<p>You are given two integer arrays <code>nums1</code> and <code>nums2</code>. We write the integers of <code>nums1</code> and <code>nums2</code> (in the order they are given) on two separate horizontal lines.</p>

<p>We may draw connecting lines: a straight line connecting two numbers <code>nums1[i]</code> and <code>nums2[j]</code> such that:</p>

<ul>
	<li><code>nums1[i] == nums2[j]</code>, and</li>
	<li>the line we draw does not intersect any other connecting (non-horizontal) line.</li>
</ul>

<p>Note that a connecting line cannot intersect even at the endpoints (i.e., each number can only belong to one connecting line).</p>

<p>Return <em>the maximum number of connecting lines we can draw in this way</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2019/04/26/142.png" style="width: 400px; height: 286px;" />
<pre>
<strong>Input:</strong> nums1 = [1,4,2], nums2 = [1,2,4]
<strong>Output:</strong> 2
<strong>Explanation:</strong> We can draw 2 uncrossed lines as in the diagram.
We cannot draw 3 uncrossed lines, because the line from nums1[1] = 4 to nums2[2] = 4 will intersect the line from nums1[2]=2 to nums2[1]=2.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums1 = [2,5,1,2,5], nums2 = [10,5,2,1,5,2]
<strong>Output:</strong> 3
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums1 = [1,3,7,1,7,5], nums2 = [1,9,2,5,1]
<strong>Output:</strong> 2
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums1.length, nums2.length &lt;= 500</code></li>
	<li><code>1 &lt;= nums1[i], nums2[j] &lt;= 2000</code></li>
</ul>

class Solution:
    def maxUncrossedLines(self, nums1: List[int], nums2: List[int]) -> int:
        '''
        Ideas
            1 4 2
          0 0 0 0 
        1 0
        2 0
        4 0
        '''
        
        nums1_index = defaultdict(list) # keep track of the indexes of each number
        nums2_index = defaultdict(list) # keep track of the index of each nmebr
        
        for i in range(len(nums1)):
            nums1_index[nums1[i]].append(i) 
        
        for i in range(len(nums2)):
            nums2_index[nums2[i]].append(i) 
        
        cache = {} 

        def dfs(index1, index2):
            if index1 >= len(nums1) or index2 >= len(nums2):
                return 0 
            if (index1, index2) in cache:
                return cache[(index1, index2)]
            num1 = nums1[index1]
            res1, res2 = 0,0 
            # use nums1[index1] 
            if len(nums2_index[num1]) > 0:
                i = 0
                newIndex2 = nums2_index[num1][i]+1 
                while newIndex2 <= index2 and i < len(nums2_index[num1]): 
                    newIndex2 = nums2_index[num1][i]+1 
                    i+=1
                print(index1, index2, newIndex2)
                if newIndex2 > index2:
                    res1 = dfs(index1+1, newIndex2) + 1
            
            # don't use nums1[index1]
            res2 = dfs(index1+1, index2) 
            cache[(index1, index2)] = max(res1, res2)
            return cache[(index1, index2)]
        
        return dfs(0, 0)
24200