Given a numeric string S representing a large number, the task is to form a Fibonacci Sequence of at least length 3 from the given string. If such a split is not possible, print -1.
Examples:
Input: S = “5712”
Output: 5 7 12
Explanation:
Since 5 + 7 = 12, the splits {5}, {7}, {12} forms a Fibonacci sequence.Input: S = “11235813″
Output: 1 1 2 3 5 8 13
Approach:
To solve the problem, the idea is to use Backtracking to find a sequence that follows the conditions of the Fibonacci Sequence.
Follow the steps below to solve the problem:
- Initialize a vector seq[] to store the Fibonacci sequence.
- Initialize a variable pos which points to the current index of the string S, initially 0.
- Iterate over the indices [pos, length – 1]:
- Add the number S[pos: i] to the Fibonacci sequence seq if the length of seq is less than 2 or the current number is equal to the sum of the last two numbers of seq. Recur for the index i + 1 and proceed.
- If the last added number S[pos: i] does not form a Fibonacci sequence and returns false after recursion, then remove it from the seq.
- Otherwise, end the loop and return true as the Fibonacci sequence is formed.
- If pos exceeds the length of S, then:
- If the length of the sequence seq is greater than or equal to 3, then a Fibonacci sequence is found, hence return true.
- Otherwise, the Fibonacci sequence is not possible and hence returns false.
- Finally, if the length of seq is greater than or equal to 3, then print the numbers in seq as the required Fibonacci sequence or, otherwise print -1.
Below is the illustration of the recursive structure where only one branch is extended to get the result:
Below is the implementation of the above approach:
C++
// C++ program of the above approach#include <bits/stdc++.h>using namespace std;#define LL long long// Function that returns true if// Fibonacci sequence is foundbool splitIntoFibonacciHelper(int pos, string S, vector<int>& seq){ // Base condition: // If pos is equal to length of S // and seq length is greater than 3 if (pos == S.length() and (seq.size() >= 3)) { // Return true return true; } // Stores current number LL num = 0; for (int i = pos; i < S.length(); i++) { // Add current digit to num num = num * 10 + (S[i] - '0'); // Avoid integer overflow if (num > INT_MAX) break; // Avoid leading zeros if (S[pos] == '0' and i > pos) break; // If current number is greater // than last two number of seq if (seq.size() > 2 and (num > ((LL)seq.back() + (LL)seq[seq.size() - 2]))) break; // If seq length is less // 2 or current number is // is equal to the last // two of the seq if (seq.size() < 2 or (num == ((LL)seq.back() + (LL)seq[seq.size() - 2]))) { // Add to the seq seq.push_back(num); // Recur for i+1 if (splitIntoFibonacciHelper(i + 1, S, seq)) return true; // Remove last added number seq.pop_back(); } } // If no sequence is found return false;}// Function that prints the Fibonacci// sequence from the split of string Svoid splitIntoFibonacci(string S){ // Initialize a vector to // store the sequence vector<int> seq; // Call helper function splitIntoFibonacciHelper(0, S, seq); // If sequence length is // greater than 3 if (seq.size() >= 3) { // Print the sequence for (int i : seq) cout << i << " "; } // If no sequence is found else { // Print -1 cout << -1; }}// Driver Codeint main(){ // Given String string S = "11235813"; // Function Call splitIntoFibonacci(S); return 0;} |
Java
// Java program of the above approach import java.util.*;class GFG{// Function that returns true if// Fibonacci sequence is foundstatic boolean splitIntoFibonacciHelper(int pos, String S, ArrayList<Long> seq){ // Base condition: // If pos is equal to length of S // and seq length is greater than 3 if (pos == S.length() && (seq.size() >= 3)) { // Return true return true; } // Stores current number long num = 0; for(int i = pos; i < S.length(); i++) { // Add current digit to num num = num * 10 + (S.charAt(i) - '0'); // Avoid integer overflow if (num > Integer.MAX_VALUE) break; // Avoid leading zeros if (S.charAt(pos) == '0' && i > pos) break; // If current number is greater // than last two number of seq if (seq.size() > 2 && (num > ((long)seq.get(seq.size() - 1) + (long)seq.get(seq.size() - 2)))) break; // If seq length is less // 2 or current number is // is equal to the last // two of the seq if (seq.size() < 2 || (num == ((long)seq.get(seq.size() - 1) + (long)seq.get(seq.size() - 2)))) { // Add to the seq seq.add(num); // Recur for i+1 if (splitIntoFibonacciHelper(i + 1, S, seq)) return true; // Remove last added number seq.remove(seq.size() - 1); } } // If no sequence is found return false;}// Function that prints the Fibonacci// sequence from the split of string Sstatic void splitIntoFibonacci(String S){ // Initialize a vector to // store the sequence ArrayList<Long> seq = new ArrayList<>(); // Call helper function splitIntoFibonacciHelper(0, S, seq); // If sequence length is // greater than 3 if (seq.size() >= 3) { // Print the sequence for (int i = 0; i < seq.size(); i++) System.out.print(seq.get(i) + " "); } // If no sequence is found else { // Print -1 System.out.print("-1"); }}// Driver codepublic static void main(String[] args){ // Given String String S = "11235813"; // Function Call splitIntoFibonacci(S);}}// This code is contributed by offbeat |
