<p>You are given two integer arrays of the same length <code>nums1</code> and <code>nums2</code>. In one operation, you are allowed to swap <code>nums1[i]</code> with <code>nums2[i]</code>.</p>

<ul>
	<li>For example, if <code>nums1 = [1,2,3,<u>8</u>]</code>, and <code>nums2 = [5,6,7,<u>4</u>]</code>, you can swap the element at <code>i = 3</code> to obtain <code>nums1 = [1,2,3,4]</code> and <code>nums2 = [5,6,7,8]</code>.</li>
</ul>

<p>Return <em>the minimum number of needed operations to make </em><code>nums1</code><em> and </em><code>nums2</code><em> <strong>strictly increasing</strong></em>. The test cases are generated so that the given input always makes it possible.</p>

<p>An array <code>arr</code> is <strong>strictly increasing</strong> if and only if <code>arr[0] &lt; arr[1] &lt; arr[2] &lt; ... &lt; arr[arr.length - 1]</code>.</p>

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

<pre>
<strong>Input:</strong> nums1 = [1,3,5,4], nums2 = [1,2,3,7]
<strong>Output:</strong> 1
<strong>Explanation:</strong> 
Swap nums1[3] and nums2[3]. Then the sequences are:
nums1 = [1, 3, 5, 7] and nums2 = [1, 2, 3, 4]
which are both strictly increasing.
</pre>

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

<pre>
<strong>Input:</strong> nums1 = [0,3,5,8,9], nums2 = [2,1,4,6,9]
<strong>Output:</strong> 1
</pre>

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

<ul>
	<li><code>2 &lt;= nums1.length &lt;= 10<sup>5</sup></code></li>
	<li><code>nums2.length == nums1.length</code></li>
	<li><code>0 &lt;= nums1[i], nums2[i] &lt;= 2 * 10<sup>5</sup></code></li>
</ul>

class Solution {
    public:
        int minSwap(vector<int>& nums1, vector<int>& nums2) {
            vector<vector<int>> minSwapCache(2, vector<int>(nums1.size(), -1));

            return _recMinSwap(nums1, nums2, 0, false, minSwapCache);
        }

    private:
        int _recMinSwap(const vector<int> &nums1, const vector<int> &nums2, int from, bool previousSwapped, vector<vector<int>> &minSwapCache) {
            int length = nums1.size();
            if (from >= length) {
                return 0;
            }

            int swapIdx = previousSwapped ? 1 : 0;
            if (minSwapCache[swapIdx][from] >= 0) {
                return minSwapCache[swapIdx][from];
            } else {
                bool mustSwap = false;
                if (from > 0) {
                    if (previousSwapped) {
                        mustSwap = nums1[from - 1] >= nums2[from] || nums2[from - 1] >= nums1[from];
                    } else {
                        mustSwap = nums1[from - 1] >= nums1[from] || nums2[from - 1] >= nums2[from];
                    }
                }

                bool mustNotSwap = false;
                if (from > 0) {
                    if (previousSwapped) {
                        mustNotSwap = nums1[from - 1] >= nums1[from] || nums2[from - 1] >= nums2[from];   
                    } else {
                        mustNotSwap = nums1[from - 1] >= nums2[from] || nums2[from - 1] >= nums1[from];
                    }
                }

                int candidate1 = 2147483647;
                if (!mustNotSwap) {
                    candidate1 = _recMinSwap(nums1, nums2, from + 1, true, minSwapCache) + 1;
                }
                int candidate2 = 2147483647;
                if (!mustSwap) {
                    candidate2 = _recMinSwap(nums1, nums2, from + 1, false, minSwapCache);
                }

                int answer = min(candidate1, candidate2);

                minSwapCache[swapIdx][from] = answer;

                return answer;
            }
        }
};
109970