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 {
public:
    vector<int> maxNumber(vector<int>& nums1, vector<int>& nums2, int k) {
        auto f = [](vector<int>& nums, int k) {
            int n = nums.size();
            vector<int> stk(k);
            int top = -1;
            int remain = n - k;
            for (int x : nums) {
                while (top >= 0 && stk[top] < x && remain > 0) {
                    --top;
                    --remain;
                }
                if (top + 1 < k) {
                    stk[++top] = x;
                } else {
                    --remain;
                }
            }
            return stk;
        };
        function<bool(vector<int>&, vector<int>&, int, int)> compare = [&](vector<int>& nums1, vector<int>& nums2, int i, int j) -> bool {
            if (i >= nums1.size()) {
                return false;
            }
            if (j >= nums2.size()) {
                return true;
            }
            if (nums1[i] > nums2[j]) {
                return true;
            }
            if (nums1[i] < nums2[j]) {
                return false;
            }
            return compare(nums1, nums2, i + 1, j + 1);
        };

        auto merge = [&](vector<int>& nums1, vector<int>& nums2) {
            int m = nums1.size(), n = nums2.size();
            int i = 0, j = 0;
            vector<int> ans(m + n);
            for (int k = 0; k < m + n; ++k) {
                if (compare(nums1, nums2, i, j)) {
                    ans[k] = nums1[i++];
                } else {
                    ans[k] = nums2[j++];
                }
            }
            return ans;
        };

        int m = nums1.size(), n = nums2.size();
        int l = max(0, k - n), r = min(k, m);
        vector<int> ans(k);
        for (int x = l; x <= r; ++x) {
            vector<int> arr1 = f(nums1, x);
            vector<int> arr2 = f(nums2, k - x);
            vector<int> arr = merge(arr1, arr2);
            if (ans < arr) {
                ans = move(arr);
            }
        }
        return ans;
    }
};