Unique Paths问题及解法
2017-07-29 10:40
344 查看
问题描述:
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.
问题分析:
本题是一个动态规划问题。经过观察我们发现:
start到finish的路径总数 = start到finish的上边一个格的路径总数 + start到finish的左边一个格的路径总数。依次依次从start开始,计算到每个位置(i,j)时的路径总数。最终可确定到位置(m,n)的路径总数。
过程详见代码:
class Solution {
public:
int uniquePaths(int m, int n) {
vector<vector<int>> mat(m + 1, vector<int>(n + 1, 0));
mat[1][1] = 1;
for (int i = 1; i <= m; i++)
{
for (int j = 1; j <= n; j++)
{
if (mat[i][j] == 0) mat[i][j] = mat[i][j - 1] + mat[i - 1][j];
}
}
return mat[m]
;
}
};
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.
问题分析:
本题是一个动态规划问题。经过观察我们发现:
start到finish的路径总数 = start到finish的上边一个格的路径总数 + start到finish的左边一个格的路径总数。依次依次从start开始,计算到每个位置(i,j)时的路径总数。最终可确定到位置(m,n)的路径总数。
过程详见代码:
class Solution {
public:
int uniquePaths(int m, int n) {
vector<vector<int>> mat(m + 1, vector<int>(n + 1, 0));
mat[1][1] = 1;
for (int i = 1; i <= m; i++)
{
for (int j = 1; j <= n; j++)
{
if (mat[i][j] == 0) mat[i][j] = mat[i][j - 1] + mat[i - 1][j];
}
}
return mat[m]
;
}
};
相关文章推荐
- 《编程之美》读书笔记(四): 卖书折扣问题的贪心解法
- 最大子数组问题的三种解法
- Convert Sorted List to Binary Search Tree问题及解法
- 与字符串有关的一些典型问题的C++解法
- Unique Paths II问题及解法
- 第11周 【项目5 - 迷宫问题之图深度优先遍历解法】
- Shortest Unsorted Continuous Subarray问题及解法
- 第12周项目5 迷宫问题之图深度优先遍历解法
- 隐马尔科夫模型,第三种问题解法,维比特算法(biterbi) algorithm python代码
- Swap Nodes in Pairs问题及解法
- Maximum Product of Word Lengths 问题及解法
- 约瑟夫环问题的两种解法(详解)
- 皇后问题最快的解法(C语言)八皇后、十六皇后时间在毫秒级
- 【原创】编程之美---小飞的电梯调度问题 (停k层的解法)
- Wiggle Subsequence问题及解法
- 史上最全最丰富的“最长公共子序列”、“最长公共子串”问题的解法与思路
- Binary Watch问题及解法
- 倒水问题通用解法
- 简说期望类问题的解法
- [CO] 无约束极值问题的解法