《剑指offer》第十二题：矩阵中的路径
// 面试题12：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。例如在下面的3×4的矩阵中包含一条字符串“bfce”的路径（路径中的字 // 母用下划线标出）。但矩阵中不包含字符串“abfb”的路径，因为字符串的第一个 // 字符b占据了矩阵中的第一行第二个格子之后，路径不能再次进入这个格子。 // A B T G // C F C S // J D E H #include <cstdio> #include <string> #include <stack> using namespace std; bool hasPathCore(const char* matrix, int rows, int cols, int row, int col, const char* str, int& pathLength, bool* visited); bool hasPath(const char* matrix, int rows, int cols, const char* str) { //鲁棒性测试 if (matrix == nullptr || str == nullptr || rows <= 0 || cols <= 0) return false; //路径记录矩阵 bool* visited = new bool[rows * cols]; memset(visited, 0, rows * cols); int pathLength = 0; //字符串索引 for (int row = 0; row < rows; ++row) //遍历寻找起点 { for (int col = 0; col < cols; ++col) { if (hasPathCore(matrix, rows, cols, row, col, str, pathLength, visited)) return true; } } delete[] visited; return false; } bool hasPathCore(const char* matrix, int rows, int cols, int row, int col, const char* str, int& pathLength, bool* visited) { if (str[pathLength] == '\0') //字符串尾部 return true; bool hasPath = false; if (row >= 0 && row < rows && col >= 0 && col < cols && matrix[row * cols + col] == str[pathLength] && !visited[row * cols + col]) //对应字符串中pathLength位置字符且从未访问过 { ++pathLength; visited[row * cols + col] = true; hasPath = hasPathCore(matrix, rows, cols, row, col - 1, str, pathLength, visited) || hasPathCore(matrix, rows, cols, row - 1, col, str, pathLength, visited) || hasPathCore(matrix, rows, cols, row, col + 1, str, pathLength, visited) || hasPathCore(matrix, rows, cols, row + 1, col, str, pathLength, visited); if (!hasPath) //此路不通, 大家就当无事发生 { --pathLength; visited[row * cols + col] = false; } } return hasPath; }
// ====================测试代码==================== void Test(const char* testName, const char* matrix, int rows, int cols, const char* str, bool expected) { if (testName != nullptr) printf("%s begins: ", testName); if (hasPath(matrix, rows, cols, str) == expected) printf("Passed.\n"); else printf("FAILED.\n"); } //ABTG //CFCS //JDEH //BFCE void Test1() { const char* matrix = "ABTGCFCSJDEH"; const char* str = "BFCE"; Test("Test1", (const char*)matrix, 3, 4, str, true); } //ABCE //SFCS //ADEE //SEE void Test2() { const char* matrix = "ABCESFCSADEE"; const char* str = "SEE"; Test("Test2", (const char*)matrix, 3, 4, str, true); } //ABTG //CFCS //JDEH //ABFB void Test3() { const char* matrix = "ABTGCFCSJDEH"; const char* str = "ABFB"; Test("Test3", (const char*)matrix, 3, 4, str, false); } //ABCEHJIG //SFCSLOPQ //ADEEMNOE //ADIDEJFM //VCEIFGGS //SLHECCEIDEJFGGFIE void Test4() { const char* matrix = "ABCEHJIGSFCSLOPQADEEMNOEADIDEJFMVCEIFGGS"; const char* str = "SLHECCEIDEJFGGFIE"; Test("Test4", (const char*)matrix, 5, 8, str, true); } //ABCEHJIG //SFCSLOPQ //ADEEMNOE //ADIDEJFM //VCEIFGGS //SGGFIECVAASABCEHJIGQEM void Test5() { const char* matrix = "ABCEHJIGSFCSLOPQADEEMNOEADIDEJFMVCEIFGGS"; const char* str = "SGGFIECVAASABCEHJIGQEM"; Test("Test5", (const char*)matrix, 5, 8, str, true); } //ABCEHJIG //SFCSLOPQ //ADEEMNOE //ADIDEJFM //VCEIFGGS //SGGFIECVAASABCEEJIGOEM void Test6() { const char* matrix = "ABCEHJIGSFCSLOPQADEEMNOEADIDEJFMVCEIFGGS"; const char* str = "SGGFIECVAASABCEEJIGOEM"; Test("Test6", (const char*)matrix, 5, 8, str, false); } //ABCEHJIG //SFCSLOPQ //ADEEMNOE //ADIDEJFM //VCEIFGGS //SGGFIECVAASABCEHJIGQEMS void Test7() { const char* matrix = "ABCEHJIGSFCSLOPQADEEMNOEADIDEJFMVCEIFGGS"; const char* str = "SGGFIECVAASABCEHJIGQEMS"; Test("Test7", (const char*)matrix, 5, 8, str, false); } //AAAA //AAAA //AAAA //AAAAAAAAAAAA void Test8() { const char* matrix = "AAAAAAAAAAAA"; const char* str = "AAAAAAAAAAAA"; Test("Test8", (const char*)matrix, 3, 4, str, true); } //AAAA //AAAA //AAAA //AAAAAAAAAAAAA void Test9() { const char* matrix = "AAAAAAAAAAAA"; const char* str = "AAAAAAAAAAAAA"; Test("Test9", (const char*)matrix, 3, 4, str, false); } //A //A void Test10() { const char* matrix = "A"; const char* str = "A"; Test("Test10", (const char*)matrix, 1, 1, str, true); } //A //B void Test11() { const char* matrix = "A"; const char* str = "B"; Test("Test11", (const char*)matrix, 1, 1, str, false); } void Test12() { Test("Test12", nullptr, 0, 0, nullptr, false); } int main(int argc, char* argv[]) { Test1(); Test2(); Test3(); Test4(); Test5(); Test6(); Test7(); Test8(); Test9(); Test10(); Test11(); Test12(); return 0; }
分析：回溯法本质为递归思想。
class Solution { public: bool hasPath(char* matrix, int rows, int cols, char* str) { if (matrix == nullptr || str == nullptr || rows <= 0 || cols <= 0) return false; bool* visited = new bool[rows * cols]; memset(visited, 0, rows * cols); int pathLength = 0; for (int row = 0; row < rows; ++row) { for (int col = 0; col < cols; ++col) { if (hasPathCore(matrix, rows, cols, row, col, str, pathLength, visited)) { return true; } } } delete[] visited; return false; } bool hasPathCore(char* matrix, int rows, int cols, int row, int col, char* str, int pathLength, bool* visited) { if (str[pathLength] == '\0') return true; bool hasPath = false; if (row >= 0 && row < rows && col >= 0 && col < cols && str[pathLength] == matrix[row * cols + col] && !visited[row * cols + col]) { ++pathLength; visited[row * cols + col] = true; hasPath = hasPathCore(matrix, rows, cols, row, col - 1, str, pathLength, visited) || hasPathCore(matrix, rows, cols, row - 1, col, str, pathLength, visited) || hasPathCore(matrix, rows, cols, row, col + 1, str, pathLength, visited) || hasPathCore(matrix, rows, cols, row + 1, col, str, pathLength, visited); if (!hasPath) { --pathLength; visited[row * cols + col] = false; } } return hasPath; } };
