FINDING GCD OF ARRAY IN O(logn)

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 Prologue

    Actually i was solving the codechef contest questions,then i came to a logic that required to calculate the gcd of array in order to solve that question,but i applied algorithm for gcd which had O(n2) time complexity and the result was TIME LIMIT EXCEEDED.Then I came across following algo which has O(nlogn)  which solved the problem.

    Basic logic was as follows =>

  • gcd(a,b,c) = gcd(a,gcd(b,c)) | gcd(gcd(a,b),c) | gcd(b,gcd(a,c))
  • gcd(a,b,c,d) = gcd(a,gcd(b,c,d)) | gcd(b,gcd(a,c,d)) & so on ....
  • and so on .....
    So we will apply following core code =>

  1. finalGcd = arr[0]
  2. for i in [1,n-1]:
    1. finalGcd = gcd(finalGcd,arr[i]]

CODE 

#include<stdio.h>
#include<stdlib.h>

int gcd(int a,int b){
    if(a == 0){
        return b;
    }
    return gcd(b%a,a);
}

int findGcd(int* arr,int n){
    int result = arr[0];
    for(int i = 1 ; i < n ; i++){
        result = gcd(arr[i],result);
        if(result == 1){
            return 1;
        }
    }
    return result;
}

int main(){
    int sampleArr[] = {1,2,3,4,5,6,7,8,9,10};
    int n = sizeof(sampleArr)/sizeof(int);
    printf("%d\n",n);
    return 0;
}

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