回溯法——01背包问题

#include <iostream>
#include <cstdio>
#include <algorithm>

using namespace std;

#define MAXN 10

struct Goods_Info
{
	int v;		//价值
	int w;		//重量
	double vw;	//价值重量比
}goods[MAXN];

int n;
int maxValue;
bool solu[MAXN];
bool optimalSolu[MAXN];

bool Cmp(const Goods_Info a, const Goods_Info b)
{
	return a.vw > b.vw;
}

//可装入一部分物品时，取得的最优价值
double Bound(int i, double v, int c)
{
	//以物品的价值重量比递减将物品装入背包
	while (i <= n && goods[i].w <= c)
	{
		v += goods[i].v;
		c -= goods[i].w;
		i++;
	}
	//将背包装满
	if (i <= n)
	{
		v += (goods[i].vw * c);
	}
	return v;
}

void Backtrack(int k, int cv, int rc)
{
	if (k > n)
	{
		if (cv > maxValue)
		{
			maxValue = cv;
			int i;
			for (i = 1; i <= n; i++)
			{
				optimalSolu[i] = solu[i];
			}
		}
	}
	else
	{
		if (goods[k].w <= rc) //当前物品能否装入背包
		{
			solu[k] = true;
			Backtrack(k+1, cv+goods[k].v, rc-goods[k].w);
		}
		if (Bound(k+1, cv, rc) > maxValue) //剩余物品的最优价值是否更优
		{
			solu[k] = false;
			Backtrack(k+1, cv, rc);
		}
	}
}

int main(void)
{
	int c;
	while (scanf("%d%d", &n, &c) != EOF)
	{
		int i;
		for (i = 1; i <= n; i++)
		{
			scanf("%d%d", &goods[i].v, &goods[i].w);
			goods[i].vw = (double)goods[i].v / goods[i].w;
		}

		//将物品按照价值重量比递减排序
		sort(goods+1, goods+n+1, Cmp);

		maxValue = 0;
		Backtrack(1, 0, c);

		printf("%d\n", maxValue); //最优值
		
		/*
		//最优解
		printf("value:");
		for (i = 1; i <= n; i++)
		{
			printf("\t%d", goods[i].v);
		}
		printf("\nweight:");
		for (i = 1; i <= n; i++)
		{
			printf("\t%d", goods[i].w);
		}
		printf("\nstatus:");
		for (i = 1; i <= n; i++)
		{
			printf("\t%d", optimalSolu[i]);
		}
		printf("\n");
		*/
	}
	return 0;
}

/*
5 27
8 3
12 7
10 5
8 4
15 9

5 27
8 8
12 12
10 10
8 8
15 15

5 26
8 8
12 12
10 10
8 8
15 15

5 28
8 8
12 12
10 10
8 8
15 15

5 29
8 8
12 12
10 10
8 8
15 15
*/