Longest sub-sequence of array containing Lucas numbers
Given an array arr[] of N elements, the task is to find the length of the longest sub-sequence in arr[] such that all the elements of the sequence are Lucas Numbers.
Examples:
Input: arr[] = {2, 3, 55, 6, 1, 18}
Output: 4
1, 2, 3 and 18 are the only elements from the Lucas sequence.Input: arr[] = {22, 33, 2, 123}
Output: 2
Approach:
- Find the maximum element in the array.
- Generate Lucas numbers upto to the max and store them in a set.
- Traverse the array arr[] and check if the current element is present in the set.
- If it is present in the set, and increment the count.
Below is the implementation of the above approach:
C++
// C++ implementation of the approach #include <bits/stdc++.h> using namespace std; // Function to return the length of // the longest required sub-sequence int LucasSequence(int arr[], int n) { // Find the maximum element from // the array int max = *max_element(arr, arr+n); // Insert all lucas numbers // below max to the set // a and b are first two elements // of the Lucas sequence unordered_set<int> s; int a = 2, b = 1, c; s.insert(a); s.insert(b); while (b < max) { int c = a + b; a = b; b = c; s.insert(b); } int count = 0; for (int i = 0; i < n; i++) { // If current element is a Lucas // number, increment count auto it = s.find(arr[i]); if (it != s.end()) count++; } // Return the count return count; } // Driver code int main() { int arr[] = { 7, 11, 22, 4, 2, 1, 8, 9 }; int n = sizeof(arr) / sizeof(arr[0]); cout << LucasSequence(arr, n); return 0; } |
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Java
// Java implementation of the approach import java.util.*; class GFG { // Function to return the length of // the longest required sub-sequence static int LucasSequence(int[] arr, int n) { // Find the maximum element from // the array int max = Arrays.stream(arr).max().getAsInt(); int counter = 0; // Insert all lucas numbers // below max to the set // a and b are first two elements // of the Lucas sequence HashSet<Integer> s = new HashSet<>(); int a = 2, b = 1; s.add(a); s.add(b); while (b < max) { int c = a + b; a = b; b = c; s.add(b); } for (int i = 0; i < n; i++) { // If current element is a Lucas // number, increment count if (s.contains(arr[i])) { counter++; } } // Return the count return counter; } // Driver code public static void main(String[] args) { int[] arr = {7, 11, 22, 4, 2, 1, 8, 9}; int n = arr.length; System.out.println(LucasSequence(arr, n)); } } // This code has been contributed by 29AjayKumar |
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Python3
# Python 3 implementation of the approach # Function to return the length of # the longest required sub-sequence def LucasSequence(arr, n): # Find the maximum element from # the array max = arr[0] for i in range(len(arr)): if(arr[i] > max): max = arr[i] # Insert all lucas numbers below max # to the set a and b are first two # elements of the Lucas sequence s = set() a = 2 b = 1 s.add(a) s.add(b) while (b < max): c = a + b a = b b = c s.add(b) count = 0 for i in range(n): # If current element is a Lucas # number, increment count if(arr[i] in s): count += 1 # Return the count return count # Driver code if __name__ == '__main__': arr = [7, 11, 22, 4, 2, 1, 8, 9] n = len(arr) print(LucasSequence(arr, n)) # This code is contributed by # Surendra_Gangwar |
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C#
// C# implementation of the approach using System; using System.Collections.Generic; using System.Linq; class GFG { // Function to return the length of // the longest required sub-sequence static int LucasSequence(int []arr, int n) { // Find the maximum element from // the array int max = arr.Max(); int counter = 0; // Insert all lucas numbers // below max to the set // a and b are first two elements // of the Lucas sequence HashSet<int> s = new HashSet<int>() ; int a = 2, b = 1 ; s.Add(a); s.Add(b); while (b < max) { int c = a + b; a = b; b = c; s.Add(b); } for (int i = 0; i < n; i++) { // If current element is a Lucas // number, increment count if (s.Contains(arr[i])) counter++; } // Return the count return counter; } // Driver code static public void Main() { int []arr = { 7, 11, 22, 4, 2, 1, 8, 9 }; int n = arr.Length ; Console.WriteLine(LucasSequence(arr, n)) ; } } // This code is contributed by Ryuga |
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Output:
5
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