<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 collections import deque

class Solution:
    def minInteger(self, num: str, k: int) -> str:
        n = len(num)
        num = list(num)
        pos = [deque() for _ in range(10)]
        
        # Store the positions of each digit in the deque
        for i, digit in enumerate(num):
            pos[int(digit)].append(i)

        result = []
        segment_tree = [0] * (4 * n)

        def update(node, start, end, index):
            if start == end:
                segment_tree[node] += 1
                return
            mid = (start + end) // 2
            if index <= mid:
                update(2 * node + 1, start, mid, index)
            else:
                update(2 * node + 2, mid + 1, end, index)
            segment_tree[node] = segment_tree[2 * node + 1] + segment_tree[2 * node + 2]

        def query(node, start, end, left, right):
            if right < start or end < left:
                return 0
            if left <= start and end <= right:
                return segment_tree[node]
            mid = (start + end) // 2
            left_sum = query(2 * node + 1, start, mid, left, right)
            right_sum = query(2 * node + 2, mid + 1, end, left, right)
            return left_sum + right_sum

        for _ in range(n):
            for digit in range(10):
                if pos[digit]:
                    index = pos[digit][0]
                    swaps_needed = index - query(0, 0, n - 1, 0, index)
                    if swaps_needed <= k:
                        k -= swaps_needed
                        result.append(str(digit))
                        pos[digit].popleft()
                        update(0, 0, n - 1, index)
                        break

        return ''.join(result)

# Example usage:
solution = Solution()
num = "4321"
k = 4
print(solution.minInteger(num, k))  # Output: "1342"
25300