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Get the kth smallest number using the digits of the given number

  • Difficulty Level : Medium
  • Last Updated : 16 Jul, 2017

Given a non-negative number n and a value k. Find the kth smallest number that can be formed using the digits of the given number n. It is guaranteed that the kth smallest number can be formed. Note that the number could be very large and may not even fit into long long int.


Input : n = 1234, k = 2
Output : 1243

Input : n = 36012679802, k = 4
Output : 10022366897

The idea is to first sort digits and find the smallest number, then find k-th permutation starting from smallest number. To sort digits, we use an frequency counting technique as number of digits are small.

// C++ implementation to get the kth smallest
// number using the digits of the given number
#include <bits/stdc++.h>
using namespace std;
// function to get the smallest digit in 'num'
// which is greater than 0
char getSmallDgtGreaterThanZero(string num, int n)
    // 's_dgt' to store the smallest digit
    // greater than 0
        char s_dgt = '9';
    for (int i=0; i<n; i++)
        if (num[i] < s_dgt && num[i] != '0')
            s_dgt = num[i];
    // required smallest digit in 'num'
    return s_dgt;
// function to get the kth smallest number
string kthSmallestNumber(string num, int k)
    // DIGITS
    // count frequency of each digit
    int freq[10];
    string final_num = "";
    memset(freq, 0, sizeof(freq));
    int n = num.size();
    // counting frequency of each digit
    for (int i = 0; i < n; i++)
        freq[num[i] - '0']++;
    // get the smallest digit greater than 0
    char s_dgt = getSmallDgtGreaterThanZero(num, n);    
    // add 's_dgt' to 'final_num'
    final_num += s_dgt;
    // reduce frequency of 's_dgt' by 1 in 'freq'
    freq[s_dgt - '0']--;
    // add each digit according to its frequency
    // to 'final_num'
    for (int i=0; i<10; i++)
        for (int j=1; j<=freq[i]; j++)
            final_num += (char)(i+48);    
    for (int i=1; i<k; i++)
      next_permutation(final_num.begin(), final_num.end());
    // required kth smallest number
    return final_num;
// Driver program to test above
int main()
    string num = "36012679802";
    int k = 4;
    cout << kthSmallestNumber(num, k);
    return 0;



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