You are given a 2D boolean matrix grid.
A collection of 3 elements of grid is 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 may not be next to each other.
Return an integer that is the number of right triangles that can be made with 3 elements of grid such that all of them have a value of 1.
Examples
Example 1
Input: grid = [[0,1,0],[0,1,1],[0,1,0]]
Output: 2
Explanation:
There are two right triangles with elements of the value 1. Notice that the blue ones do not form a right triangle because the 3 elements are in the same column.
Example 2
Input: grid = [[1,0,0,0],[0,1,0,1],[1,0,0,0]]
Output: 0
Explanation:
There are no right triangles with elements of the value 1. Notice that the blue ones do not form a right triangle.
Example 3
Input: grid = [[1,0,1],[1,0,0],[1,0,0]]
Output: 2
Explanation:
There are two right triangles with elements of the value 1.
Constraints
1 <= grid.length <= 1000
1 <= grid[i].length <= 1000
0 <= grid[i][j] <= 1
3128. Right Triangles
Medium
30 Points
Array
Hash Table
Math
Combinatorics
Counting
You are given a 2D boolean matrix grid.
A collection of 3 elements of grid is 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 may not be next to each other.
Return an integer that is the number of right triangles that can be made with 3 elements of grid such that all of them have a value of 1.
Examples
Example 1
Input: grid = [[0,1,0],[0,1,1],[0,1,0]]
Output: 2
Explanation:
There are two right triangles with elements of the value 1. Notice that the blue ones do not form a right triangle because the 3 elements are in the same column.
Example 2
Input: grid = [[1,0,0,0],[0,1,0,1],[1,0,0,0]]
Output: 0
Explanation:
There are no right triangles with elements of the value 1. Notice that the blue ones do not form a right triangle.
Example 3
Input: grid = [[1,0,1],[1,0,0],[1,0,0]]
Output: 2
Explanation:
There are two right triangles with elements of the value 1.