[LeetCode116]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.

Analysis:

DP, transction function is DP[i][j] = DP[i-1][j]+DP[i][j-1];

this could be implemented in one dimension DP

java

public int uniquePaths(int m, int n) {        // IMPORTANT: Please reset any member data you declared, as        // the same Solution instance will be reused for each test case.        if(m==0 || n==0) return 0;        int [][] dp = new int [m][n];        for(int i=0; i<m; i++){        dp[i][0]=1;        for(int j=1;j<n;j++){        if(i==0) dp[i][j] = 1;        else dp[i][j] = dp[i-1][j] + dp[i][j-1];        }        }        return dp[m-1][n-1];    }

s2:

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

c++

int uniquePaths(int m, int n) {    vector <int> maxpath(n,0);    maxpath[0] = 1;    for(int i=0; i<m;i++){        for(int j=1; j<n;j++){            maxpath[j] = maxpath[j-1]+maxpath[j];        }    }    return maxpath[n-1];}