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

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.

Examples:

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)` `{` ` ` `// FIND SMALLEST POSSIBLE NUMBER BY SORTING` ` ` `// 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); ` ` ` ` ` `// FIND K-TH PERMUTATION OF SMALLEST NUMBER` ` ` `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;` `}` |

Output:

10022366897

This article is contributed by **Ayush Jauhari**. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.