<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 solveTab(vector<int> &nums1, vector<int> &nums2){
        int n = nums1.size();
        vector<int>swap(n, 0); //considering swapping senario
        vector<int>noSwap(n, 0); //considering not swapping 
        int ans=0;
        if(nums1.back()<=nums1[n-2] || nums2.back()<=nums2[n-2] ) ans=1; 
        swap[n-1]=1; // base case

        for(int i=n-2; i>=0; i--){
            if(nums1[i]>=nums1[i+1] || nums2[i]>=nums2[i+1]){
                //invalid case either swap i or swap i+1
                swap[i]=1+noSwap[i+1];
                noSwap[i]=swap[i+1];
                ans=max(ans, min(swap[i], noSwap[i]));
            }else{
                //No swap needed
                if(nums2[i]>=nums1[i+1] || nums1[i]>=nums2[i+1]){
                    //If swapped it will become Invalid so you would have to swap again
                    swap[i]=1+swap[i+1];
                    noSwap[i]=noSwap[i+1];
                }else{
                    swap[i]=1+min(swap[i+1], noSwap[i+1]);
                    noSwap[i]=min(swap[i+1], noSwap[i+1]);
                }
                ans=max(ans, min(swap[i], noSwap[i]));
            }
        }
        return ans;
    }

    int minSwap(vector<int>& nums1, vector<int>& nums2) {
        return solveTab(nums1, nums2);
    }
};
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