【Leetcode】Unique Paths (DP)

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.

递推式

f(x,y)=f(x-1,y)+f(x,y-1)

代码如下

public int uniquePaths(int m, int n) {
int[][] result = new int[m]
;
for (int i = 0; i < m; i++)
result[i][0] = 1;
for (int i = 0; i < n; i++)
result[0][i] = 1;

for (int i = 1; i < m; i++) {
for (int j = 1; j < n; j++) {
result[i][j] = result[i - 1][j] + result[i][j - 1];
}
}
return result[m - 1][n - 1];
}