Number of Rectangles in a Grid
Project Euler 85: Investigating the number of rectangles in a rectangular grid
Number of Rectangles in a Grid
Given a grid of size m x n, calculate the total number of rectangles contained in this rectangle. All integer sizes and positions are counted.
Examples:
numberOfRectangles(3, 2) == 18
numberOfRectangles(4, 4) == 100
Here is how the 3x2 grid works (Thanks to GiacomoSorbi for the idea):
1 rectangle of size 3x2:
[][][]
[][][]
2 rectangles of size 3x1:
[][][]
4 rectangles of size 2x1:
[][]
2 rectangles of size 2x2
[][]
[][]
3 rectangles of size 1x2:
[]
[]
6 rectangles of size 1x1:
[]
As you can see (1 + 2 + 4 + 2 + 3 + 6) = 18, and is the solution for the 3x2 grid.
There is a very simple solution to this!
public class Grid { public static int NumberOfRectangles(int m, int n) { // Your code here! int sum = 0; for (int i = 1; i <= m; i++) { for (int j = 1; j <= n; j++) { sum += (m - i + 1) * (n - j + 1); } } return sum; } }