poj1160 区间DP

最新推荐文章于 2020-12-20 21:34:20 发布

原创最新推荐文章于 2020-12-20 21:34:20 发布 · 684 阅读

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经典区间DP，朴素的时间复杂度O(n^3)，四边形优化O(n^2)。

ACcode:

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;

const int NS=305;
const int INF=0x3f3f3f3f;

int n,m;
int p[NS],dp[NS][NS],s[NS][NS];

int main()
{
    while (~scanf("%d %d",&n,&m))
    {
        for (int i=1;i<=n;i++)
        scanf("%d",&p[i]);
        for (int i=1;i<=n;i++)
        {
            s[i][i]=0;
            for (int j=i+1;j<=n;j++)
            s[i][j]=s[i][j-1]+p[j]-p[(i+j)>>1];
        }
        for (int i=1;i<=n;i++) dp[i][0]=INF;
        dp[0][0]=0;
        for (int i=1;i<=n;i++)
        for (int j=1;j<=m;j++)
        {
            dp[i][j]=INF;
            for (int k=0;k<i;k++)
            dp[i][j]=min(dp[i][j],dp[k][j-1]+s[k+1][i]);
        }
        printf("%d\n",dp[n][m]);
    }
    return 0;
}

/**
四边形优化
*/
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;

const int NS=305;
const int INF=0x3f3f3f3f;

int n,m;
int p[NS],dp[NS][NS],s[NS][NS],lim[NS][NS];

int main()
{
    while (~scanf("%d %d",&n,&m))
    {
        for (int i=1; i<=n; i++)
            scanf("%d",&p[i]);
        for (int i=1; i<=n; i++)
        {
            s[i][i]=lim[i][1]=dp[i][i]=0,
            lim[i][i]=i-1,dp[i][1]=s[1][i];
            for (int j=i+1; j<=n; j++)
            dp[j][i]=INF,s[i][j]=s[i][j-1]+p[j]-p[(i+j)>>1];
        }
        for (int j=2; j<=m; j++)
        {
            lim[n+1][j]=n-1;
            for (int i=n; i>j; i--)
            for (int k=lim[i][j-1]; k<=lim[i+1][j]; k++)
            if (dp[i][j]>dp[k][j-1]+s[k+1][i])
            lim[i][j]=k,dp[i][j]=dp[k][j-1]+s[k+1][i];
        }
        printf("%d\n",dp[n][m]);
    }
    return 0;
}