K’th Boom Number

Boom numbers are numbers consisting only of digits 2 and 3. Given an integer k (0<k<=10^7) , display the k-th Boom number.

Input : k = 2
Output: 3

Input : k = 3
Output: 22

Input : k = 100
Output: 322323

Input: k = 1000000
Output: 3332322223223222223

Reference: http://www.spoj.com/problems/TSHOW1/
The idea is very simple like Generate Binary Numbers . Here also we use same approach ,
we use queue data structure to solve this problem. First enqueue “2” then “3” these two are first and second boom number respectively. Now set count=2, for each time pop() front of queue and append “2” in poped number and increment count++ if (count==k) then print current Boom number else append “3” in poped number and increment count++ if (count==k) then print current Boom number. Repeat the process untill we reach to K’th Boom number.

This approach can be seen as BFS of a tree with root as empty string. Left child of every node has a 2 appended and right child has 3 appended. Below is C++ implementation of this idea.

// C++ program to find K'th Boom number
using namespace std;
typedef long long int ll;

// This function uses queue data structure to K'th
// Boom number
void  boomNumber(ll k)
    // Create an empty queue of strings
    queue<string> q;

    // Enqueue an empty string

    // counter for K'th element
    ll count = 0;

    // This loop checks the value of count to
    // become equal to K when value of count
    // will be equals to k we will print the
    // Boom number
    while (count <= k)
        // current Boom number
        string s1 = q.front();

        // pop front

        // Store current Boom number before changing it
        string s2 = s1;

        // Append "2" to string s1 and enqueue it

        // check if count==k
        if (count==k)
            cout << s1 << endl; // K'th Boom number

        // Append "3" to string s2 and enqueue it.
        // Note that s2 contains the previous front

        // check if count==k
        if (count==k)
            cout << s2 << endl; // K'th Boom number
    return ;

// Driver program to test above function
int main()
    ll k = 1000000;
    return 0;



This article is contributed by Shashank Mishra (Gullu). This article is reviewed by team GeeksforGeeks.

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