HDU 1059 Dividing（多重背包）

Dividing

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 13321 Accepted Submission(s): 3739

Problem 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 describes one collection of marbles to be divided. The lines consist of six non-negative integers n1, n2, ..., 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 colletcion, 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.

 

01背包，完全背包，多重背包 ，模板代码：http://blog.csdn.net/deng_hui_long/article/details/10603015

题意：Marsha and Bill 收集了一些弹珠，每个弹珠的价值，都不一样，要求你写一个程序，是否可以平分这个弹珠。

思路： 这是一个多重背包的问题， 求两个人是否可以平分，我们先要求出它的总价值，如果可以平分，说明的两个人的按价值是一样的，即总价值/2，平分给他们呢两个人。

import java.io.*;
import java.util.*;
/*
 *
 * author : denghuilong 
 * Date   : 2013-8-30
 *
*/
public class Main {
	int n = 6;
	int dp[] = new int[2000000];
	int sum;

	public static void main(String[] args) {
		new Main().work();
	}

	void work() {
		Scanner sc = new Scanner(new BufferedInputStream(System.in));
		int Case = 1;
		while (sc.hasNext()) {

			Node node = new Node();
			Arrays.fill(dp, 0);
			sum = 0;
			for (int i = 1; i <= n; i++) {
				node.num[i] = sc.nextInt();//弹珠的数量
				node.val[i] = i;//弹珠的价值
				sum += (node.num[i] * node.val[i]);//总价值
			}

			if (sum == 0)
				break;

			if ((sum & 1) != 0) {//等价于 sum%2 是否等于0，如果不等于0，说明他们不可以平分
				System.out.println("Collection #" + Case++ + ":");
				System.out.println("Can't be divided.");
				System.out.println();
			} else {
				sum >>= 1;//右一位，表示除以2， 要求平分即：总价值/2；
			
				for (int i = 1; i <= n; i++) {
					multiplePack(node.val[i], node.val[i], node.num[i]);
				}
				System.out.println("Collection #" + Case++ + ":");
				if (dp[sum] != sum)
					System.out.println("Can't be divided.");
				else
					System.out.println("Can be divided.");
				System.out.println();
			}
		}
	}
	//多重背包
	void multiplePack(int cost, int weight, int amount) {
		if (cost * amount >= sum) {// 如果大于一半，数量是无限的，按完全背包处理
			completePack(cost, weight);
		} else {//小于一半按01背包处理
			int k = 1;
			while (k < amount) {
				ZeroOnePack(k * cost, k * weight);
				amount -= k;
				k <<= 1;
			}
			ZeroOnePack(amount * cost, amount * weight);
		}
	}
	//01背包
	void ZeroOnePack(int cost, int weight) {
		for (int i = sum; i >= cost; i--) {
			dp[i] = Math.max(dp[i], dp[i - cost] + weight);
		}
	}
	// 完全背包
	void completePack(int cost, int weight) {
		for (int i = cost; i <= sum; i++) {
			dp[i] = Math.max(dp[i], dp[i - cost] + weight);
		}
	}

	class Node {
		int num[] = new int[n + 1];
		int val[] = new int[n + 1];
	}
}