# Ugly Numbers

Data StructureDynamic ProgrammingAlgorithms

Ugly numbers are those number whose prime factors are 2, 3 or 5. From 1 to 15, there are 11 ugly numbers 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15. The numbers 7, 11, 13 are not ugly because they are prime. The number 14 is not ugly because in its prime factor the 7 will come.

In this program, we will try to find the nth ugly number.

## Input and Output

Input:
Take the term number. Say it is 10
Output:
The 10th ugly number is 12

## Algorithm

getUglyNumbers(n)

Input: The number of terms.

Output: Find nth Ugly numbers.

Begin
define array named uglyNum of size n
i2 := 0, i3 := 0, i5 := 0
next2mul := 2, next3mul := 3, next5Mul := 5
next := 1
ugluNum := 1

for i := 1 to n, do
next := minimum of next2Mul, next3Mul and next5Mul
uglyNum[i] := next
if next = next2Mul, then
i2 := i2 + 1
next2mul := uglyNum[i2] * 2
if next = next3Mul, then
i3 := i3 + 1
next3mul := uglyNum[i3] * 3
if next = next5Mul, then
i5 := i5 + 1
next5mul := uglyNum[i5] * 5
done
return next
End

## Example

# include<iostream>
using namespace std;

int min(int x, int y, int z) {            //find smallest among three numbers
if(x < y) {
if(x < z)
return x;
else
return z;
}else {
if(y < z)
return y;
else
return z;
}
}

int getUglyNum(int n) {
int uglyNum[n];          // To store ugly numbers
int i2 = 0, i3 = 0, i5 = 0;

//find next multiple as 1*2, 1*3, 1*5

int next2mul = 2;
int next3mul = 3;
int next5mul = 5;
int next = 1;              //initially the ugly number is 1

uglyNum = 1;

for (int i=1; i<n; i++) {
next = min(next2mul, next3mul, next5mul);       //find next ugly number
uglyNum[i] = next;

if (next == next2mul) {
i2++;             //increase iterator of ugly numbers whose factor is 2
next2mul = uglyNum[i2]*2;
}

if (next == next3mul) {
i3++;             //increase iterator of ugly numbers whose factor is 3
next3mul = uglyNum[i3]*3;
}

if (next == next5mul) {
i5++;              //increase iterator of ugly numbers whose factor is 5
next5mul = uglyNum[i5]*5;
}
}
return next;        //the nth ugly number
}

int main() {
int n;
cout << "Enter term: "; cin >> n;
cout << n << "th Ugly number is: " << getUglyNum(n) << endl;
}

## Output

Enter term: 10
10th Ugly number is: 12