The Sultan's Successors UVA167

最新推荐文章于 2018-04-01 22:24:15 发布

最新推荐文章于 2018-04-01 22:24:15 发布 · 238 阅读

本文介绍了一个基于八皇后问题的变种算法题——苏丹的继承者挑战。任务是在多个棋盘上放置8个皇后，使得它们不互相攻击且位于高价值的位置。通过递归深度优先搜索算法实现解决方案。

The Sultan's Successors

The Sultan of Nubia has no children, so she has decided that the country will be split into up tokseparate parts on her death and each part will be inherited by whoever performs best at some test. It is possible for any individual to inherit more than one or indeed all of the portions. To ensure that only highly intelligent people eventually become her successors, the Sultan has devised an ingenious test. In a large hall filled with the splash of fountains and the delicate scent of incense have been placedkchessboards. Each chessboard has numbers in the range 1 to 99 written on each square and is supplied with 8 jewelled chess queens. The task facing each potential successor is to place the 8 queens on the chess board in such a way that no queen threatens another one, and so that the numbers on the squares thus selected sum to a number at least as high as one already chosen by the Sultan. (For those unfamiliar with the rules of chess, this implies that each row and column of the board contains exactly one queen, and each diagonal contains no more than one.)

Write a program that will read in the number and details of the chessboards and determine the highest scores possible for each board under these conditions. (You know that the Sultan is both a good chess player and a good mathematician and you suspect that her score is the best attainable.)

Input

Input will consist ofk(the number of boards), on a line by itself, followed byksets of 64 numbers, each set consisting of eight lines of eight numbers. Each number will be a positive integer less than 100. There will never be more than 20 boards.

Output

Output will consist ofknumbers consisting of yourkscores, each score on a line by itself and right justified in a field 5 characters wide.

Sample input

1
 1  2  3  4  5  6  7  8
 9 10 11 12 13 14 15 16
17 18 19 20 21 22 23 24
25 26 27 28 29 30 31 32
33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48
48 50 51 52 53 54 55 56
57 58 59 60 61 62 63 64

Sample output

一道典型的变异八皇后问题，每个节点带权值了。

#include<iostream>
#include<cstring>
#include<iomanip>

using namespace std;

int arry[10][10],vis[3][20];
int maxnum;

void dfs(int pos,int num)
{
    int i,j;
    if(pos==8)
    {
        if(num>maxnum)
        {
            maxnum=num;
        }
        return;
    }
    else
    {
        for(i=0;i<8;i++)
        {
            if(!vis[0][i]&&!vis[1][i+pos]&&!vis[2][pos-i+8])
            {
                vis[0][i]=vis[1][i+pos]=vis[2][pos-i+8]=1;
                dfs(pos+1,num+arry[pos][i]);
                vis[0][i]=vis[1][i+pos]=vis[2][pos-i+8]=0;
            }
        }
    }
}

int main()
{
    int n;
    cin>>n;
    while(n--)
    {
        int i,j;
        for(i=0;i<8;i++)
        {
            for(j=0;j<8;j++)
            {
                cin>>arry[i][j];
            }
        }
        memset(vis,0,sizeof(vis));
        maxnum=0;
        dfs(0,0);
        cout<<setw(5)<<maxnum<<endl;
    }
    return 0;
}