<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 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);
    }
    //not swap
    if(nums1[index] > prev1 && nums2[index] > prev2){
        ans = solveMem(nums1, nums2, index+1, 0,dp);
    }

    //swap
    if( nums1[index] > prev2 && nums2[index] > prev1){           //diagonal case
        ans = min( ans, 1 + solveMem( nums1, nums2, index+1, 1,dp));
    }
    return dp[index][swapped] = ans;
 }

 int solveTab(vector<int>& nums1, vector<int>& nums2 ){       //bottom up
    int n = nums1.size();
    vector<vector<int>>dp( n+5, vector<int>(2, 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){
            swap( prev1, prev2);
        }
        //not swap
        if(nums1[index] > prev1 && nums2[index] > prev2){
            ans = dp[index+1][0];
        }

        //swap
        if( nums1[index] > prev2 && nums2[index] > prev1){           //diagonal case
            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);
        bool swapped = 0;
     //   int n = nums1.size(); 

        // vector<vector<int>>dp( n, vector<int>(2, -1));
        // return solveMem( nums1, nums2, 1, swapped,dp);
        return solveTab( nums1, nums2);
    }
};
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