Coin Change 动态规划

最新推荐文章于 2021-03-07 14:36:57 发布

原创最新推荐文章于 2021-03-07 14:36:57 发布 · 528 阅读

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本文介绍了一种使用动态规划解决硬币找零问题的算法，旨在找出给定金额下所有可能的找零组合数。通过实例说明了算法的运行过程，并提供了一个能够处理高达7489美分的C++程序代码。

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Suppose there are 5 types of coins: 50-cent, 25-cent, 10-cent, 5-cent, and 1-cent. We want to make
changes with these coins for a given amount of money.
For example, if we have 11 cents, then we can make changes with one 10-cent coin and one 1-cent
coin, two 5-cent coins and one 1-cent coin, one 5-cent coin and six 1-cent coins, or eleven 1-cent coins.
So there are four ways of making changes for 11 cents with the above coins. Note that we count that
there is one way of making change for zero cent.
Write a program to find the total number of different ways of making changes for any amount of
money in cents. Your program should be able to handle up to 7489 cents.
Input
The input file contains any number of lines, each one consisting of a number for the amount of money
in cents.
Output
For each input line, output a line containing the number of different ways of making changes with the
above 5 types of coins.
Sample Input
11
26
Sample Output
4
13

代码：

#include<bits/stdc++.h>
using namespace std;
long long dp[8100];
int main()
{
	int aa[6]={0,1,5,10,25,50};
	memset(dp,0,sizeof(dp));
		dp[0]=1;
		for(int i=1;i<=5;i++){
			for(int j=aa[i];j<8000;j++){
				dp[j]+=dp[j-aa[i]];
			}
		}
	int n;
	while(cin>>n){
		printf("%lld\n",dp[n]);
	}
	
	return 0;
}