<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)  {
        // base case
        if(index==nums1.size())
            return 0;
        int ans= INT_MAX;
        int prev1=nums1[index-1];
        int prev2=nums2[index-1];
        // catch
        if(swapped)
            swap(prev1, prev2);
        // no swap
        if(nums1[index] > prev1 && nums2[index]> prev2)
            ans= solve(nums1, nums2, index+1, 0);
        // swap
        if(nums1[index]>prev2 && nums2[index] > prev1)
            ans=min(ans, 1+solve(nums1, nums2, index+1, 1));
        return ans;


    }
    int solveMem(vector<int>& nums1, vector<int>& nums2, int index, bool swapped, vector<vector<int> > & dp)  {
        // base case
        if(index==nums1.size())
            return 0;
        if(dp[index][swapped]!=-1)
            return dp[index][swapped];
        int ans= INT_MAX;
        int prev1=nums1[index-1];
        int prev2=nums2[index-1];
        // catch
        if(swapped)
            swap(prev1, prev2);
        // no swap
        if(nums1[index] > prev1 && nums2[index]> prev2)
            ans= solveMem(nums1, nums2, index+1, 0, dp);
        // swap
        if(nums1[index]>prev2 && nums2[index] > prev1)
            ans=min(ans, 1+solveMem(nums1, nums2, index+1, 1,dp));
        return dp[index][swapped] = ans;

    }
    int solveTab(vector<int>& nums1, vector<int>& nums2) {
        int n= nums1.size();
         int swap=0;
         int noswap=0;
         int currswap=0;
         int currnoswap=0;
       
        for(int index = n-1; index>= 1; index--) {
            for(int swapped=1; swapped>=0; swapped--) {
                    int ans= INT_MAX;
                    int prev1=nums1[index-1];
                    int prev2=nums2[index-1];
                    // catch
                    if(swapped) {
                        int temp=prev2;
                        prev2=prev1;
                        prev1=temp;
                    }
                        
                     // no swap
                    if(nums1[index] > prev1 && nums2[index]> prev2)
                        ans = noswap;
                     // swap
                    if(nums1[index]>prev2 && nums2[index] > prev1)
                        ans=min(ans, 1+swap);
                    if(swapped)
                         currswap=ans;
                    else 
                        currnoswap=ans;

    


            }
            swap=currswap;
            noswap=currnoswap;
        }
        return min(swap,noswap);
    }
    int minSwap(vector<int>& nums1, vector<int>& nums2) {
        nums1.insert(nums1.begin(), -1);
        nums2.insert(nums2.begin(), -1);
        bool swapped=0;
        int n=nums1.size();
        // vector<vector<int> > dp(n, vector<int>(2,-1));

        return solveTab(nums1, nums2);
     
        
    }
};

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