ZOJ 2561 Order-Preserving Codes（四边形优化DP）

题目链接：http://acm.zju.edu.cn/onlinejudge/showProblem.do?problemId=1561

题意：给出n个点的权值，构造一棵特殊的哈夫曼树满足：（1）叶子节点从左到右依次是n个点给出的顺序；（2）每个点的代价为深度乘以权值，（3）总代价最小？

思路：f[i][j]=min(f[i][k]+f[k+1][j]+sum[j]-sum[i-1])。

#include <iostream>

#include <stdio.h>

#include <string.h>

#include <algorithm>

#include <cmath>

#include <vector>

#include <queue>

#include <set>

#include <stack>

#include <string>

#include <map>





#define max(x,y) ((x)>(y)?(x):(y))

#define min(x,y) ((x)<(y)?(x):(y))

#define abs(x) ((x)>=0?(x):-(x))

#define i64 long long

#define u32 unsigned int

#define u64 unsigned long long

#define clr(x,y) memset(x,y,sizeof(x))

#define CLR(x) x.clear()

#define ph(x) push(x)

#define pb(x) push_back(x)

#define Len(x) x.length()

#define SZ(x) x.size()

#define PI acos(-1.0)

#define sqr(x) ((x)*(x))

#define MP(x,y) make_pair(x,y)

#define EPS 1e-9



#define FOR0(i,x) for(i=0;i<x;i++)

#define FOR1(i,x) for(i=1;i<=x;i++)

#define FOR(i,a,b) for(i=a;i<=b;i++)

#define FORL0(i,a) for(i=a;i>=0;i--)

#define FORL1(i,a) for(i=a;i>=1;i--)

#define FORL(i,a,b)for(i=a;i>=b;i--)





#define rush(n) for(scanf("%d",&C);C--;)

#define Rush(n)  while(scanf("%d",&n)!=-1)

using namespace std;





void RD(int &x){scanf("%d",&x);}

void RD(u32 &x){scanf("%u",&x);}

void RD(double &x){scanf("%lf",&x);}

void RD(int &x,int &y){scanf("%d%d",&x,&y);}

void RD(u32 &x,u32 &y){scanf("%u%u",&x,&y);}

void RD(double &x,double &y){scanf("%lf%lf",&x,&y);}

void RD(int &x,int &y,int &z){scanf("%d%d%d",&x,&y,&z);}

void RD(int &x,int &y,int &z,int &t){scanf("%d%d%d%d",&x,&y,&z,&t);}

void RD(u32 &x,u32 &y,u32 &z){scanf("%u%u%u",&x,&y,&z);}

void RD(double &x,double &y,double &z){scanf("%lf%lf%lf",&x,&y,&z);}

void RD(char &x){x=getchar();}

void RD(char *s){scanf("%s",s);}

void RD(string &s){cin>>s;}





void PR(int x) {printf("%d\n",x);}

void PR(int x,int y) {printf("%d %d\n",x,y);}

void PR(int x,int y,int z) {printf("%d %d %d\n",x,y,z);}

void PR(i64 x) {printf("%lld\n",x);}

void PR(u32 x) {printf("%u\n",x);}

void PR(double x) {printf("%.5lf\n",x);}

void PR(char x) {printf("%c\n",x);}

void PR(char *x) {printf("%s\n",x);}

void PR(string x) {cout<<x<<endl;}





const i64 inf=((i64)1)<<60;

const int INF=1000000000;

const int N=2005;







int s[N][N],n,a[N];

i64 f[N][N],sum[N];







void DFS(int x,int L,int R)

{

    if(L>=R) return;

    if(x<=s[L][R]) putchar('0'),DFS(x,L,s[L][R]);

    else putchar('1'),DFS(x,s[L][R]+1,R);

}



int main()

{

    Rush(n)

    {

        int i,j,k,L;

        i64 temp;

        FOR1(i,n)

        {

            RD(a[i]);

            sum[i]=sum[i-1]+a[i];

            s[i][i]=i;

            f[i][i]=a[i];

        }

        for(L=2;L<=n;L++) for(i=1;i+L-1<=n;i++)

        {

            j=i+L-1; f[i][j]=inf;

            FOR(k,s[i][j-1],s[i+1][j])

            {

                temp=f[i][k]+f[k+1][j]+sum[j]-sum[i-1];

                if(temp<f[i][j]) f[i][j]=temp,s[i][j]=k;

            }

        }

        FOR1(i,n) DFS(i,1,n),puts("");

    }

    return 0;

}