First occurrence of a digit in a given fraction

• Difficulty Level : Medium
• Last Updated : 14 Apr, 2021

Given three integers a, b and c, find the first occurrence of c in a/b after the decimal point. If it does not exists, print -1.
Examples:

Input : a = 2 b = 3 c = 6
Output : 1
Explanation:
0.666666.. so 6 occurs at first place
of a/b after decimal point

Input : a = 1 b = 4 c = 5
Output : 2
Explanation:
1 / 4 = 0.25 which gives 5's position
to be 2.

A naive approach will be to perform the division and keep the decimal part and iterate and check if the given number exists or not. This will not work well when divisions such as 2/3 is done as it yields 0.666666666, but in programming language it will round it off to 0.666667 so we get a 7 also which does not exists in the original a/b
An efficient approach will be the mathematical one, if we modulate every-time a by b and multiply it with 10 we get the integers after the decimal part every-time. The number of modulations required will be b as it will have a maximum of b integers after decimal point. So, we compare it with c and get our desired value if it is present.
Below is the implementation of the above approach :

C++

 // CPP program to find first occurrence// of c in a/b#include using namespace std; // function to print the first digitint first(int a, int b, int c){    // reduce the number to its mod    a %= b;     // traverse for every decimal places    for (int i = 1; i <= b; i++)    {        // get every fraction places        // when (a*10/b)/c        a = a * 10;                 // check if it is equal to        // the required integer        if (a / b == c)            return i;                 // mod the number        a %= b;    }    return -1;} // driver program to test the above functionint main(){    int a = 1, b = 4, c = 5;    cout << first(a, b, c);    return 0;}

Java

 // Java program to find first occurrence// of c in a/bimport java.util.*;import java.lang.*; public class GfG{    // Function to print the first digit    public static int first(int a, int b, int c)    {        // Reduce the number to its mod        a %= b;         // Traverse for every decimal places        for (int i = 1; i <= b; i++)        {            // Get every fraction places            // when (a*10/b)/c            a = a * 10;                     // Check if it is equal to            // the required integer            if (a / b == c)                return i;                     // Mod the number            a %= b;        }        return -1;    }         // Driver function    public static void main(String argc[]){        int a = 1, b = 4, c = 5;        System.out.println(first(a, b, c));    }     }/* This code is contributed by Sagar Shukla */

Python3

 # Python3 program to find first occurrence# of c in a/b # function to print the first digitdef first( a , b , c ):     # reduce the number to its mod    a %= b         # traverse for every decimal places    for i in range(1, b + 1):         # get every fraction places        # when (a*10/b)/c        a = a * 10         # check if it is equal to        # the required integer        if int(a / b) == c:            return i                 # mod the number        a %= b         return -1 # driver code to test the above functiona = 1b = 4c = 5print(first(a, b, c)) # This code is contributed by "Sharad_Bhardwaj".

C#

 // C# program to find first occurrence// of c in a/busing System; public class GfG{         // Function to print the first digit    public static int first(int a, int b, int c)    {         // Reduce the number to its mod        a %= b;         // Traverse for every decimal places        for (int i = 1; i <= b; i++)        {             // Get every fraction places            // when (a*10/b)/c            a = a * 10;                     // Check if it is equal to            // the required integer            if (a / b == c)                return i;                     // Mod the number            a %= b;        }         return -1;    }         // Driver function    public static void Main() {                 int a = 1, b = 4, c = 5;                 Console.WriteLine(first(a, b, c));    }} /* This code is contributed by vt_m */



Javascript



Output:

2

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