<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:
    vector<int>numsOne;
    vector<int>numsTwo;
    int DP[100001][2];
    int sz;
    int solve(int idx, bool prevSwapped) {
        if (idx == sz) {
            return 0;
        }
        
        if (DP[idx][prevSwapped] != -1) {
            return DP[idx][prevSwapped];
        }
        
        int prevOne = numsOne[idx - 1], prevTwo = numsTwo[idx - 1];
        if (prevSwapped) {
            swap(prevOne, prevTwo);
        }
        int noSwap = numsOne[idx] > prevOne and numsTwo[idx] > prevTwo ? solve(idx + 1, false) : 1e9;
        int yesSwap = numsTwo[idx] > prevOne and numsOne[idx] > prevTwo ? solve(idx + 1, true) : 1e9;
        return DP[idx][prevSwapped] = min(noSwap, yesSwap + 1);
    }
    int minSwap(vector<int>& nums1, vector<int>& nums2) {
        numsOne = nums1;
        numsTwo = nums2;
        sz = nums1.size();
        memset(DP, -1, sizeof(DP));
        return min(solve(1, false), solve(1, true) + 1);
    }
};
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