<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:
    void func(vector<int>& nums){
        for(int i=nums.size()-2;i>=0;i--){
            swap(nums[i],nums[i+1]);
        }
    }
    int f(vector<int>& nums1, vector<int>& nums2, int i,bool isSwapped,vector<vector<int>>&dp){
        // base case
        int n = nums1.size();
        int r = (int)isSwapped;
        if(i>=n){
            return 0;
        }
        if(dp[r][i]!=-1){
            return dp[r][i];
        }
        int yes = INT_MAX;
        int no = INT_MAX;
        if(!isSwapped && nums1[i]>nums1[i-1] && nums2[i]>nums2[i-1]){
            // may or may not swap
            if(nums2[i]>nums1[i-1] && nums1[i]>nums2[i-1])
                yes = 1 + f(nums1,nums2,i+1,true,dp);
            no = 0 + f(nums1,nums2,i+1,false,dp);
        }
        else if(isSwapped && nums1[i]>nums2[i-1] && nums2[i]>nums1[i-1]){
            // may or may not swap
            if(nums2[i]>nums2[i-1] && nums1[i]>nums1[i-1])
                yes = 1 + f(nums1,nums2,i+1,true,dp);
            no = 0 + f(nums1,nums2,i+1,false,dp);
        }
        else{
            // must swap
            yes = 1 + f(nums1,nums2,i+1,true,dp);
        }
        return dp[r][i] = min(yes,no);
    }
    int minSwap(vector<int>& nums1, vector<int>& nums2) {
        nums1.push_back(INT_MIN);
        nums2.push_back(INT_MIN);
        func(nums1);
        func(nums2);
        vector<vector<int>>dp(2,vector<int>(nums1.size()+1,-1));
        int ans = f(nums1,nums2,1,false,dp);
        return ans;
    }
};
111103