750. Number Of Corner Rectangles

750. Number Of Corner Rectangles

Given a grid where each entry is only 0 or 1, find the number of corner rectangles.

A corner rectangle is 4 distinct 1s on the grid that form an axis-aligned rectangle. Note that only the corners need to have the value 1. Also, all four 1s used must be distinct.

Example 1:

Input: grid = 
[[1, 0, 0, 1, 0],
 [0, 0, 1, 0, 1],
 [0, 0, 0, 1, 0],
 [1, 0, 1, 0, 1]]
Output: 1
Explanation: There is only one corner rectangle, with corners grid[1][2], grid[1][4], grid[3][2], grid[3][4].

Example 2:

Input: grid = 
[[1, 1, 1],
 [1, 1, 1],
 [1, 1, 1]]
Output: 9
Explanation: There are four 2x2 rectangles, four 2x3 and 3x2 rectangles, and one 3x3 rectangle.

Example 3:

Input: grid = 
[[1, 1, 1, 1]]
Output: 0
Explanation: Rectangles must have four distinct corners.

Note:

1. The number of rows and columns of grid will each be in the range [1, 200].
2. Each grid[i][j] will be either 0 or 1.
3. The number of 1s in the grid will be at most 6000.

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找出每两个row之间的矩形个数。
O(m^2 * n)
可以优化的地方是把计算第一个row的时候把1额外开一个数组存好

class Solution {
    public int countCornerRectangles(int[][] grid) {
        
        int rt = 0;
        for (int i = 0; i < grid.length - 1; i++) {
            for (int j = i + 1; j < grid.length; j++) {
                int count = 0;
                for (int col = 0; col < grid[0].length; col++) {
                    if (grid[i][col] == 1 && grid[j][col] == 1) count++;
                }
                
                if (count > 0) rt += count * (count - 1) / 2;
            }
        }
        
        return rt;
    }
}

另一种算法 ref: https://leetcode.com/problems/number-of-corner-rectangles/solution/