BZOJ1037 ZJOI2008生日聚会（动态规划）

　　设f[i][j][x][y]为安排了i个男孩j个女孩，后缀最大男孩-女孩数为x，最大女孩-男孩数为y的方案数。转移显然。

#include<iostream> 
#include<cstdio>
#include<cmath>
#include<cstdlib>
#include<cstring>
#include<algorithm>
using namespace std;
int read()
{
    int x=0,f=1;char c=getchar();
    while (c<'0'||c>'9') {if (c=='-') f=-1;c=getchar();}
    while (c>='0'&&c<='9') x=(x<<1)+(x<<3)+(c^48),c=getchar();
    return x*f;
}
#define N 151
#define M 22
#define P 12345678
int n,m,k,f[N][N][M][M];
void inc(int &x,int y){x+=y;if (x>=P) x-=P;}
int main()
{
#ifndef ONLINE_JUDGE
    freopen("bzoj1037.in","r",stdin);
    freopen("bzoj1037.out","w",stdout);
    const char LL[]="%I64d\n";
#else
    const char LL[]="%lld\n";
#endif
    n=read(),m=read(),k=read();
    f[0][0][0][0]=1;
    for (int i=1;i<=n+m;i++)
        for (int j=max(0,i-m);j<=min(n,i);j++)
        {
            int x=j,y=i-j;
            for (int p=0;p<=min(k,x);p++)
                for (int q=0;q<=min(k,y);q++)
                {
                    if (x&&p)
                    {
                        inc(f[x][y][p][q],f[x-1][y][p-1][q+1]);
                        if (q==0) inc(f[x][y][p][q],f[x-1][y][p-1][q]);
                    }
                    if (y&&q)
                    {
                        inc(f[x][y][p][q],f[x][y-1][p+1][q-1]);
                        if (p==0) inc(f[x][y][p][q],f[x][y-1][p][q-1]);
                    }
                }
        }
    int ans=0;
    for (int i=0;i<=k;i++)
        for (int j=0;j<=k;j++)
        inc(ans,f[n][m][i][j]);
    cout<<ans;
    return 0;
}