LeetCode 62 Unique Paths（记忆化搜索）

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.

题目大意：有一个m行n列的格子矩阵，一个机器人要从左上角走到右下角，机器人只能向右或向下移动，问最终有多少种方案可以走到右下角。

解题思路：令f[m, n]为从[1, 1]走到[m, n]的方案数，那么从图上可以看出：

    当m != 1且n != 1时，f[m, n] = f[m-1, n] + f[m, n-1]

    当m == 1且n != 1时，f[m, n] = f[m, n-1]

    当m != 1且n == 1时，f[m, n] = f[m-1, n]

    当m == 1且n == 1时, f[m, n] = 1

注意要用一个数组将结果保存起来，否则大量的重复计算会造成TLE。

代码如下：

#define maxn 105int f[maxn][maxn];int  uniquePaths(int m, int n) {    if(f[m][n]) return f[m][n];    if(m == 1 && n == 1) return 1;    else if(m == 1) f[m][n] = uniquePaths(m, n - 1) ;     else if(n == 1) f[m][n] = uniquePaths(m - 1, n) ;    else f[m][n] = uniquePaths(m - 1, n) + uniquePaths(m, n - 1);    return f[m][n];}