<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:
    // METHOD 1 RECCURSION
    int solve1(vector<int> nums1, vector<int> nums2, int index, bool swapped){

        // base case
        if(index == nums1.size())
            return 0;
        
        int prev1 = nums1[index-1];
        int prev2 = nums2[index-1];

        if(swapped == 1){
            swap(prev1, prev2);
        }

        int ans = INT_MAX;

        // no swap
        if(prev1 < nums1[index] && prev2 < nums2[index]){
            ans = solve1(nums1, nums2, index+1, 0);
        }

        // swapped
        if(nums1[index] > prev2 && nums2[index] > prev1){
            ans = min(ans, 1 + solve1(nums1, nums2, index+1, 1));
        }

        return ans;
    }

    //METHOD 2 TOP DOWN
    int solve2(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 prev1 = nums1[index-1];
        int prev2 = nums2[index-1];

        int ans = INT_MAX;

        if(swapped == 1)
            swap(prev1, prev2);

        // no swap
        if(nums1[index] > prev1 && nums2[index] > prev2)
            ans = solve2(nums1, nums2, index+1, 0, dp); 

        // swap
        if(nums1[index] > prev2 && nums2[index] > prev1)
            ans = min(ans, 1 + solve2(nums1, nums2, index+1, 1, dp));

        dp[index][swapped] = ans;

        return dp[index][swapped];
    }

    //METHOD 3 BOTTOM UP
    int solve3(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 prev1 = nums1[index-1];
                int prev2 = nums2[index-1];

                int ans = INT_MAX;

                if(swapped == 1)
                    swap(prev1, prev2);

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

                // swap
                if(nums1[index] > prev2 && nums2[index] > prev1)
                    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;

        //METHOD 1 RECCURSION
        //return solve1(nums1, nums2, 1, swapped);

        //METHOD 2 TOP DOWN
        // vector<vector<int>> dp(nums1.size(), vector<int> (2, -1));
        // return solve2(nums1, nums2, 1, swapped, dp);

        //METHOD 3 BOTTOM UP
        return solve3(nums1, nums2);
    }
};
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