POJ 1753(Flip Game)

tips：
1、对于每个棋子，翻转偶数次相当于原封不动，翻转奇数次相当于翻转一次
2、总共有16个棋格子，利用组合数（关键就是“从16个格子里面任意选取n个元素的所有组合”如何实现：DFS），共 2^16 种不同翻转选择

#include<iostream>using namespace std;int a[16], b[16];bool achieve = false;int result[16]; //存储某个可能的组合情况bool check(int a[]) //检查是否全黑或全白{bool all = true;for (int i = 1; i < 16; ++i)if (a[i] != a[0]) all = false;return all;}void flip(int a[], int i){a[i] ^= 1;int m = i % 4, n = i / 4;if (m > 0) a[i - 1] ^= 1;if (m < 3) a[i + 1] ^= 1;if (n > 0) a[i - 4] ^= 1;if (n < 3) a[i + 4] ^= 1;}void DFS(int a[], int start, int a_len, int *result, int count, int num){for (int i = start; i < a_len + 1 - count; ++i){result[count - 1] = i;if (count == 1){for (int i = 0; i < 16; i++) b[i] = a[i]; //数组b作为数组a的副本for (int j = num - 1; j >= 0; --j){flip(b, result[j]);}if (check(b)) achieve = true;}else DFS(a, i + 1, a_len, result, count - 1, num);}}int main(void){char t;//因为该棋盘的规模已知，且比较小，所以可以逐个字符输入，不会TLE//不过最好逐行字符串输入，保证不会TLEfor (int i = 0; i < 16; ++i){cin >> t;if (t == 'w') a[i] = 1;else a[i] = 0;}if (check(a)) cout << 0 << endl;else{for (int i = 1; i <= 16; ++i) //翻转1~16个棋子的各个情况都尝试一下{DFS(a, 0, 16, result, i, i);if (achieve){cout << i << endl;break;}}if (!achieve) cout << "Impossible" << endl;}return 0;}//字符串输入版本#include<iostream>using namespace std;int a[16], b[16];bool achieve = false;int result[16];bool check(int a[]){bool all = true;for (int i = 1; i < 16; ++i)if (a[i] != a[0]) all = false;return all;}void flip(int a[], int i){a[i] ^= 1;int m = i % 4, n = i / 4;if (m > 0) a[i - 1] ^= 1;if (m < 3) a[i + 1] ^= 1;if (n > 0) a[i - 4] ^= 1;if (n < 3) a[i + 4] ^= 1;}void DFS(int a[], int start, int a_len, int *result, int count, int num){for (int i = start; i < a_len + 1 - count; ++i){result[count - 1] = i;if (count == 1){for (int i = 0; i < 16; i++) b[i] = a[i]; for (int j = num - 1; j >= 0; --j){flip(b, result[j]);}if (check(b)) achieve = true;}else DFS(a, i + 1, a_len, result, count - 1, num);}}int main(void){char str[5][5]; //数组开大些，不能开成str[4][4]，因为输入的每个字符串末尾有空字符'\0'int len = 4;for (int i = 0; i < 4; i++) cin >> str[i];for (int i = 0; i < 4; i++){for (int j = 0; j < 4; j++){if (str[i][j] == 'w') a[i * 4 + j] = 1;else a[i * 4 + j] = 0;}}if (check(a)) cout << 0 << endl;else{for (int i = 1; i <= 16; ++i) {DFS(a, 0, 16, result, i, i);if (achieve){cout << i << endl;break;}}if (!achieve) cout << "Impossible" << endl;}return 0;}