Given a string ‘str’ containing lowercase English alphabets, the task is to find whether the frequencies of the characters of the string are in Lucas sequence or not. You are free to arrange the frequency numbers in any way, in order to form the Lucas sequence. If possible then print YES otherwise NO. Lucas Sequence.
Note: All the frequencies must be used to check if they are in Lucas Sequence.
Examples:
Input: str = “gggeek”
Output: YES frequency of ‘g’ = 3 frequency of ‘e’ = 2 frequency of ‘k’ = 1 These frequency can be arranged to form first 3 terms of Lucas sequence, {2, 1, 3}.Input: str = “neveropen”
Output: NO
Approach:
- Store the frequency of each character in a vector using map STL. Sort the vector afterwards.
- Change the first and second element of first vector to ‘2’ and ‘1’ respectively, since Lucas sequence has ‘2’ and ‘1’ as first two numbers. However, change must only be made if ‘1’ and ‘2’ are present in the vector. If it is not present, then the frequencies can never be in Lucas sequence and output NO.
- Then, make another vector. Let the size of first vector be n.
- Insert first ‘n’ Lucas numbers in the 2nd vector.
- Then, compare each element in both vectors. If both vectors are same, output ‘YES’, otherwise output ‘NO’.
Below is the implementation of the above approach:
C++
// C++ implementation of// the approach#include <bits/stdc++.h>using namespace std;// function that checks// if the frequencies// are in Lucas sequence.string lucas_sequence(string s, int n){ // map is used to store // character frequencies map<char, int> m; for (int i = 0; i < n; i++) { if (m.find(s[i]) == m.end()) m[s[i]] = 1; else m[s[i]]++; } vector<int> v1, v2; map<char, int>::iterator it; // frequencies are extracted from // map and stored in vector v1 for (it = m.begin(); it != m.end(); it++) v1.push_back((*it).second); // vector v1 elements are sorted, // but first and second element are // changed to '2' and '1' respectively, // only if '1' and '2' are present in the vector. sort(v1.begin(), v1.end()); if (v1[0] == 1 && v1[1] == 2) { v1[0] = 2; v1[1] = 1; } else return "NO"; // a and b are first and // second terms of // Lucas sequence int a = 2, b = 1; int c; v2.push_back(a); v2.push_back(b); // v2 contains Lucas sequence for (int i = 0; i < v1.size() - 2; i++) { v2.push_back(a + b); c = a + b; a = b; b = c; } int flag = 1; // both vectors are compared for (int i = 0; i < v1.size(); i++) { if (v1[i] != v2[i]) { flag = 0; break; } } if (flag == 1) return "YES"; else return "NO";}// Driver codeint main(){ string s = "oooeeeeqkk"; int n = s.length(); cout << lucas_sequence(s, n); return 0;} |
Java
// Java implementation of the approach import java.util.Collections;import java.util.HashMap;import java.util.Vector;class GFG { // function that checks // if the frequencies // are in Lucas sequence. static String lucas_sequence(String s, int n) { // map is used to store // character frequencies HashMap<Character, Integer> m = new HashMap<>(); for (int i = 0; i < n; i++) m.put(s.charAt(i), m.get(s.charAt(i)) == null ? 1 : m.get(s.charAt(i)) + 1); Vector<Integer> v1 = new Vector<>(); Vector<Integer> v2 = new Vector<>(); // frequencies are extracted from // map and stored in vector v1 for (HashMap.Entry<Character, Integer> entry : m.entrySet()) v1.add(entry.getValue()); // vector v1 elements are sorted, // but first and second element are // changed to '2' and '1' respectively, // only if '1' and '2' are present in the vector. Collections.sort(v1); if (v1.elementAt(0) == 1 && v1.elementAt(1) == 2) { v1.set(0, 2); v1.set(1, 1); } else return "NO"; // a and b are first and // second terms of // Lucas sequence int a = 2, b = 1; int c; v2.add(a); v2.add(b); // v2 contains Lucas sequence for (int i = 0; i < v1.size() - 2; i++) { v2.add(a + b); c = a + b; a = b; b = c; } int flag = 1; // both vectors are compared for (int i = 0; i < v1.size(); i++) { if (v1.elementAt(i) != v2.elementAt(i)) { flag = 0; break; } } if (flag == 1) return "YES"; else return "NO"; } // Driver Code public static void main(String[] args) { String s = "oooeeeeqkk"; int n = s.length(); System.out.println(lucas_sequence(s, n)); }}// This code is contributed by// sanjeev2552 |
