# 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; ` `} ` |

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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.

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