清北暑假模拟day1 生活

/*
数字三角形，要求第K大的值，可以推知，如果得知k的范围，那么一定是在上一行可转移状态的对应范围内（反证法可以证明），这个在背包九讲里也有提及
*/
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<algorithm>

using namespace std;

int n,k,f[110][110][15],z[110][110],y[1010];

int main()
{
    freopen("live.in","r",stdin);
    freopen("live.out","w",stdout);

    scanf("%d%d",&n,&k);
    for (int a=1;a<=n;a++)
        for (int b=1;b<=a;b++)
            scanf("%d",&z[a][b]);
    for (int a=1;a<=n;a++)
        for (int b=1;b<=a;b++)
            for (int c=1;c<=k;c++)
                f[a][b][c]=-12345;
    f[1][1][1]=z[1][1];
    for (int a=1;a<n;a++)
        for (int b=1;b<=a;b++)
            for (int c=1;c<=k;c++)
                if (f[a][b][c]!=-12345)
                {
                    int v=f[a][b][c]+z[a+1][b];
                    for (int d=1;d<=k;d++)
                        if (v>=f[a+1][b][d])
                        {
                            for (int e=k;e>d;e--)
                                f[a+1][b][e]=f[a+1][b][e-1];
                            f[a+1][b][d]=v;
                            break;
                        }
                    v=f[a][b][c]+z[a+1][b+1];
                    for (int d=1;d<=k;d++)
                        if (v>=f[a+1][b+1][d])
                        {
                            for (int e=k;e>d;e--)
                                f[a+1][b+1][e]=f[a+1][b+1][e-1];
                            f[a+1][b+1][d]=v;
                            break;
                        }
                }
    int cnt=0;
    for (int a=1;a<=n;a++)
        for (int b=1;b<=k;b++)
            y[++cnt]=f[n][a][b];
    sort(y+1,y+cnt+1);
    printf("%d\n",y[cnt-k+1]);

    return 0;
}