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?

img

Above is a 3 x 7 grid. How many possible unique paths are there?


Solution

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public class {
public int uniquePaths(int m, int n) {
if(m==0 || n==0) return 0;
if(m==1 || n==1) return 1;
int[][] dp = new int[m][n];
for(int i=0;i<m;i++) dp[i][0] = 1;
for(int i=0;i<n;i++) dp[0][i] = 1;
for(int i=1; i<m; i++)
for(int j=1; j<n; j++) {
dp[i][j] = dp[i-1][j] + dp[i][j-1];
}
return dp[m-1][n-1];
}
}