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  • 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.

    //1.深搜
    /*
    class Solution {
        int dfs(int m,int n,int r,int c,int end_r,int end_c)
        {
            if(r<0 || r>=m || c<0 || c>=n)
            {
                return 0;
            }
            if(end_r == r && end_c==c){
                return 1;
            }
            return dfs(m,n,r+1,c,end_r,end_c)+dfs(m,n,r,c+1,end_r,end_c);
        }
    public:
        int uniquePaths(int m, int n) {
            return dfs(m,n,0,0,m-1,n-1);
        }
    };
    */
    
    //2.动态
    class Solution {
    public:
        int uniquePaths(int m, int n) {
            vector<int> help(n,1);
            for(int i=1;i<m;i++){
                for(int j=0;j<n;j++){
                    if(j==0){
                        help[j] = 1;
                    }else{
                        help[j] = help[j]+help[j-1];
                    }
                }
            }
            return m>0&&n>0 ? help[n-1]:0;
        }
    };
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  • 原文地址:https://www.cnblogs.com/zengzy/p/5024594.html
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