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Find length of period in decimal value of 1/n in C++
Suppose we have a number n. We have to find the length of period in decimal value of 1/n. So if the value of n is 7, then 1/7 = 0.142857142857… That part in bold letters are repeating. So here the length of period is 6.
For a number n, there can be n distinct remainders in the output, but the period may not begin from the first remainder as some initial remainders are non-repeating. So we have to make sure that a remainder from period is picked, start from (n+1)th remainder, and start looking for the next occurrence. The distance between (n+1)th remainder and the next occurrence, is the length of the period.
Example
#include<iostream>
using namespace std;
int periodLength(int n) {
int remainder = 1;
int length = 0;
for (int i = 1; i <= n+1; i++)
remainder = (10*remainder) % n;
int d = remainder;
do {
remainder = (10*remainder) % n;
length++;
} while(remainder != d);
return length;
}
int main() {
int n = 7;
cout << "Period length of 1/"<<n<<" is: " << periodLength(n) << endl;
}Output
Period length of 1/7 is: 6
Updated on: 18-Dec-2019
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