<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
{
    int minSwap(vector<int>& nums1, vector<int>& nums2, int currentIndex, bool isSwapped, vector<pair<int, int>>& dp)
    {
        if(currentIndex >= nums1.size())
        {
            return 0;
        }

        if(isSwapped)
        {
            if(dp[currentIndex].first != -1)
            {
                return dp[currentIndex].first;
            }
        }
        else
        {
            if(dp[currentIndex].second != -1)
            {
                return dp[currentIndex].second;
            }
        }

        int swapCount = INT_MAX;
        int previous1 = nums1[currentIndex - 1];
        int previous2 = nums2[currentIndex - 1];
        if(isSwapped)
        {
            swap(previous1, previous2);
        }

        if(previous1 < nums1[currentIndex] && previous2 < nums2[currentIndex])
        {
            swapCount = minSwap(nums1, nums2, currentIndex + 1, false, dp);
        }

        if(previous1 < nums2[currentIndex] && previous2 < nums1[currentIndex])
        {
            const auto swapCountSwapping = 1 + minSwap(nums1, nums2, currentIndex + 1, true, dp);
            if(swapCount > swapCountSwapping)
            {
                swapCount = swapCountSwapping;
            }
        }
        
        if(isSwapped)
        {
            dp[currentIndex].first = swapCount;
        }
        else
        {
            dp[currentIndex].second = swapCount;
        }
        return swapCount;
    }
    
public:
    int minSwap(vector<int>& nums1, vector<int>& nums2)
    {
        nums1.insert(nums1.begin(), -1);
        nums2.insert(nums2.begin(), -1);
        vector<pair<int, int>> dp(nums1.size(), pair<int, int>(-1, -1));
        return minSwap(nums1, nums2, 1, false, dp);
    }
};

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