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Longest sub-sequence with maximum GCD

 3 years ago
source link: https://www.geeksforgeeks.org/longest-sub-sequence-with-maximum-gcd/
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Longest sub-sequence with maximum GCD
  • Last Updated : 06 Nov, 2019

Given an array arr[] of length N, the task is to find the length of the longest sub-sequence with maximum possible GCD.

Examples:

Input: arr[] = {2, 1, 2}
Output: 2
{2}, {2} and {2, 2} are the subsequences
with the maximum possible GCD.

Input: arr[] = {1, 2, 3}
Output: 1
{3} is the required subsequence.

Approach: The maximum possible GCD from the array will be equal to the value of the largest element in the array. Now, to maximize the length of the resulting subsequence, find the number of elements with a value equal to this largest value in the array and the count of these elements is the required answer.

Below is the implementation of the above approach:

  • Python3

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// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
// Function to return the length
// of the largest subsequence with
// maximum possible GCD
int maxLen(int* arr, int n)
{
// Maximum value from the array
int max_val = *max_element(arr, arr + n);
// To store the frequency of the
// maximum element in the array
int freq = 0;
for (int i = 0; i < n; i++) {
// If current element is equal
// to the maximum element
if (arr[i] == max_val)
freq++;
}
return freq;
}
// Driver code
int main()
{
int arr[] = { 3, 2, 2, 3, 3, 3 };
int n = sizeof(arr) / sizeof(int);
cout << maxLen(arr, n);
return 0;
}
Output:
4

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