HDU2069 Coin change HDU 1114 Piggy-Bank HDU1712 ACboy needs your help-优快云博客

本文通过三个实例详细解析了背包问题的不同类型：换零钱问题、求最小方案问题及分组背包问题。每种问题都提供了具体的C++实现代码，帮助读者理解如何运用动态规划解决这些典型问题。

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HDU 2069 Coin Change

换零钱, 计算有多少方案数

#include <stdio.h>
#include <string.h>
#include <algorithm>
using namespace std;
#define N 100010
int dp[N], w[5], v[5], n, m;

int main()
{
    w[0] = 1; w[1] = 5; w[2] = 10; w[3] = 25; w[4] = 50;
    memset(dp, 0, sizeof(dp));
    dp[0] = 1;
    for(int i = 0; i < 5; i++)
		{
			for(int j = w[i]; j <= 7800; j++)
			{
				dp[j] = dp[j] + dp[j - w[i]];
			}
		}
	while(~scanf("%d", &n))
	{
		printf("%d\n", dp[n]);
	}
	return 0;
}

HDU 1114 Piggy-Bank

这个是求最小的方案,而以前做的都是求最大

#include <stdio.h>
#include <string.h>
#include <algorithm>
using namespace std;
#define N 100010
int dp[N], w[N], v[N], n, m;

int main()
{
	int t;
	scanf("%d", &t);
	while(t--)
	{
		int x, y, z;
		scanf("%d %d", &x, &y);
		z = y - x;
		scanf("%d", &n);
		for(int i = 0; i < n; i++)
		{
			scanf("%d %d", &v[i], &w[i]);
		}
		for(int i = 0;i <= z; i++)
				dp[i] = 9999999;
		dp[0] = 0;
		for(int i = 0; i < n; i++)
		{
			for(int j = w[i]; j <= z; j++)
			{
				dp[j] = min(dp[j], dp[j - w[i]] + v[i]);
			}
		}
		if(dp[z] == 9999999 ) printf("This is impossible.\n");
		else printf("The minimum amount of money in the piggy-bank is %d.\n", dp[z]);
	}
	return 0;
}

HDU1712 ACboy needs your help

典型的分组背包,每个course 是一组, 注意三层循环的次序问题

#include <stdio.h>
#include <string.h>
#include <algorithm>
using namespace std;
#define N 200
int dp[N], w[N][N], n, m;

int main()
{
	while(~scanf("%d %d", &n, &m))
	{
		if(m + n == 0) break;
		memset(w, 0, sizeof(w));
		for(int i = 1; i <= n; i++)
		{
			for(int j = 1; j <= m; j++)
				scanf("%d", &w[i][j]);
		}

		memset(dp, 0, sizeof(dp));
		for(int i = 1; i <= n; i++)
		{
			for(int j = m; j >= 0; j--)
			{
				for(int k = 0; k <= j; k++)
					dp[j] = max(dp[j], dp[j - k] + w[i][k]);
					//printf("dp[%d][%d] = %d\n", i, j, dp[j]);
			}
		}
		printf("%d\n", dp[m]);
	}
	return 0;
}

转载于:https://www.cnblogs.com/tenlee/p/4420111.html