面试题73：矩阵中的路径

题目：

请设计一个函数，用来判断在一个矩阵中是否存在一条包含某字符串所有字符的路径。路径可以从矩阵中任意一格开始，每一步可以在矩阵中向左、右、上、下移动一格。如果一条路径经过了矩阵的某一格，那么该路径不能再次进入该格子。

思路：

用回溯来做。

#include <iostream>
#include <vector>
#include <stack>
#include <queue>
#include <algorithm>  //堆算法
#include <functional> //仿函数
using namespace std;

bool HasPathCore(char **matrix, int row, int column, int rIndex, int cIndex, char *str, int &pathLength, vector<vector<bool>>&visited)
{
if (str[pathLength] == '\0') return true;
bool hasPath = false;
if (rIndex >= 0 && rIndex < row && cIndex >= 0 && cIndex < column && matrix[rIndex][cIndex] == str[pathLength] && !visited[rIndex][cIndex])
{
++pathLength;
visited[rIndex][cIndex] = 1;
hasPath = HasPathCore(matrix, row, column, rIndex + 1, cIndex, str, pathLength, visited) ||//下
HasPathCore(matrix, row, column, rIndex - 1, cIndex, str, pathLength, visited) ||      //上
HasPathCore(matrix, row, column, rIndex, cIndex + 1, str, pathLength, visited) ||      //右
HasPathCore(matrix, row, column, rIndex, cIndex - 1, str, pathLength, visited);        //左
if (!hasPath)
{
--pathLength;
visited[rIndex][cIndex] = 0;
}
}
return hasPath;
}

bool HasPath(char **matrix, int row, int column, char *str)
{
if (row < 1 || column < 1 || str == NULL)
return false;
vector<vector<bool>> visited(row, vector<bool>(column, 0));
int pathLength = 0;
for (int rIndex = 0; rIndex < row; rIndex++)
for (int cIndex = 0; cIndex < column; cIndex++)
{
if (HasPathCore(matrix, row, column, rIndex, cIndex - 1, str, pathLength, visited))
return true;
}
return false;
}

int main()
{
char *matrix[] = { "abce", "sfcs", "adee" };
cout << HasPath(matrix, 3, 4, "abfc") << endl;
return 0;
}