hdu 1171 Big Event in HDU 01背包

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本文介绍了一个关于设施分配的问题，即如何将不同价值的设施平均分配给计算机学院和软件学院，确保两者的总价值尽可能接近且前者不低于后者。通过01背包问题的算法思路，实现了最优解的求解。

Big Event in HDU

Problem Description

Nowadays, we all know that Computer College is the biggest department in HDU. But, maybe you don't know that Computer College had ever been split into Computer College and Software College in 2002.
The splitting is absolutely a big event in HDU! At the same time, it is a trouble thing too. All facilities must go halves. First, all facilities are assessed, and two facilities are thought to be same if they have the same value. It is assumed that there is N (0<N<1000) kinds of facilities (different value, different kinds).

Input

Input contains multiple test cases. Each test case starts with a number N (0 < N <= 50 -- the total number of different facilities). The next N lines contain an integer V (0<V<=50 --value of facility) and an integer M (0<M<=100 --corresponding number of the facilities) each. You can assume that all V are different.
A test case starting with a negative integer terminates input and this test case is not to be processed.

Output

For each case, print one line containing two integers A and B which denote the value of Computer College and Software College will get respectively. A and B should be as equal as possible. At the same time, you should guarantee that A is not less than B.

Sample Input

Sample Output

20 10
40 40

题意：输入n组数，每组两个数a,b，a是数的价值，b是数的数量。把总数分为两个，尽量相等，若不相等，前者>=后者。

思路：本质还是01背包，用变量sum记录总数的质量，sum/2 <= 所求的后者数，在sum/2的范围内求最优值。

#include<stdio.h>
#include<string.h>
#define N 300000
int dp[N];
int v[5100];
int  sum ,w;
int max(int a,int b)
{
	if(a > b)
		return a;
	return b;
}
int main()
{
	int n,i,j;
	int a,b;
	int l;	
	while(scanf("%d",&n),n > 0)
	{
		memset(dp,0,sizeof(dp));
		sum = 0;
		l = 1;
		for( i = 1; i <= n; i ++)
		{
			scanf("%d%d",&b,&a);
			sum += b*a;
			while(a--)
			{
				v[l++] = b;
			}
			
		}
		w = sum/2;;
		for( i = 1; i < l; i ++)
		{
			for( j = w; j >= v[i]; j --)
			{
				dp[j] = max(dp[j],dp[j-v[i]]+v[i]);
			}
		}
		printf("%d %d\n",sum- dp[w],dp[w]);
	}
	return 0;
}