题目链接：HDU 1284 钱币兑换问题

钱币兑换问题

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)

Total Submission(s): 5467    Accepted Submission(s): 3123

2934

12553

718831

13137761

思路1：母函数思想，求系数

代码：

#include <iostream>

#include <cstdio>

#include <cstring>

using namespace std;

#define maxn 32770

int n, c1[maxn], c2[maxn];

void Init()

{

    for(int i = 0; i <= maxn; i++)

    {

        c1[i] = 1;

        c2[i] = 0;

    }

    for(int i = 2; i <= 3; i++)

    {

        for(int j = 0; j <= maxn; j++)

            for(int k = 0; k+j <= maxn; k+=i)

                c2[j+k] += c1[j];

        for(int j = 0; j <= maxn; j++)

        {

            c1[j] = c2[j];

            c2[j] = 0;

        }

    }

}

int main()

{

    Init();

    while(~scanf("%d", &n))

        printf("%d\n", c1[n]);

    return 0;

}

思路2：DP，后面的钱能够由前面的钱推出。

代码：

#include <iostream>

#include <cstdio>

using namespace std;

#define maxn 32770

int n, dp[maxn];

void Init()

{

    dp[0] = 1;

    for(int i = 1; i <= 3; i++)

        for(int j = i; j <= maxn; j++)

            dp[j] += dp[j-i];

}

int main()

{

    Init();

    while(~scanf("%d", &n))

        printf("%d\n", dp[n]);

    return 0;

}