Python3
# Python3 implementation of the approach from collections import defaultdict# Function that checks if the # frequencies are in Lucas sequence. def lucas_sequence(s, n): # map is used to store # character frequencies m = defaultdict(lambda:0) for i in range(0, n): m[s[i]] += 1 v1, v2 = [], [] # frequencies are extracted from # map and stored in vector v1 for it in m: v1.append(m[it]) # vector v1 elements are sorted, but # first and second element are changed # to '2' and '1' respectively, only if # '1' and '2' are present in the vector. v1.sort() if v1[0] == 1 and v1[1] == 2: v1[0], v1[1] = 2, 1 else: return "NO" # a and b are first and second terms # of Lucas sequence a, b = 2, 1 v2.append(a) v2.append(b) # v2 contains Lucas sequence for i in range(0, len(v1) - 2): v2.append(a + b) a, b = b, a + b flag = 1 # both vectors are compared for i in range(0, len(v1)): if v1[i] != v2[i]: flag = 0 break if flag == 1: return "YES" else: return "NO"# Driver code if __name__ == "__main__": s = "oooeeeeqkk" n = len(s) print(lucas_sequence(s, n)) # This code is contributed by Rituraj Jain |
C#
// C# implementation of the approachusing System;using System.Collections.Generic; class GFG { // function that checks // if the frequencies // are in Lucas sequence. static String lucas_sequence(String s, int n) { // map is used to store // character frequencies Dictionary<char, int> m = new Dictionary<char, int>(); for (int i = 0; i < n; i++) { if(m.ContainsKey(s[i])) { m[s[i]] = m[s[i]] + 1; } else { m.Add(s[i], 1); } } List<int> v1 = new List<int>(); List<int> v2 = new List<int>(); // frequencies are extracted from // map and stored in vector v1 foreach(KeyValuePair<char, int> entry in m) v1.Add(entry.Value); // vector v1 elements are sorted, // but first and second element are // changed to '2' and '1' respectively, // only if '1' and '2' are present in the vector. v1.Sort(); if (v1[0] == 1 && v1[1] == 2) { v1[0] = 2; v1[1] = 1; } else return "NO"; // a and b are first and // second terms of // Lucas sequence int a = 2, b = 1; int c; v2.Add(a); v2.Add(b); // v2 contains Lucas sequence for (int i = 0; i < v1.Count - 2; i++) { v2.Add(a + b); c = a + b; a = b; b = c; } int flag = 1; // both vectors are compared for (int i = 0; i < v1.Count; i++) { if (v1[i] != v2[i]) { flag = 0; break; } } if (flag == 1) return "YES"; else return "NO"; } // Driver Code public static void Main(String[] args) { String s = "oooeeeeqkk"; int n = s.Length; Console.WriteLine(lucas_sequence(s, n)); }}// This code is contributed by Rajput-Ji |
Javascript
function lucasSequence(s, n) { let m = new Map(); for (let i = 0; i < n; i++) { if (!m.has(s[i])) { m.set(s[i], 1); } else { m.set(s[i], m.get(s[i]) + 1); } } let v1 = [], v2 = []; for (let [key, value] of m) { v1.push(value); } v1.sort(); if (v1[0] === 1 && v1[1] === 2) { v1[0] = 2; v1[1] = 1; } else { return "NO"; } let a = 2, b = 1, c; v2.push(a); v2.push(b); for (let i = 0; i < v1.length - 2; i++) { v2.push(a + b); c = a + b; a = b; b = c; } let flag = 1; for (let i = 0; i < v1.length; i++) { if (v1[i] !== v2[i]) { flag = 0; break; } } return flag === 1 ? "YES" : "NO";}let s = "oooeeeeqkk";let n = s.length;console.log(lucasSequence(s, n)); |
Output
YES
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