UVA 136 Ugly Numbers

最新推荐文章于 2020-07-03 17:20:48 发布

原创最新推荐文章于 2020-07-03 17:20:48 发布 · 354 阅读

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本文介绍了一个程序，用于找到并打印出第1500个丑数，即只包含质因数2、3或5的自然数。通过使用贪心算法，程序高效地生成了所需的丑数序列。

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Ugly numbers are numbers whose only prime factors are 2, 3 or 5. The sequence

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, ...

shows the first 11 ugly numbers. By convention, 1 is included.

Write a program to find and print the 1500'th ugly number.

Input and Output

There is no input to this program. Output should consist of a single line as shown below, with <number> replaced by the number computed.

Sample output

The 1500'th ugly number is <number>.

#include<iostream>
#include<cstdio>
using namespace std;
int ugly[1506];
int getmin(int a,int b,int c)//找出三个数中最小的 
{
    if(a<=b)
    {
        if(a<=c) return a;
        else return c;
    }
    else
    {
        if(b<=c) return b;
        else return c;
    }
}


int find_ugly(int n)
{
    int i2=1,i3=1,i5=1;//设定三个游标因子 
    ugly[1]=1; 
    int i=2;
    int min;
    while(i<=n)
    {
        min=getmin(ugly[i2]*2,ugly[i3]*3,ugly[i5]*5);
        ugly[i]=min;
        //如果因子被用过，那么游标就加一，确保不重不漏 
        if(min==ugly[i2]*2) i2++; 
        if(min==ugly[i3]*3) i3++;
        if(min==ugly[i5]*5) i5++;  
        i++;
    }
    return ugly[n];
}


int main()
{
	int n;
	while(cin>>n)
	{
		cout<<find_ugly(n)<<endl;
	}
    return 0;
}