062 - Unique Paths

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.

Hide Tags

Array Dynamic Programming

Hide Similar Problems

(M) Unique Paths II (M) Minimum Path Sum (H) Dungeon Game

 

起先写了个递归的，断然是超时了，

改成动规的，从终点推回到起点，ok了，0ms。

class Solution {
public:
    int uniquePaths(int m, int n)
    {
        int* matrix = new int[m*n];
        memset(matrix, 0, m*n*sizeof(int));
        matrix[(m-1)*n + n-1]=1;
        for(int ii=m-1; ii>=0; ii--)
        {
            for(int jj=n-1; jj>=0; jj--)
            {
                int idx = (ii)*n + jj;
                if(jj<n-1)
                    matrix[idx] += matrix[idx+1];
                if(ii<m-1)
                    matrix[idx] += matrix[idx+n];
            }
        }
        int rst = matrix[0];
        if(matrix)
            delete[] matrix;
        return rst;
    }

 

/********** recursive call, timeout ***********/

    int uniquePaths_timeout(int m, int n) {
        return go(m, n, 0, 0);
    }
   
    int go(int m, int n, int x, int y)
    {
        int rst=0;
       
        if((x==(n-1))&&((0-y)==(m-1)))
            return 1;
       
        if(x<(n-1))
            rst += go(m, n, x+1, y);
       
        if((0-y)<(m-1))
            rst += go(m, n, x, y-1);
        return rst;
    }
};