1850 - Minimum Adjacent Swaps to Reach the Kth Smallest Number.

Medium

You are given a string num, representing a large integer, and an integer k.

We call some integer wonderful if it is a permutation of the digits in num and is greater in value than num. There can be many wonderful integers. However, we only care about the smallest-valued ones.

• For example, when num = "5489355142":

Return the minimum number of adjacent digit swaps that needs to be applied to num to reach the <code>k^th</code> smallest wonderful integer.

The tests are generated in such a way that <code>k^th</code> smallest wonderful integer exists.

Example 1:

Input: num = "5489355142", k = 4

Output: 2

Explanation: The 4^th smallest wonderful number is "5489355421". To get this number:

• Swap index 7 with index 8: "5489355142" -> "5489355412"

• Swap index 8 with index 9: "5489355412" -> "5489355421"

Example 2:

Input: num = "11112", k = 4

Output: 4

Explanation: The 4^th smallest wonderful number is "21111". To get this number:

• Swap index 3 with index 4: "11112" -> "11121"

• Swap index 2 with index 3: "11121" -> "11211"

• Swap index 1 with index 2: "11211" -> "12111"

• Swap index 0 with index 1: "12111" -> "21111"

Example 3:

Input: num = "00123", k = 1

Output: 1

Explanation: The 1^st smallest wonderful number is "00132". To get this number:

• Swap index 3 with index 4: "00123" -> "00132"

Constraints:

• 2 <= num.length <= 1000

• 1 <= k <= 1000

• num only consists of digits.