Check whether frequency of characters in a string makes Fibonacci Sequence

Given a string with lowercase English alphabets. The task is to check whether the frequency of the characters in the string can be arranged as a Fibonacci series. If yes, print “YES”, otherwise print “NO”.

Note:

• Frequencies can be arranged in any way to form Fibonacci Series.
• The Fibonacci Series starts from 1. That is the series is 1,1,2,3,5,…..

Examples:

Input : str = "abeeedd"
Output : YES
Frequency of 'a' => 1
Frequency of 'b' => 1
Frequency of 'e' => 3
Frequency of 'd' => 2
These frequencies are first 4 terms of 
Fibonacci series => {1, 1, 2, 3}

Input : str = "dzzddz"
Output : NO
Frequencies are not in Fibonacci series

Approach:

• Store the frequencies of each character of the string in a map. Let the size of the map be after storing frequencies.
• Then, make a vector and insert first ‘n’ elements of the Fibonacci series in this vector.
• Then, compare each element of the vector with values of the map. If both elements of vector and values of the map are same, print ‘YES’, otherwise print ‘NO’.

Below is the implementation of the above approach:

C++

// C++ program to check whether frequency of
// characters in a string makes
// Fibonacci Sequence

#include <bits/stdc++.h>
using namespace std;

int main() {
    string s = "abeedddccccc";

    // create a map to store the frequency of each character
    map<char, int> freq;
    for (char c : s) {
        freq++;
    }

    // create an array to store the frequency values
    int f[freq.size()];
    int i = 0;
    for (auto p : freq) {
        f[i] = p.second;
        i++;
    }

    // check if the frequency values form a Fibonacci sequence
    int n = freq.size();
    bool isFibonacci = true;
    sort(f, f + freq.size());
    if(f[0] != 1 || f[1] != 1)
        isFibonacci = false;
    else{
        for (int j = 2; j < n; j++) {
            if (f[j] != f[j-1] + f[j-2]) {
                isFibonacci = false;
                break;
            }
        }
    }

    // print the result
    if (isFibonacci) {
        cout << "YES" << endl;
    } else {
        cout << "NO" << endl;
    }

    return 0;
}

Java

// Java program to check whether frequency of
// characters in a string makes
// Fibonacci Sequence
import java.util.HashMap;
import java.util.Vector;

class GFG
{

    // Function to check if the frequencies
    // are in Fibonacci series
    static String isFibonacci(String s)
    {

        // map to store the
        // frequencies of character
        HashMap<Character,
                Integer> m = new HashMap<>();
        for (int i = 0; i < s.length(); i++)
            m.put(s.charAt(i),
            m.get(s.charAt(i)) == null ? 1 :
            m.get(s.charAt(i)) + 1);

        // Vector to store first n
        // fibonacci numbers
        Vector<Integer> v = new Vector<>();

        // Get the size of the map
        int n = m.size();

        // a and b are first and second terms of
        // fibonacci series
        int a = 1, b = 1;

        int c;
        v.add(a);
        v.add(b);

        // vector v contains elements of
        // fibonacci series
        for (int i = 0; i < n - 2; i++)
        {
            v.add(a + b);
            c = a + b;
            a = b;
            b = c;
        }

        int flag = 1;
        int i = 0;

        // Compare vector elements with values in Map
        for (HashMap.Entry<Character,
                           Integer> entry : m.entrySet())
        {
            if (entry.getValue() != v.elementAt(i))
            {
                flag = 1;
                break;
            }

            i++;
        }

        if (flag == 1)
            return "YES";
        else
            return "NO";
    }

    // Driver Code
    public static void main(String[] args)
    {
        String s = "abeebbbccccc";
        System.out.println(isFibonacci(s));
    }
}

// This code is contributed by
// sanjeev2552

Python3

# Python3 program to check whether the frequency
# of characters in a string make Fibonacci Sequence
from collections import defaultdict

