- Difficulty: Medium
- Tags: LeetCode, Medium, Array, Hash Table, Math, Combinatorics, Counting, leetcode-3128, O(n * m), O(min(n, m)), Freq Table
Problem
You are given a 2D boolean matrix grid.
Return an integer that is the number of right triangles that can be made with the 3 elements of grid such that all of them have a value of 1.
Note:
- A collection of 3 elements of
gridis a right triangle if one of its elements is in the same row with another element and in the same column with the third element. The 3 elements do not have to be next to each other.
Example 1:
| 0 | 1 | 0 |
| 0 | 1 | 1 |
| 0 | 1 | 0 |
| 0 | 1 | 0 |
| 0 | 1 | 1 |
| 0 | 1 | 0 |
Input: grid = [[0,1,0],[0,1,1],[0,1,0]]
Output: 2
Explanation:
There are two right triangles.
Example 2:
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 1 |
| 1 | 0 | 0 | 0 |
Input: grid = [[1,0,0,0],[0,1,0,1],[1,0,0,0]]
Output: 0
Explanation:
There are no right triangles.
Example 3:
| 1 | 0 | 1 |
| 1 | 0 | 0 |
| 1 | 0 | 0 |
| 1 | 0 | 1 |
| 1 | 0 | 0 |
| 1 | 0 | 0 |
Input: grid = [[1,0,1],[1,0,0],[1,0,0]]
Output: 2
Explanation:
There are two right triangles.
Constraints:
1 <= grid.length <= 10001 <= grid[i].length <= 10000 <= grid[i][j] <= 1