<p>You are given a string <code>num</code> representing <strong>the digits</strong> of a very large integer and an integer <code>k</code>. You are allowed to swap any two adjacent digits of the integer <strong>at most</strong> <code>k</code> times.</p>

<p>Return <em>the minimum integer you can obtain also as a string</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/06/17/q4_1.jpg" style="width: 500px; height: 40px;" />
<pre>
<strong>Input:</strong> num = &quot;4321&quot;, k = 4
<strong>Output:</strong> &quot;1342&quot;
<strong>Explanation:</strong> The steps to obtain the minimum integer from 4321 with 4 adjacent swaps are shown.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> num = &quot;100&quot;, k = 1
<strong>Output:</strong> &quot;010&quot;
<strong>Explanation:</strong> It&#39;s ok for the output to have leading zeros, but the input is guaranteed not to have any leading zeros.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> num = &quot;36789&quot;, k = 1000
<strong>Output:</strong> &quot;36789&quot;
<strong>Explanation:</strong> We can keep the number without any swaps.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= num.length &lt;= 3 * 10<sup>4</sup></code></li>
	<li><code>num</code> consists of only <strong>digits</strong> and does not contain <strong>leading zeros</strong>.</li>
	<li><code>1 &lt;= k &lt;= 10<sup>9</sup></code></li>
</ul>

from bisect import bisect


class Solution:
    def minInteger(self, num: str, k: int) -> str:
        len_num = len(num)
        if k >= len_num * (len_num - 1) / 2:
            return ''.join(sorted(num))
        pos = [[] for _ in range(10)]
        for i in range(len_num - 1, -1, -1):
            pos[int(num[i])].append(i)
        prev = []
        ans = ''
        candi = list(range(10))
        while k and len(ans) < len_num:
            for di in candi[:]:
                if pos[di]:
                    index = pos[di][-1]
                    place = bisect(prev, index)
                    if index - place <= k:
                        prev.insert(place, index)
                        k -= index - place
                        pos[di].pop()
                        ans += str(di)
                        break
                else:
                    candi.remove(di)
        if k == 0 and len(ans) < len_num:
            prev = set(prev)
            return ans + ''.join(ch for i, ch in enumerate(num) if i not in prev)
        else:
            return ans
19100