UVA 167 The Sultan's Successors （带权8皇后）

The Sultan of Nubia has no children, so she has decided that the country will be split into up to kseparate parts on her death and each part will be inherited by whoever performs best at some test. Itis possible for any individual to inherit more than one or indeed all of the portions. To ensure thatonly highly intelligent people eventually become her successors, the Sultan has devised an ingenioustest. In a large hall filled with the splash of fountains and the delicate scent of incense have beenplaced k chessboards. Each chessboard has numbers in the range 1 to 99 written on each square and issupplied with 8 jewelled chess queens. The task facing each potential successor is to place the 8 queenson the chess board in such a way that no queen threatens another one, and so that the numbers onthe squares thus selected sum to a number at least as high as one already chosen by the Sultan. (Forthose unfamiliar with the rules of chess, this implies that each row and column of the board containsexactly 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 thehighest scores possible for each board under these conditions. (You know that the Sultan is both agood chess player and a good mathematician and you suspect that her score is the best attainable.)

InputInput

will consist of k (the number of boards), on a line by itself, followed by k sets of 64 numbers,each set consisting of eight lines of eight numbers. Each number will be a positive integer less than100. There will never be more than 20 boards.

Output

Output will consist of k numbers consisting of your k scores, each score on a line by itself and rightjustified in a field 5 characters wide.

Sample Input

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

260

题意：

第一行一个整数k，代表k组输入。

每组输入一个8*8的矩阵的各个位置上权值。

求一种8皇后的摆法(皇后无法相互攻击)，使其权值和最大。

思路：

枚举所有摆法，求权值最大值。（注意：答案输出靠右，占5个字符）

看了一下位运算n皇后解法，试试水，详见代码

代码：

#include<stdio.h>

#define For(a,b,c) for(int a = b; a <= c; a++)

//maxn存储当前最大值，v存储权值，limit存储没有皇后时可摆放的位置
int maxn, v[10][10], limit = (1 << 8)-1;

//row某一列无法占据，ld左斜，rd右斜，sum当前权值，cnt当前层数
void n_queue(int row, int ld, int rd, int sum, int cnt)
{
    if(cnt == 8)
    {
        maxn = sum > maxn ? sum : maxn;
        return;
    }

    //abl存储能放棋子位置，a枚举每个能放棋子的位置，index存储放在第几位
    int abl = limit & (~(row | ld | rd)), a, index;

    while(abl)
    {
        a = abl & (~abl + 1);
        abl -= a;
        index = 0;
        while(a>>index) index++;
        //因为摆法对称所以 sum传参也可以是sum + v[cnt+1][index]
        n_queue(row | a, (ld | a) << 1, (rd | a) >> 1, sum + v[cnt+1][8-index+1], cnt+1);
    }

}

int main()
{
    int T;
    scanf("%d",&T);
    while(T--)
    {
        For(i,1,8)
        {
            For(j,1,8)
            {
                scanf("%d",&v[i][j]);
            }
        }
        maxn = 0;
        n_queue(0,0,0,0,0);
        printf("%5.d\n",maxn);//注意输出格式控制
    }
    return 0;
}

UVA 167 The Sultan's Successors （带权8皇后）

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