Overview

An ugly number is a number whose prime factors are limited to 2,3 and 5. We have already seen a program where given a number n returns true if it is an ugly number otherwise returns false. Below is the link to that program https://techbyexample.com/program-ugly-number/

In this tutorial, we will write a program where given a number n, find the nth ugly number

Example 1

Input: 5
Output: 5
Reason: First five ugly numbers are 1, 2, 3, 4, 5 hence 5th ugly number is 5

Example 2

Input: 20
Output: 36

The idea is to use dynamic programming here. We will keep track of multiple of 2, 3, and 5. The next ugly number will always be the minimum of these three.

Program

Below is the program for the same

package main

import "fmt"

func nthUglyNumber(n int) int {
	dpUgly := make([]int, n)

	dpUgly[0] = 1

	next_multiple_of_2 := 2
	next_multiple_of_3 := 3
	next_multiple_of_5 := 5

	i2 := 0
	i3 := 0
	i5 := 0

	for i := 1; i < n; i++ {
		nextUglyNumber := minOfThree(next_multiple_of_2, next_multiple_of_3, next_multiple_of_5)
		dpUgly[i] = nextUglyNumber

		if nextUglyNumber == next_multiple_of_2 {
			i2++
			next_multiple_of_2 = 2 * dpUgly[i2]
		}

		if nextUglyNumber == next_multiple_of_3 {
			i3++
			next_multiple_of_3 = 3 * dpUgly[i3]
		}

		if nextUglyNumber == next_multiple_of_5 {
			i5++
			next_multiple_of_5 = 5 * dpUgly[i5]
		}

	}

	return dpUgly[n-1]

}

func minOfThree(a, b, c int) int {
	if a < b && a < c {
		return a
	}

	if b < c {
		return b
	}

	return c
}

func main() {
	output := nthUglyNumber(5)
	fmt.Println(output)

	output = nthUglyNumber(20)
	fmt.Println(output)
}

Output

5
36

Note: Check out our Golang Advanced Tutorial. The tutorials in this series are elaborative and we have tried to cover all concepts with examples. This tutorial is for those who are looking to gain expertise and a solid understanding of golang – Golang Advance Tutorial

Also if you are interested in understanding how all design patterns can be implemented in Golang. If yes, then this post is for you – All Design Patterns Golang

Also, check out our system design tutorial series here – System Design Tutorial Series