The "eight queens puzzle" is the problem of placing eight chess queens on an 8×8 chessboard so that no two queens threaten each other. Thus, a solution requires that no two queens share the same row, column, or diagonal. The eight queens puzzle is an example of the more general N queens problem of placing N non-attacking queens on an N×N chessboard. (From Wikipedia - "Eight queens puzzle".)
Here you are NOT asked to solve the puzzles. Instead, you are supposed to judge whether or not a given configuration of the chessboard is a solution. To simplify the representation of a chessboard, let us assume that no two queens will be placed in the same column. Then a configuration can be represented by a simple integer sequence (Q~1~, Q~2~, ..., Q~N~), where Q~i~ is the row number of the queen in the i-th column. For example, Figure 1 can be represented by (4, 6, 8, 2, 7, 1, 3, 5) and it is indeed a solution to the 8 queens puzzle; while Figure 2 can be represented by (4, 6, 7, 2, 8, 1, 9, 5, 3) and is NOT a 9 queens' solution.
Figure 1 Figure 2
Input Specification:
Each input file contains several test cases. The first line gives an integer K (1 < K <= 200). Then K lines follow, each gives a configuration in the format "N Q~1~ Q~2~ ... Q~N~", where 4 <= N <= 1000 and it is guaranteed that 1 <= Q~i~ <= N for all i=1, ..., N. The numbers are separated by spaces.
Output Specification:
For each configuration, if it is a solution to the N queens problem, print "YES" in a line; or "NO" if not.
Sample Input:
4
8 4 6 8 2 7 1 3 5
9 4 6 7 2 8 1 9 5 3
6 1 5 2 6 4 3
5 1 3 5 2 4
Sample Output:
YES
NO
NO
YES
额,没想到暴力膜居然通过了,三层循环嵌套,啧啧;
思路:对于合法的放置, 任意两个棋子不在同一行, 或者连线的斜率不为1或者-1; 如果存在则输出NO, 反之输出YES
1 #include<iostream> 2 #include<vector> 3 using namespace std; 4 int main(){ 5 int n, k, i, j; 6 cin>>n; 7 for(i=1; i<=n; i++){ 8 cin>>k; 9 vector<int> v(k+1); 10 bool flag=true; 11 for(j=1; j<=k; j++){ 12 scanf("%d", &v[j]); 13 for(int y=1; y<j && flag; y++){ 14 if(v[j]-v[y]==j-y || v[j]-v[y]==y-j || v[j]==v[y]){ 15 cout<<"NO"<<endl; 16 flag=false; 17 } 18 } 19 } 20 if(flag) cout<<"YES"<<endl; 21 } 22 return 0; 23 }