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Day-25_Uncrossed_Lines.py
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Day-25_Uncrossed_Lines.py
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'''
We write the integers of A and B (in the order they are given) on two separate horizontal lines.
Now, we may draw connecting lines: a straight line connecting two numbers A[i] and B[j] such that:
A[i] == B[j];
The line we draw does not intersect any other connecting (non-horizontal) line.
Note that a connecting lines cannot intersect even at the endpoints: each number can only belong to one connecting line.
Return the maximum number of connecting lines we can draw in this way.
Example 1:
Input: A = [1,4,2], B = [1,2,4]
Output: 2
Explanation: We can draw 2 uncrossed lines as in the diagram.
We cannot draw 3 uncrossed lines, because the line from A[1]=4 to B[2]=4 will intersect the line from A[2]=2 to B[1]=2.
Example 2:
Input: A = [2,5,1,2,5], B = [10,5,2,1,5,2]
Output: 3
Example 3:
Input: A = [1,3,7,1,7,5], B = [1,9,2,5,1]
Output: 2
Note:
1 <= A.length <= 500
1 <= B.length <= 500
1 <= A[i], B[i] <= 2000
'''
class Solution:
def maxUncrossedLines(self, A: List[int], B: List[int]) -> int:
len_a = len(A)
len_b = len(B)
dp = [[0 for _ in range(len_a+1)] for _ in range(len_b+1)]
for i in range(1, len_b+1):
for j in range(1, len_a+1):
if A[j-1] == B[i-1]:
if (dp[i-1][j] == dp[i][j-1]):
dp[i][j] = dp[i-1][j-1] + 1
else:
dp[i][j] = max(dp[i-1][j],dp[i][j-1])
else:
dp[i][j] = max(dp[i-1][j],dp[i][j-1])
return dp[len_b][len_a]