LeetCode 1074: Number of Submatrices That Sum to Target Solution

Master LeetCode problem 1074 (Number of Submatrices That Sum to Target), a hard challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

1074. Number of Submatrices That Sum to Target

Hard

Array Hash Table Matrix Prefix Sum

Problem Explanation

Explanation

To solve this problem, we can use the concept of prefix sum along with hashing. We iterate over all possible pairs of rows and for each pair, we calculate the prefix sum of columns between these two rows. Then, we use a hashmap to store the frequency of prefix sums encountered so far. As we iterate through the columns, we calculate the sum of submatrices in this range by subtracting the prefix sum from the target. If the target - sum is present in the hashmap, we increment the count of submatrices by the corresponding frequency. Finally, we update the hashmap with the current prefix sum frequency.

Time Complexity: O(m^2 * n) where m is the number of rows and n is the number of columns in the matrix. Space Complexity: O(n).

Solution Code

class Solution {
    public int numSubmatrixSumTarget(int[][] matrix, int target) {
        int m = matrix.length;
        int n = matrix[0].length;
        int count = 0;

        for (int i = 0; i < m; i++) {
            int[] sum = new int[n];
            for (int j = i; j < m; j++) {
                Map<Integer, Integer> map = new HashMap<>();
                int prefixSum = 0;
                map.put(0, 1);
                
                for (int k = 0; k < n; k++) {
                    sum[k] += matrix[j][k];
                    prefixSum += sum[k];
                    count += map.getOrDefault(prefixSum - target, 0);
                    map.put(prefixSum, map.getOrDefault(prefixSum, 0) + 1);
                }
            }
        }

        return count;
    }
}

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