Create Maximum Number
<p>You are given two integer arrays <code>nums1</code> and <code>nums2</code> of lengths <code>m</code> and <code>n</code> respectively. <code>nums1</code> and <code>nums2</code> represent the digits of two numbers. You are also given an integer <code>k</code>.</p>

<p>Create the maximum number of length <code>k &lt;= m + n</code> from digits of the two numbers. The relative order of the digits from the same array must be preserved.</p>

<p>Return an array of the <code>k</code> digits representing the answer.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums1 = [3,4,6,5], nums2 = [9,1,2,5,8,3], k = 5
<strong>Output:</strong> [9,8,6,5,3]
</pre>

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

<pre>
<strong>Input:</strong> nums1 = [6,7], nums2 = [6,0,4], k = 5
<strong>Output:</strong> [6,7,6,0,4]
</pre>

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

<pre>
<strong>Input:</strong> nums1 = [3,9], nums2 = [8,9], k = 3
<strong>Output:</strong> [9,8,9]
</pre>

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

<ul>
	<li><code>m == nums1.length</code></li>
	<li><code>n == nums2.length</code></li>
	<li><code>1 &lt;= m, n &lt;= 500</code></li>
	<li><code>0 &lt;= nums1[i], nums2[i] &lt;= 9</code></li>
	<li><code>1 &lt;= k &lt;= m + n</code></li>
	<li><code>nums1</code> and <code>nums2</code> do not have leading zeros.</li>
</ul>
Stack; Greedy; Array; Two Pointers; Monotonic Stack
class Solution:
    def maxNumber(self, nums1: List[int], nums2: List[int], k: int) -> List[int]:
        def f(nums: List[int], k: int) -> List[int]:
            n = len(nums)
            stk = [0] * k
            top = -1
            remain = n - k
            for x in nums:
                while top >= 0 and stk[top] < x and remain > 0:
                    top -= 1
                    remain -= 1
                if top + 1 < k:
                    top += 1
                    stk[top] = x
                else:
                    remain -= 1
            return stk

        def compare(nums1: List[int], nums2: List[int], i: int, j: int) -> bool:
            if i >= len(nums1):
                return False
            if j >= len(nums2):
                return True
            if nums1[i] > nums2[j]:
                return True
            if nums1[i] < nums2[j]:
                return False
            return compare(nums1, nums2, i + 1, j + 1)

        def merge(nums1: List[int], nums2: List[int]) -> List[int]:
            m, n = len(nums1), len(nums2)
            i = j = 0
            ans = [0] * (m + n)
            for k in range(m + n):
                if compare(nums1, nums2, i, j):
                    ans[k] = nums1[i]
                    i += 1
                else:
                    ans[k] = nums2[j]
                    j += 1
            return ans

        m, n = len(nums1), len(nums2)
        l, r = max(0, k - n), min(k, m)
        ans = [0] * k
        for x in range(l, r + 1):
            arr1 = f(nums1, x)
            arr2 = f(nums2, k - x)
            arr = merge(arr1, arr2)
            if ans < arr:
                ans = arr
        return ans
