全排列&&八皇后问题
子问题，子问题，递归 is beautiful。八皇后问题也可以用这个来解决，加一个判断就行了。
1 #include <iostream> 2 3 using namespace std; 4 static int num = 0; 5 bool check(int * arry, int length) 6 { 7 int i, j; 8 for(i = 0; i < length; ++i) 9 {
11 for(j = i+1; j < length; ++j) 12 { 13 if(arry[i] - arry[j] == j - i || arry[i] - arry[j] == i - j) 14 return false; 15 } 16 } 17 return true; 18 } 19 void permutation(int * arry, int start, int length) 20 { 21 if(start == length && check(arry, length)) 22 { 23 for(int j = 0; j < length; ++j) 24 cout << arry[j] << " "; 25 cout << endl; 26 num++; 27 return; 28 } 29 for(int i = start; i < length; ++i) 30 { 31 int temp = arry[start]; 32 arry[start] = arry[i]; 33 arry[i] = temp; 34 permutation(arry, start+1, length); 35 temp = arry[start]; 36 arry[start] = arry[i]; 37 arry[i] = temp; 38 } 39 } 40 int main() 41 { 42 int n; 43 while(cin >> n) 44 { 45 int * arry = new int[n]; 46 for(int i = 0; i < n; ++i) 47 arry[i] = i + 1; 48 num = 0; 49 permutation(arry, 0, n); 50 cout << "The number of total solutions is " << num << endl; 51 delete arry; 52 } 53 return 0; 54 }
1 #include <iostream> 2 3 using namespace std; 4 5 void permutation(int * arry, int start, int length) 6 { 7 if(start == length) 8 { 9 for(int j = 0; j < length; ++j) 10 cout << arry[j] << " "; 11 cout << endl; 12 return; 13 } 14 for(int i = start; i < length; ++i) 15 { 16 int temp = arry[start]; 17 arry[start] = arry[i]; 18 arry[i] = temp; 19 permutation(arry, start+1, length); 20 temp = arry[start]; 21 arry[start] = arry[i]; 22 arry[i] = temp; 23 } 24 } 25 int main() 26 { 27 int n; 28 while(cin >> n) 29 { 30 int * arry = new int[n]; 31 for(int i = 0; i < n; ++i) 32 arry[i] = i + 1; 33 permutation(arry, 0, n); 34 delete arry; 35 } 36 return 0; 37 }
