[wikioi]乌龟棋

http://wikioi.com/problem/1068/

多重背包。边界f[0,0,0,0]=a[1]（初始时没有用任何卡片，获得棋盘第一格的分数）
DP方程：f[i,j,k,l]=max(f[i-1,j,k,l],f[i,j-1,k,l],f[i,j,k-1,l],f[i,j,k,l-1])+a[i+j*2+k*3+l*4+1 /*此处+1是必须的，因为初始一格没有用卡片*/ ]
使用了备忘录+递归。

#include <cstdio>

#include <iostream>

#define MAX(a, b) a>b?a:b

using namespace std;



int N;

int M;

int f[45][45][45][45];

int step[355];

int card[5];



void init()     

{     

    scanf("%d%d", &N, &M);

    for (int i = 1; i <= N; i++) {

        scanf("%d", &step[i]);

    }

    for (int i = 1; i <= M; i++) {

        int c;

        scanf("%d", &c);

        card[c]++;

    }

    for (int a = 0; a < 45; a++)

        for (int b = 0; b < 45; b++)

            for (int c = 0; c < 45; c++)

                for (int d = 0; d < 45; d++)

                    f[a][b][c][d] = -1;

    f[0][0][0][0] = step[1];

}     



int dp(int a, int b, int c, int d)

{

    if (a < 0 || b < 0 || c < 0 || d < 0) return 0;

    if (f[a][b][c][d] != -1) return f[a][b][c][d];

    int m = dp(a-1, b, c, d);

    m = MAX(m, dp(a, b-1, c, d));

    m = MAX(m, dp(a, b, c-1, d));

    m = MAX(m, dp(a, b, c, d-1));

    m = m + step[1*a+2*b+3*c+4*d+1];

    f[a][b][c][d] = m;

    return m;

}



int main()

{

    init();

    int result = dp(card[1], card[2], card[3], card[4]);

    printf("%d\n", result);

    return 0;

}