62. Unique Paths

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.

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Solution:

Tips:

easy dp.

dp[i][j] = dp[i - 1][j] + dp[i][j - 1];

Java Code:

public class Solution {
public int uniquePaths(int m, int n) {
if (m == 0 || n == 0) {
return 0;
}
if (m == 1) {
return 1;
}

int[][] grid = new int[m]
;
// init row
Arrays.fill(grid[0], 1);
// init column
for (int i = 0; i < m; i++) {
grid[i][0] = 1;
}

for (int i = 1; i < m; i++) {
for (int j = 1; j < n; j++) {
grid[i][j] = grid[i][j - 1] + grid[i - 1][j];
//System.out.printf("%d + %d = %d\n", grid[i][j - 1], grid[i - 1][j], grid[i][j]);
}
}

return grid[m - 1][n - 1];
}
}