<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) {
        int n = nums1.size();
        vector<int> swap(n, n);      // swap[i] represents the minimum swaps if we swap at index i
        vector<int> not_swap(n, n);  // not_swap[i] represents the minimum swaps if we don't swap at index i

        swap[0] = 1;     // We start with 1 swap at index 0 if we swap
        not_swap[0] = 0; // No swap at index 0 initially

        for (int i = 1; i < n; i++) {
            // Case 1: When nums1[i] > nums1[i-1] and nums2[i] > nums2[i-1]
            if (nums1[i] > nums1[i - 1] && nums2[i] > nums2[i - 1]) {
                not_swap[i] = not_swap[i - 1];           // No need to swap at i
                swap[i] = swap[i - 1] + 1;               // If swapped at i-1, swap at i
            }

            // Case 2: When nums1[i] > nums2[i-1] and nums2[i] > nums1[i-1]
            if (nums1[i] > nums2[i - 1] && nums2[i] > nums1[i - 1]) {
                not_swap[i] = min(not_swap[i], swap[i - 1]);  // No swap at i if swapped at i-1
                swap[i] = min(swap[i], not_swap[i - 1] + 1);  // Swap at i if no swap at i-1
            }
        }

        // The result is the minimum between swapping or not swapping at the last index
        return min(swap[n - 1], not_swap[n - 1]);
    }
};

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