CODE 71. Unique Paths

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A robot is located at the top-left corner of a m x n grid (marked ‘Start’ in the diagram below).
The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked ‘Finish’ in the diagram below).
How many possible unique paths are there?

Above is a 3 x 7 grid. How many possible unique paths are there?
Note: m and n will be at most 100.

public int uniquePaths(int m, int n) {
	// Note: The Solution object is instantiated only once and is reused by
	// each test case.
	int[][] sum = new int[m][n];
	for (int i = 0; i < m; i++) {
		sum[i][0] = 1;
	}
	for (int i = 0; i < n; i++) {
		sum[0][i] = 1;
	}
	for (int i = 1; i < m; i++) {
		for (int j = 1; j < n; j++) {
			sum[i][j] = sum[i - 1][j] + sum[i][j - 1];
		}
	}
	return sum[m - 1][n - 1];
}