1128 N Queens Puzzle (20 分)

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1128 N Queens Puzzle (20 分)

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.

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 Q1​ Q2​​ … 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

当有两个皇后同行或者在对角线上时判断为NO否则为YES

#include<bits/stdc++.h>
using namespace std;
int main() {int k;scanf("%d", &k);for (int i = 0; i < k; i++) {int n;bool flag = true;scanf("%d", &n);vector<int> v(n);for (int j = 0; j < n; j++) {scanf("%d", &v[j]);for (int t = 0; t < j; t++) {if (v[t] == v[j] || abs(j - t) == abs(v[j] - v[t])) {flag = false;break;}}}printf("%s", flag == true ? "YES\n" : "NO\n");}
}

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