A1068 Find More Coins （30 分）01背包问题

最新推荐文章于 2020-03-24 01:49:38 发布

原创最新推荐文章于 2020-03-24 01:49:38 发布 · 219 阅读

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本文介绍了一个使用动态规划解决背包问题的C++程序实现。通过排序和状态转移方程，算法能够在多项式时间内找到最大价值的物品组合。文章详细展示了如何通过回溯选择的物品来输出解决方案。

#include<cstdio>
#include<algorithm>
using namespace std;
const int maxn = 10010,maxv=110;
int w[maxn], dp[maxv] = { 0 };
bool choice[maxn][maxv] = { 0 }, flag[maxn] = { 0 };
bool cmp(int a, int b){ return a > b;}
int n, m;
int main()
{
	scanf("%d%d", &n, &m);
	for (int i = 1; i <= n; i++) scanf("%d", &w[i]);
	sort(w+1, w + n+1, cmp);//注意一下范围
	for (int i = 1; i <= n; i++)
	{
		for (int v = m; v >= w[i]; v--)
		{
			if (dp[v] <= dp[v - w[i]] + w[i])
			{
				dp[v] = dp[v - w[i]] + w[i];
				choice[i][v] = 1;
			}
			else choice[i][v] = 0;
		}
	}
	if (dp[m] != m)
	{
		printf("No Solution");
		return 0;
	}
	int v = m,num=0;
	for (int i = n; i >= 0; i--)
	{
		if (choice[i][v] == 1)
		{
			flag[i] = 1;
			v -= w[i];
			num++;
		}
		else flag[i] = 0;
	}
	for (int i = n; i >= 1; i--)
	{
		if (flag[i] == 1)
		{
			printf("%d", w[i]);
			num--;
			if (num != 0) printf(" ");
		}
	}
	return 0;
}