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Ugly Numbers
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[0] := 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[0] = 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
Updated on: 17-Jun-2020
3K+ Views
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