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1128 N Queens Puzzle

Statement

Metadata

  • 作者: CHEN, Yue
  • 单位: 浙江大学
  • 代码长度限制: 16 KB
  • 时间限制: 300 ms
  • 内存限制: 64 MB

The "eight queens puzzle" is the problem of placing eight chess queens on an 8\times 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\times 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, \cdots , 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.

8q.jpg 9q.jpg
Figure 1 Figure 2

Input Specification

Each input file contains several test cases. The first line gives an integer K (1). Then K lines follow, each gives a configuration in the format "N Q_1 Q_2 … Q_N", where 4\le N\le 1000 and it is guaranteed that 1\le Q_i\le N for all i=1, \cdots , 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

Solution

#include <ctype.h>
#include <algorithm>
#include <climits>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <deque>
#include <iomanip>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <vector>

#define CLR(a) memset(a, 0, sizeof(a))
#define pb push_back

using namespace std;
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<string, int> psi;
typedef pair<string, string> pss;

const double PI = 3.14159265358979323846264338327;
const double E = exp(1);
const double eps = 1e-30;

const int INF = 0x3f3f3f3f;
const int maxn = 1e5 + 5;
const int MOD = 1e9 + 7;

int main() {
    int t;
    cin >> t;
    while (t--) {
        int n, num;
        int flag = 1;
        cin >> n;
        map<int, int> l, m, r;
        for (int i = 1; i <= n; i++) {
            scanf("%d", &num);
            if (m[num] || l[num - i] || r[num + i])
                flag = 0;
            m[num] = 1;
            l[num - i] = 1;
            r[num + i] = 1;
        }
        if (flag)
            printf("YES\n");
        else
            printf("NO\n");
    }
}
Last update: May 4, 2022
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