        // Check if needed sum exists in seen array
        bool found = false;
        for (int j = 0; j < seenCount; j++) {
            if (seen[j] == needed) {
                found = true;
                break;
            }
        }
        
        if (found) {
            count++;
            // Reset for next subarray search
            seenCount = 0;
            seen[seenCount++] = 0;
            prefixSum = 0;
        } else {
            seen[seenCount++] = prefixSum;
        }
    }
    
    return count;
}

int main() {
    char line[1000];
    fgets(line, sizeof(line), stdin);
    
    // Parse array
    int nums[100], numsSize = 0;
    char* token = strtok(line, "[],\n");
    while (token != NULL) {
        nums[numsSize++] = atoi(token);
        token = strtok(NULL, "[],\n");
    }
    
    int target;
    scanf("%d", &target);
    
    int result = solution(nums, numsSize, target);
    printf("%d\n", result);
    
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n)

Single pass through array with O(1) hash set operations

✓ Linear Growth

Space Complexity

O(n)

Hash set stores up to n prefix sum values

⚡ Linearithmic Space

25.4K Views

Medium Frequency

~15 min Avg. Time

892 Likes

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Smart Actions

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Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Greedy Approach with Prefix Sum — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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