<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:
    vector<int> num1;
    vector<int> num2;  
    int mp[100005][2];
    int dp(int i,bool swapped, int prev1, int prev2){
        if (i>=(num1.size()))return 0;
        if (mp[i][swapped]!=-1)return mp[i][swapped];
        int call1 = 1e9,call2 = 1e9;
        if (prev1 < num1[i] && prev2 < num2[i]){
            call1 = dp(i+1,false,num1[i],num2[i]);
        }
        if (prev1<num2[i] && prev2<num1[i]){
            call2 = 1 + dp(i+1,true,num2[i],num1[i]);
        }
        return mp[i][swapped] = min(call1,call2);
    }
    int minSwap(vector<int>& nums1, vector<int>& nums2) {
        num1 = nums1;
        num2 = nums2;
        /*for (int i = 0; i<100005; ++i){
            for (int j = 0; j<2; ++j){
                mp[i][j] = -1;
            }
        }*/
        mp[num1.size()][0] = mp[num1.size()][1] =  0;
        for (int i = num1.size()-1; i>=0; --i){
            for (int swapped = 0; swapped<2; ++swapped){
                int prev1 = ((i-1)<0)?-1:num1[i-1];
                int prev2 = ((i-1)<0)?-1:num2[i-1];
                if (swapped){
                    swap(prev1,prev2);
                }
                int call1 = 1e9,call2 = 1e9;
                if (prev1 < num1[i] && prev2 < num2[i]){
                    call1 = mp[i+1][0];
                }
                if (prev1<num2[i] && prev2<num1[i]){
                    call2 = 1 + mp[i+1][1];
                }
                mp[i][swapped] = min(call1,call2);
            }
        }
        return mp[0][0];
        //return dp(0,false,-1,-1);
    }
};
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