<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 solve(vector<int>& nums1, vector<int>& nums2,int index,bool swapped,vector<vector<int>>&dp)
    {
        if(index==nums1.size())
        return 0;

        int prev1=nums1[index-1];
        int prev2=nums2[index-1];
        if(dp[index][swapped]!=-1)
        {
            return dp[index][swapped];
        }
        if(swapped)
        {
            swap(prev1,prev2);
        }
        int ans=INT_MAX;
        if(nums1[index]>prev1 && nums2[index]> prev2)
        {
          ans=  solve(nums1,nums2,index+1,0,dp);
        }
        if(nums1[index]>prev2 && nums2[index]> prev1)
        {
           ans=min(ans,1+ solve(nums1,nums2,index+1,1,dp));
        }  
        dp[index][swapped]=ans;
        return ans;    
    }
    int solve2(vector<int>nums1,vector<int>nums2)
    {
        vector<vector<int>>dp(nums1.size()+1,vector<int>(2,0));
        for(int index=nums1.size()-1;index>0;index--)
        {
            for(int swapped=1;swapped>=0;swapped--)
         {   int prev1=nums1[index-1];
            int prev2=nums2[index-1];
            if(swapped)
            swap(prev1,prev2);
            int ans=INT_MAX;
        if(nums1[index]>prev1 && nums2[index]> prev2)
        {
          ans=  dp[index+1][0];
        }
        if(nums1[index]>prev2 && nums2[index]> prev1)
        {
           ans=min(ans,1+dp[index+1][1]);
        }  
        dp[index][swapped]=ans;}
        }
        return dp[1][0];
    }


    int minSwap(vector<int>& nums1, vector<int>& nums2) {
        nums1.insert(nums1.begin(),-1);
        nums2.insert(nums2.begin(),-1);
        return solve2(nums1,nums2);
    }
};
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