<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> keep(n, INT_MAX);  // Keep array: no swap at index i
        vector<int> swap(n, INT_MAX);  // Swap array: swap at index i
        
        // Base case: No swaps needed at the first index
        keep[0] = 0;
        swap[0] = 1;  // One swap at the first index

        for (int i = 1; i < n; ++i) {
            // Condition 1: If both arrays are already increasing without a swap at i
            if (nums1[i] > nums1[i - 1] && nums2[i] > nums2[i - 1]) {
                keep[i] = keep[i - 1];  // No swap at i
                swap[i] = swap[i - 1] + 1;  // Swap at i
            }

            // Condition 2: If swapping nums1[i] with nums2[i] makes both arrays increasing
            if (nums1[i] > nums2[i - 1] && nums2[i] > nums1[i - 1]) {
                keep[i] = min(keep[i], swap[i - 1]);  // No swap at i, but swapped at i-1
                swap[i] = min(swap[i], keep[i - 1] + 1);  // Swap at i, no swap at i-1
            }
        }

        // The minimum of the last index, whether we swapped or not
        return min(keep[n - 1], swap[n - 1]);
    }
};

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