Given a number N. The task is to find the first N terms of the Golomb Sequence. Golomb sequence is a non-decreasing integer sequence where the n-th term is equal to the number of times n appears in the sequence.
Input: N = 11
Output: 1 2 2 3 3 4 4 4 5 5 5
Explanation:
The first term is 1. 1 appears only once.
The second term is 2. 2 appears two times.
The third term is 2. 3 appears two times.
The fourth term is 3. 4 appears three times.
the fifth term is 3. 5 appears three times.Input: N = 6
Output: 1 2 2 3 3 4
Approach:
- Initialise the array arr[] with [1] as the Golomb sequence starts with 1.
- Store the value of last index in map M.
- For Golomb sequence till N:
- Initialise cnt = 0 and map the .
- If cnt is not equals to 0 then, then current element in Golomb sequence is the previous element in the sequence and decrease the cnt.
- Else the current element in Golomb sequence is equals to 1 + previous element in the sequence and cnt is updated as the value of map at current element in Golomb sequence and decrease the cnt.
- Map the current index with the current value at Golomb Sequence.
- Print all the element of Golomb Sequence stored in array arr[].
Below is the implementation of the above approach:
C++
// C++ program to find the first// N terms of Golomb Sequence#include "bits/stdc++.h"#define MAX 100001using namespace std;// Function to print the Golomb// Sequencevoid printGolombSequence(int N){ // Initialise the array int arr[MAX]; // Initialise the cnt to 0 int cnt = 0; // First and second element // of Golomb Sequence is 0, 1 arr[0] = 0; arr[1] = 1; // Map to store the count of // current element in Golomb // Sequence map<int, int> M; // Store the count of 2 M[2] = 2; // Iterate over 2 to N for (int i = 2; i <= N; i++) { // If cnt is equals to 0 // then we have new number // for Golomb Sequence // which is 1 + previous // element if (cnt == 0) { arr[i] = 1 + arr[i - 1]; cnt = M[arr[i]]; cnt--; } // Else the current element // is the previous element // in this Sequence else { arr[i] = arr[i - 1]; cnt--; } // Map the current index to // current value in arr[] M[i] = arr[i]; } // Print the Golomb Sequence for (int i = 1; i <= N; i++) { cout << arr[i] << ' '; }}// Driver Codeint main(){ int N = 11; printGolombSequence(N); return 0;} |
Java
// Java program to find the first// N terms of Golomb Sequenceimport java.util.*;class GFG{static int MAX = 1000;// Function to print the Golomb// Sequencestatic void printGolombSequence(int N){ // Initialise the array int []arr = new int[MAX]; for(int i = 0; i < MAX; i++) arr[i] = 0; // Initialise the cnt to 0 int cnt = 0; // First and second element // of Golomb Sequence is 0, 1 arr[0] = 0; arr[1] = 1; // Map to store the count of // current element in Golomb // Sequence Map<Integer,Integer> M=new HashMap<Integer,Integer>(); // Store the count of 2 M.put(2,2); // Iterate over 2 to N for (int i = 2; i <= N; i++) { // If cnt is equals to 0 // then we have new number // for Golomb Sequence 1 2 2 3 3 4 4 4 5 5 5 // which is 1 + previous // element if (cnt == 0) { arr[i] = 1 + arr[i - 1]; cnt = M.get(arr[i]); cnt--; } // Else the current element // is the previous element // in this Sequence else { arr[i] = arr[i - 1]; cnt--; } // Map the current index to // current value in arr[] M.put(i, arr[i]); } // Print the Golomb Sequence for (int i = 1; i <= N; i++) { System.out.print(arr[i]+" "); }}// Driver Codepublic static void main(String args[]){ int N = 11; printGolombSequence(N);}}// This code is contributed by Surendra_Gangwar |
Python3
# Python3 program to find the first# N terms of Golomb SequenceMAX = 100001# Function to print the Golomb# Sequencedef printGolombSequence(N): # Initialise the array arr = [0] * MAX # Initialise the cnt to 0 cnt = 0 # First and second element # of Golomb Sequence is 0, 1 arr[0] = 0 arr[1] = 1 # Map to store the count of # current element in Golomb # Sequence M = dict() # Store the count of 2 M[2] = 2 # Iterate over 2 to N for i in range(2, N + 1): # If cnt is equals to 0 # then we have new number # for Golomb Sequence # which is 1 + previous # element if (cnt == 0): arr[i] = 1 + arr[i - 1] cnt = M[arr[i]] cnt -= 1 # Else the current element # is the previous element # in this Sequence else: arr[i] = arr[i - 1] cnt -= 1 # Map the current index to # current value in arr[] M[i] = arr[i] # Print the Golomb Sequence for i in range(1, N + 1): print(arr[i], end=" ")# Driver CodeN = 11printGolombSequence(N)# This code is contributed by mohit kumar 29 |
C#
// C# program to find the first // N terms of Golomb Sequence using System;using System.Collections.Generic;class GFG{ static int MAX = 1000; // Function to print the Golomb // Sequence static void printGolombSequence(int N) { // Initialise the array int[] arr = new int[MAX]; for(int i = 0; i < MAX; i++) arr[i] = 0; // Initialise the cnt to 0 int cnt = 0; // First and second element // of Golomb Sequence is 0, 1 arr[0] = 0; arr[1] = 1; // Map to store the count of // current element in Golomb // Sequence Dictionary<int, int> M = new Dictionary<int, int>(); // Store the count of 2 M.Add(2, 2); // Iterate over 2 to N for(int i = 2; i <= N; i++) { // If cnt is equals to 0 // then we have new number // for Golomb Sequence 1 2 2 3 3 4 4 4 5 5 5 // which is 1 + previous // element if (cnt == 0) { arr[i] = 1 + arr[i - 1]; cnt = M[arr[i]]; cnt--; } // Else the current element // is the previous element // in this Sequence else { arr[i] = arr[i - 1]; cnt--; } // Map the current index to // current value in arr[] if(M.ContainsKey(i)) { M[i] = arr[i]; } else { M.Add(i, arr[i]); } } // Print the Golomb Sequence for(int i = 1; i <= N; i++) { Console.Write(arr[i] + " "); } } // Driver Codestatic void Main() { int N = 11; printGolombSequence(N); }}// This code is contributed by divyeshrabadiya07 |
Javascript
<script>// Javascript program to find the first// N terms of Golomb Sequencevar MAX = 100001;// Function to print the Golomb// Sequencefunction printGolombSequence(N){ // Initialise the array var arr = Array(MAX); // Initialise the cnt to 0 var cnt = 0; // First and second element // of Golomb Sequence is 0, 1 arr[0] = 0; arr[1] = 1; // Map to store the count of // current element in Golomb // Sequence var M = new Map(); // Store the count of 2 M.set(2, 2); // Iterate over 2 to N for (var i = 2; i <= N; i++) { // If cnt is equals to 0 // then we have new number // for Golomb Sequence // which is 1 + previous // element if (cnt == 0) { arr[i] = 1 + arr[i - 1]; cnt = M.get(arr[i]); cnt--; } // Else the current element // is the previous element // in this Sequence else { arr[i] = arr[i - 1]; cnt--; } // Map the current index to // current value in arr[] M.set(i, arr[i]); } // Print the Golomb Sequence for (var i = 1; i <= N; i++) { document.write( arr[i] + ' '); }}// Driver Codevar N = 11;printGolombSequence(N);</script> |
Output:
1 2 2 3 3 4 4 4 5 5 5
Time Complexity: O(N)
Auxiliary Space: O(N)
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