1504. Count Submatrices With All Ones

Given a rows * columns matrix mat of ones and zeros, return how many submatrices have all ones.

 

Example 1:

Input: mat = [[1,0,1],
              [1,1,0],
              [1,1,0]]
Output: 13
Explanation:
There are 6 rectangles of side 1x1.
There are 2 rectangles of side 1x2.
There are 3 rectangles of side 2x1.
There is 1 rectangle of side 2x2. 
There is 1 rectangle of side 3x1.
Total number of rectangles = 6 + 2 + 3 + 1 + 1 = 13.

Example 2:

Input: mat = [[0,1,1,0],
              [0,1,1,1],
              [1,1,1,0]]
Output: 24
Explanation:
There are 8 rectangles of side 1x1.
There are 5 rectangles of side 1x2.
There are 2 rectangles of side 1x3. 
There are 4 rectangles of side 2x1.
There are 2 rectangles of side 2x2. 
There are 2 rectangles of side 3x1. 
There is 1 rectangle of side 3x2. 
Total number of rectangles = 8 + 5 + 2 + 4 + 2 + 2 + 1 = 24.

Example 3:

Input: mat = [[1,1,1,1,1,1]]
Output: 21

Example 4:

Input: mat = [[1,0,1],[0,1,0],[1,0,1]]
Output: 5

 

Constraints:

• 1 <= rows <= 150
• 1 <= columns <= 150
• 0 <= mat[i][j] <= 1

class Solution {
  public int numSubmat(int[][] mat) {
        int m = mat.length, n = mat[0].length, height[] = new int[n], res = 0; 
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                height[j] = mat[i][j] == 0 ? 0 : height[j] + 1;   // horizontal height of histogram;
                for (int k = j, min = height[j]; k >= 0 && min > 0; k--) {
                    min = Math.min(min, height[k]);
                    res += min;
                }
            }
        }
        return res;
    }
}

https://leetcode.com/problems/count-submatrices-with-all-ones/discuss/720280/Java-histogram-count

和largest rectangle有点像