<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){
        if(index == nums1.size()) return 0;
        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 = solve(nums1 , nums2 , index + 1 , 0);
        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){
        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];
        if(swapped) swap(prev1 , prev2);
        if(nums1[index] > prev1 && nums2[index] > prev2) 
            ans = solveMem(nums1 , nums2 , index + 1 , 0 , dp);
        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();
        vector<vector<int>> dp(n + 1 , 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];
                if(swapped) swap(prev1 , prev2);
                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 solveTabSO(vector<int>& nums1, vector<int>& nums2){
        int n = nums1.size();
        // vector<vector<int>> dp(n + 1 , vector<int>(2 , 0));
        vector<int> curr(2 , 0);
        vector<int> next(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];
                if(swapped) swap(prev1 , prev2);
                if(nums1[index] > prev1 && nums2[index] > prev2) 
                    ans = next[0];
                if(nums1[index] > prev2 && nums2[index] > prev1) 
                    ans = min(ans , 1 + next[1]);
                curr[swapped] = ans;
            }
            next = curr;
        }
        return next[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 + 1 , vector<int>(2 , -1));
        // return solve(nums1 , nums2 , 1 , swapped);
        // return solveMem(nums1 , nums2 , 1 , swapped , dp);
        return solveTabSO(nums1 , nums2);
    }
};
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