UVA 1629 Cake slicing

Posted 2020-08-14

题解:

记忆化搜索

如何判断每个区域只有一个点？转化为区间和，只要区间和为1即可

代码:

#include<bits/stdc++.h>
using namespace std;
#define pb push_back
#define mp make_pair
#define se second
#define fs first
#define LL long long
#define CLR(x) memset(x,0,sizeof x)
#define MC(x,y) memcpy(x,y,sizeof(x))  
#define SZ(x) ((int)(x).size())
#define FOR(it,c) for(__typeof((c).begin()) it=(c).begin();it!=(c).end();it++)
#define lson l,m,rt<<1
#define rson m+1,r,rt<<1|1 
typedef pair<int,int> P;
const double eps=1e-9;
const int maxn=200100;
const int mod=1e9+7;
const int INF=1e9;


int n,m,k,a,b;
int M[25][25],Sum[25][25];
int dp[25][25][25][25];

int getsum(int x1,int y1,int x2,int y2)
{
    return Sum[x2][y2]-Sum[x2][y1-1]-Sum[x1-1][y2]+Sum[x1-1][y1-1];
}

int DP(int x1,int y1,int x2,int y2)
{
    if(dp[x1][y1][x2][y2]>=0)  return dp[x1][y1][x2][y2];
    if(getsum(x1,y1,x2,y2)==1) return dp[x1][y1][x2][y2]=0;
    int Min=INF;
    for(int i=x1;i<x2;i++)
    {
        if(getsum(x1,y1,i,y2)>0&&getsum(i+1,y1,x2,y2)>0) Min=min(Min,DP(x1,y1,i,y2)+DP(i+1,y1,x2,y2)+y2-y1+1);
    }
    for(int i=y1;i<y2;i++)
    {
        if(getsum(x1,y1,x2,i)>0&&getsum(x1,i+1,x2,y2)>0) Min=min(Min,DP(x1,y1,x2,i)+DP(x1,i+1,x2,y2)+x2-x1+1);
    }
    return dp[x1][y1][x2][y2]=Min;
}

int main()
{
    int Case=1;
    while(~scanf("%d%d%d",&n,&m,&k))
    {
        CLR(M);CLR(Sum);
        memset(dp,-1,sizeof(dp));
        for(int i=1;i<=k;i++)
        {
            scanf("%d%d",&a,&b);
            M[a][b]=1;
        }
        for(int i=1;i<=n;i++)
        for(int j=1;j<=m;j++)
        {
            Sum[i][j]=M[i][j];
            Sum[i][j]+=Sum[i][j-1];
            Sum[i][j]+=Sum[i-1][j];
            Sum[i][j]-=Sum[i-1][j-1];
        }
        printf("Case %d: %d\n",Case++,DP(1,1,n,m));
    }
    return 0;
}