# Function to check if the frequencies
# are in Fibonacci series
def isFibonacci(s):

    # map to store the frequencies of character
    m = defaultdict(lambda:0)

    for i in range(0, len(s)):
        m[s[i]] += 1

    # Vector to store first n fibonacci numbers
    v = []

    # Get the size of the map
    n = len(m)

    # a and b are first and second
    # terms of fibonacci series
    a = b = 1

    v.append(a)
    v.append(b)

    # vector v contains elements of
    # fibonacci series
    for i in range(0, n - 2):
        v.append(a + b)
        c = a + b
        a, b = b, c

    flag, i = 1, 0

    # Compare vector elements with values in Map
    for itr in sorted(m):
        if m[itr] != v[i]:
            flag = 0
            break

        i += 1

    if flag == 1:
        return "YES"
    else:
        return "NO"

# Driver code
if __name__ == "__main__":

    s = "abeebbbccccc"
    print(isFibonacci(s))

# This code is contributed by Rituraj Jain

C#

// C# program to check whether frequency of
// characters in a string makes
// Fibonacci Sequence
using System;
using System.Collections.Generic;

class GFG
{

    // Function to check if the frequencies
    // are in Fibonacci series
    static String isFibonacci(String s)
    {

        // map to store the
        // frequencies of character
        int i = 0;
        Dictionary<int,
                   int> mp = new Dictionary<int,
                                            int>();
        for (i = 0; i < s.Length; i++)
        {
            if(mp.ContainsKey(s[i]))
            {
                var val = mp[s[i]];
                mp.Remove(s[i]);
                mp.Add(s[i], val + 1);
            }
            else
            {
                mp.Add(s[i], 1);
            }
        }

        // List to store first n
        // fibonacci numbers
        List<int> v = new List<int>();

        // Get the size of the map
        int n = mp.Count;

        // a and b are first and second terms of
        // fibonacci series
        int a = 1, b = 1;

        int c;
        v.Add(a);
        v.Add(b);

        // vector v contains elements of
        // fibonacci series
        for (i = 0; i < n - 2; i++)
        {
            v.Add(a + b);
            c = a + b;
            a = b;
            b = c;
        }

        int flag = 1;

        // Compare vector elements with values in Map
        foreach(KeyValuePair<int, int> entry in mp)
        {
            if (entry.Value != v[i])
            {
                flag = 1;
                break;
            }
            i++;
        }

        if (flag == 1)
            return "YES";
        else
            return "NO";
    }

    // Driver Code
    public static void Main(String[] args)
    {
        String s = "abeebbbccccc";
        Console.WriteLine(isFibonacci(s));
    }
}

// This code is contributed by 29AjayKumar

Javascript

<script>

// Javascript program to check whether frequency of
// characters in a string makes
// Fibonacci Sequence

// Function to check if the frequencies
// are in Fibonacci series
function isFibonacci(s)
{
    // map to store the
    // frequencies of character
    var m = new Map();

    for (var i = 0; i < s.length; i++) {

        if(m.has(s[i]))
        {
            m.set(s[i], m.get(s[i]));
        }
        else
        {
            m.set(s[i], 1);
        }
    }

    // Vector to store first n
    // fibonacci numbers
    var v = [];

    // Get the size of the map
    var n = m.length;

    // a and b are first and second terms of
    // fibonacci series
    var a = 1, b = 1;

    var c;
    v.push(a);
    v.push(b);

    // vector v contains elements of fibonacci series
    for (var i = 0; i < n - 2; i++) {
        v.push(a + b);
        c = a + b;
        a = b;
        b = c;
    }

    var flag = 1;
    var i = 0;

    // Compare vector elements with values in Map
    m.forEach((value, key) => {
        if (value != v[i]) {
            flag = 0;
        }
    });

    if (flag == 1)
        return "YES";
    else
        return "NO";
}

// Driver code
var s = "abeeedd";
document.write( isFibonacci(s));

</script>

Output

YES

Complexity Analysis:

• Time Complexity: O(n), where n is the length of the given string.
• Auxiliary Space: O(n)