DP------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?

Note

m and n will be at most 100.

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public class Solution {
/**
* @param n, m: positive integer (1 <= n ,m <= 100)
* @return an integer
*/

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

int[][] sum = new int[m]
;
for (int i = 0; i < m; i++) {
sum[i][0] = 1;//初始化
}
for (int i = 0; i < n; i++) {
sum[0][i] = 1;//初始化
}
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];//状态转移方程
}
}
return sum[m - 1][n - 1];
}
}