详细见：leetcode.com/problems/unique-paths
Java Solution: github
package leetcode; import java.util.Arrays; public class P062_UniquePaths { public static void main(String[] args) { System.out.println(new Solution().uniquePaths(3, 3)); } /* * 先写一份空间O(m * n)，时间O(m * n)的版本 * 1 ms * 5.22% */ static class Solution { public int uniquePaths(int m, int n) { if (m < 1 || n < 1) return 0; int[][] route = new int[m][n]; Arrays.fill(route[0], 1); for (int i = 1; i < m; i ++) route[i][0] = 1; for (int i = 1; i < m; i ++) { for (int j = 1; j < n; j ++) { route[i][j] = route[i - 1][j] + route[i][ j - 1]; } } return route[m - 1][n - 1]; } } /* * 1 ms * 5.22% */ static class Solution2 { public int uniquePaths(int m, int n) { if (m < 1 || n < 1) return 0; if (m > n) return uniquePaths(n, m); int[] route = new int[m]; Arrays.fill(route, 1); for (int i = 1; i < n; i ++) for (int j = 1; j < m; j ++) route[j] += route[j - 1]; return route[m - 1]; } } }C Solution: github
/* url: leetcode.com/problems/unique-paths AC 3ms 2.33% */ int uniquePaths(int m, int n) { int* dp = (int*) malloc(sizeof(int) * n); int i = 0, j = 0; for (i = n-1; i > -1; i --) { dp[i] = 1; } for (j = m-2; j > -1; j --) { for (i = n-2; i > -1; i --) { dp[i] += dp[i+1]; } } i = dp[0]; free(dp); return i; } int main() { }Python Solution: github
#coding=utf-8 ''' url: leetcode.com/problems/unique-paths @author: zxwtry @email: zxwtry@qq.com @date: 2017年4月13日 @details: Solution: 79ms 10.36% ''' class Solution(object): def uniquePaths(self, m, n): """ :type m: int :type n: int :rtype: int """ dp = [1] * n for j in range(m-2, -1, -1): for i in range(n-2, -1, -1): dp[i] += dp[i+1] return dp[0]