POJ1014Dividing[多重背包可行性]-优快云博客

本文介绍了一个关于公平分配问题的经典算法实现案例。问题的核心是将一组具有不同价值的物品（如不同大小或美观程度的弹珠）分成两份，使得两份的价值相等。通过两种不同的算法实现方式，探讨了如何有效地解决这一问题，并提供了完整的代码实现。

Dividing

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 68769		Accepted: 17955

Description

Marsha and Bill own a collection of marbles. They want to split the collection among themselves so that both receive an equal share of the marbles. This would be easy if all the marbles had the same value, because then they could just split the collection in half. But unfortunately, some of the marbles are larger, or more beautiful than others. So, Marsha and Bill start by assigning a value, a natural number between one and six, to each marble. Now they want to divide the marbles so that each of them gets the same total value. Unfortunately, they realize that it might be impossible to divide the marbles in this way (even if the total value of all marbles is even). For example, if there are one marble of value 1, one of value 3 and two of value 4, then they cannot be split into sets of equal value. So, they ask you to write a program that checks whether there is a fair partition of the marbles.

Input

Each line in the input file describes one collection of marbles to be divided. The lines contain six non-negative integers n1 , . . . , n6 , where ni is the number of marbles of value i. So, the example from above would be described by the input-line "1 0 1 2 0 0". The maximum total number of marbles will be 20000.
The last line of the input file will be "0 0 0 0 0 0"; do not process this line.

Output

For each collection, output "Collection #k:", where k is the number of the test case, and then either "Can be divided." or "Can't be divided.".
Output a blank line after each test case.

Sample Input

1 0 1 2 0 0 
1 0 0 0 1 1 
0 0 0 0 0 0

Sample Output

Collection #1:
Can't be divided.

Collection #2:
Can be divided.

Source

Mid-Central European Regional Contest 1999

裸题

回顾一下两种做法

然而O(nv)反而被二进制拆分虐了

//
//  main.cpp
//  poj1014
//
//  Created by Candy on 9/21/16.
//  Copyright © 2016 Candy. All rights reserved.
//

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int N=2e4*6+5;
int read(){
    char c=getchar();int x=0,f=1;
    while(c<'0'||c>'9'){if(c=='-')f=-1; c=getchar();}
    while(c>='0'&&c<='9'){x=x*10+c-'0'; c=getchar();}
    return x*f;
}
int n[10],sum=0,cnt=0;
int f[N];
inline void zp(int v){
    for(int i=sum;i>=v;i--) f[i]|=f[i-v];
}
inline void cp(int v){
    for(int i=v;i<=sum;i++) f[i]|=f[i-v];
}
void mp(int v,int c){
    if(c*v>sum) {cp(v);return;}
    int k=1;
    while(k<c){
        zp(k*v);
        c-=k;
        k*=2;
    }
    zp(c*v);
}
int main(int argc, const char * argv[]) {
    while(true){
        ++cnt; sum=0; memset(f,0,sizeof(f)); f[0]=1;
        int flag=1;
        for(int i=1;i<=6;i++) {n[i]=read();sum+=i*n[i];if(n[i]) flag=0;}
        if(flag) break;
        if(sum%2) {
            printf("Collection #%d:\nCan't be divided.\n\n",cnt);
            continue;
        }
        sum/=2;
        for(int i=1;i<=6;i++) mp(i,n[i]);
        if(!f[sum]) printf("Collection #%d:\nCan't be divided.\n\n",cnt);
        else printf("Collection #%d:\nCan be divided.\n\n",cnt);
    }
    
    return 0;
}

//
//  main.cpp
//  poj1014
//
//  Created by Candy on 9/21/16.
//  Copyright © 2016 Candy. All rights reserved.
//

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int N=2e4*6+5;
int read(){
    char c=getchar();int x=0,f=1;
    while(c<'0'||c>'9'){if(c=='-')f=-1; c=getchar();}
    while(c>='0'&&c<='9'){x=x*10+c-'0'; c=getchar();}
    return x*f;
}
int n[10],v[10],sum=0,cnt=0;
int f[10][N];
void mpAble(){
    memset(f,-1,sizeof(f));
    f[0][0]=0;
    for(int i=1;i<=6;i++){
        for(int j=0;j<=sum;j++){
            if(f[i-1][j]>=0) f[i][j]=n[i];
            else f[i][j]=-1;
        }
        for(int j=v[i];j<=sum;j++)
            if(f[i][j-v[i]]>0) f[i][j]=max(f[i][j],f[i][j-v[i]]-1);
    }
}
int main(int argc, const char * argv[]) {
    while(true){
        ++cnt; sum=0; memset(f,0,sizeof(f));
        int flag=1;
        for(int i=1;i<=6;i++){
            n[i]=read();v[i]=i;sum+=i*n[i];
            if(n[i]) flag=0;
        }
        if(flag) break;
        if(sum%2) {
            printf("Collection #%d:\nCan't be divided.\n\n",cnt);
            continue;
        }
        sum/=2;
        mpAble();
        if(f[6][sum]==-1) printf("Collection #%d:\nCan't be divided.\n\n",cnt);
        else printf("Collection #%d:\nCan be divided.\n\n",cnt);
    }
    
    return 0;
}