Ugly Numbers

Dynamic Programming

#include <iostream>

using namespace std;

unsigned int min(unsigned int a, unsigned int b, unsigned int c)
{
	if(a <= b)
    {
		if(a <= c)
		{
			return a;
		}      
		else
		{
			return c;
		}        
    }
	else
	{
		if (b <= c)
		{
			return b;
		}
		else
		{
			return c;
		}
	}
}

unsigned int getNthUglyNo(unsigned int n)
{
    unsigned int *ugly = new unsigned int [n];
    unsigned int i2 = 0, i3 = 0, i5 = 0;
    unsigned int i;
    unsigned int next_multiple_of_2 = 2;
    unsigned int next_multiple_of_3 = 3;
    unsigned int next_multiple_of_5 = 5;
    unsigned int next_ugly_no = 1;

    *(ugly+0) = 1; 
    
	for(i=1; i<n; i++)
    {	
		next_ugly_no = min(next_multiple_of_2, next_multiple_of_3, next_multiple_of_5);       
		*(ugly+i) = next_ugly_no;                    
      
		if(next_ugly_no == next_multiple_of_2)       
		{          
			i2 = i2+1;                  
			next_multiple_of_2 = *(ugly+i2)*2;      
		}
      
		if(next_ugly_no == next_multiple_of_3)      
		{         
			i3 = i3+1;           
			next_multiple_of_3 = *(ugly+i3)*3;       
		}   

		if(next_ugly_no == next_multiple_of_5)       
		{          
			i5 = i5+1;           
			next_multiple_of_5 = *(ugly+i5)*5;      
		}    
	}   

	return next_ugly_no;
}

int main()
{
	unsigned int n;
	cin>>n;
	unsigned int no = getNthUglyNo(n);
    printf("%dth ugly no. is %d\n", n, no);

    system("pause");
    return 0;
}

Time Complexity: O(n)

Storage Complexity:O(n)