<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 {
private:
    //1 : recursion : tle
    int solveRec(int i, vector<int>& nums1, vector<int>& nums2, bool swapped){
        //base case
        if(i == nums1.size()){
            return 0;
        }

        int ans = INT_MAX;

        int prev1 = nums1[i-1];
        int prev2 = nums2[i-1];

        //catch
        if(swapped){
            swap(prev1, prev2);
        }

        //no swap
        if(nums1[i] > prev1 && nums2[i] > prev2){
            ans = solveRec(i+1, nums1, nums2, 0);
        }

        //swap
        if(nums1[i] > prev2 && nums2[i] > prev1){
            ans = min(ans, 1 + solveRec(i+1, nums1, nums2, 1));
        }

        return ans;
    }

    //2 : memoization
    int solveMem(int i, vector<int>& nums1, vector<int>& nums2, bool swapped, vector<vector<int>>& dp){
        //base case
        if(i == nums1.size()){
            return 0;
        }

        if(dp[i][swapped] != -1){
            return dp[i][swapped];
        }

        int ans = INT_MAX;

        int prev1 = nums1[i-1];
        int prev2 = nums2[i-1];

        //catch
        if(swapped){
            swap(prev1, prev2);
        }

        //no swap
        if(nums1[i] > prev1 && nums2[i] > prev2){
            ans = solveMem(i+1, nums1, nums2, 0, dp);
        }

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

        return dp[i][swapped] = ans;
    }
    
    //3 : tabulation
    int solveTab(vector<int>& nums1, vector<int>& nums2){
        int n = nums1.size();
        vector<vector<int>> dp(n+1, vector<int>(2, 0));

        for(int i=n-1; i>=1; i--){
            for(int swapped=1; swapped>=0; swapped--){
                int ans = INT_MAX;
                int prev1 = nums1[i-1];
                int prev2 = nums2[i-1];

                //catch
                if(swapped){
                    swap(prev1, prev2);
                }

                //no swap
                if(nums1[i] > prev1 && nums2[i] > prev2){
                    ans = dp[i+1][0];
                }

                //swap
                if(nums1[i] > prev2 && nums2[i] > prev1){
                    ans = min(ans, 1 + dp[i+1][1]);
                }
                dp[i][swapped] = ans;
            }
        }
        return dp[1][0];
    }

public:
    int minSwap(vector<int>& nums1, vector<int>& nums2) {
        nums1.insert(nums1.begin(), -1);
        nums2.insert(nums2.begin(), -1);

        bool swapped = 0;

        //1 : recursion : tle
        // return solveRec(1, nums1, nums2, swapped);

        //2 : memoization
        // int n = nums1.size();
        // vector<vector<int>> dp(n, vector<int>(2, -1));
        // return solveMem(1, nums1, nums2, swapped, dp);

        //3 : tabulation
        return solveTab(nums1, nums2);
    }
};
114500