Python3
# Python3 program of the above approachimport sys# Function that returns true if# Fibonacci sequence is founddef splitIntoFibonacciHelper(pos, S, seq): # Base condition: # If pos is equal to length of S # and seq length is greater than 3 if (pos == len(S) and (len(seq) >= 3)): # Return true return True # Stores current number num = 0 for i in range(pos, len(S)): # Add current digit to num num = num * 10 + (ord(S[i]) - ord('0')) # Avoid integer overflow if (num > sys.maxsize): break # Avoid leading zeros if (ord(S[pos]) == ord('0') and i > pos): break # If current number is greater # than last two number of seq if (len(seq) > 2 and (num > (seq[-1] + seq[len(seq) - 2]))): break # If seq length is less # 2 or current number is # is equal to the last # two of the seq if (len(seq) < 2 or (num == (seq[-1] + seq[len(seq) - 2]))): # Add to the seq seq.append(num) # Recur for i+1 if (splitIntoFibonacciHelper( i + 1, S, seq)): return True # Remove last added number seq.pop() # If no sequence is found return False# Function that prints the Fibonacci# sequence from the split of string Sdef splitIntoFibonacci(S): # Initialize a vector to # store the sequence seq = [] # Call helper function splitIntoFibonacciHelper(0, S, seq) # If sequence length is # greater than 3 if (len(seq) >= 3): # Print the sequence for i in seq: print(i, end = ' ') # If no sequence is found else: # Print -1 print(-1, end = '') # Driver Codeif __name__=='__main__': # Given String S = "11235813" # Function Call splitIntoFibonacci(S)# This code is contributed by pratham76 |
C#
// C# program of the above approach using System;using System.Collections; using System.Collections.Generic; class GFG{ // Function that returns true if// Fibonacci sequence is foundstatic bool splitIntoFibonacciHelper(int pos, string S, ArrayList seq){ // Base condition: // If pos is equal to length of S // and seq length is greater than 3 if (pos == S.Length && (seq.Count >= 3)) { // Return true return true; } // Stores current number long num = 0; for(int i = pos; i < S.Length; i++) { // Add current digit to num num = num * 10 + (S[i] - '0'); // Avoid integer overflow if (num > Int64.MaxValue) break; // Avoid leading zeros if (S[pos] == '0' && i > pos) break; // If current number is greater // than last two number of seq if (seq.Count> 2 && (num > ((long)seq[seq.Count - 1] + (long)seq[seq.Count - 2]))) break; // If seq length is less // 2 or current number is // is equal to the last // two of the seq if (seq.Count < 2 || (num == ((long)seq[seq.Count - 1] + (long)seq[seq.Count - 2]))) { // Add to the seq seq.Add(num); // Recur for i+1 if (splitIntoFibonacciHelper(i + 1, S, seq)) return true; // Remove last added number seq.Remove(seq.Count - 1); } } // If no sequence is found return false;}// Function that prints the Fibonacci// sequence from the split of string Sstatic void splitIntoFibonacci(string S){ // Initialize a vector to // store the sequence ArrayList seq = new ArrayList(); // Call helper function splitIntoFibonacciHelper(0, S, seq); // If sequence length is // greater than 3 if (seq.Count >= 3) { // Print the sequence for(int i = 0; i < seq.Count; i++) Console.Write(seq[i] + " "); } // If no sequence is found else { // Print -1 Console.Write("-1"); }}// Driver Codepublic static void Main(string[] args){ // Given String string S = "11235813"; // Function call splitIntoFibonacci(S);}}// This code is contributed by rutvik_56 |
Javascript
<script> // Javascript program of the above approach // Function that returns true if // Fibonacci sequence is found function splitIntoFibonacciHelper(pos, S, seq) { // Base condition: // If pos is equal to length of S // and seq length is greater than 3 if (pos == S.length && (seq.length >= 3)) { // Return true return true; } // Stores current number let num = 0; for(let i = pos; i < S.length; i++) { // Add current digit to num num = num * 10 + (S[i] - '0'); // Avoid integer overflow if (num > Number.MAX_VALUE) break; // Avoid leading zeros if (S[pos] == '0' && i > pos) break; // If current number is greater // than last two number of seq if (seq.length> 2 && (num > (seq[seq.length - 1] + seq[seq.length - 2]))) break; // If seq length is less // 2 or current number is // is equal to the last // two of the seq if (seq.length < 2 || (num == (seq[seq.length - 1] + seq[seq.length - 2]))) { // Add to the seq seq.push(num); // Recur for i+1 if (splitIntoFibonacciHelper(i + 1, S, seq)) return true; // Remove last added number seq.pop(); } } // If no sequence is found return false; } // Function that prints the Fibonacci // sequence from the split of string S function splitIntoFibonacci(S) { // Initialize a vector to // store the sequence let seq = []; // Call helper function splitIntoFibonacciHelper(0, S, seq); // If sequence length is // greater than 3 if (seq.length >= 3) { // Print the sequence for(let i = 0; i < seq.length; i++) document.write(seq[i] + " "); } // If no sequence is found else { // Print -1 document.write("-1"); } } // Given String let S = "11235813"; // Function call splitIntoFibonacci(S);// This code is contributed by suresh07.</script> |
Output:
1 1 2 3 5 8 13
Time Complexity: O(N2)
Space Complexity: O(N)
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