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find_max_path_sum.py
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96 lines (78 loc) · 2.38 KB
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'''
Find max path sum
Wrie a function that takes a Binary Tree and returns its max path sum.
Input:
1
/ \
2 3
/ \ / \
4 5 6 7
Output: 18
Output explanation: 5 -> 2 -> 1 -> 3 -> 7
Input:
-1
/ \
-2 3
/ \ / \
-4 -5 2 5
Output: 10
Output explanation: 2 -> 3 -> 5
=========================================
Traverse the tree and in each node compare create a new path where the left and right max subpaths are merging in the current node.
Time Complexity: O(N)
Space Complexity: O(N) , because of the recursion stack (but this is the tree is one branch), O(LogN) if the tree is balanced.
'''
############
# Solution #
############
# import TreeNode class from tree_helpers.py
from tree_helpers import TreeNode
def max_path_sum(tree):
return find_max_path_sum(tree)[0]
def find_max_path_sum(node):
if node is None:
return (0, 0)
# get the result from the left subtree
left_result = find_max_path_sum(node.left)
# get the result from the right subtree
right_result = find_max_path_sum(node.right)
# create a new path by merging the max left and right subpaths
current_path = left_result[1] + node.val + right_result[1]
# find the max path till now, comparing the new path, max path from the left and right subtree
max_path = max(left_result[0], current_path, right_result[0])
# find the max subpath, min value for a subpath sum is 0
max_subpath = max(left_result[1] + node.val, right_result[1] + node.val, node.val, 0)
return (max_path, max_subpath)
###########
# Testing #
###########
# Test 1
# Correct result => 18
tree = TreeNode(1, TreeNode(2, TreeNode(4), TreeNode(5)), TreeNode(3, TreeNode(6), TreeNode(7)))
print(max_path_sum(tree))
# Test 2
# Correct result => 10
tree = TreeNode(-1, TreeNode(-2, TreeNode(-4), TreeNode(-5)), TreeNode(3, TreeNode(2), TreeNode(5)))
print(max_path_sum(tree))
# Test 3
'''
1
/ \
7 3
/ \ / \
-4 -5 6 2
'''
# Correct result => 17 (7 -> 1 -> 3 -> 6)
tree = TreeNode(1, TreeNode(7, TreeNode(-4), TreeNode(-5)), TreeNode(3, TreeNode(6), TreeNode(2)))
print(max_path_sum(tree))
# Test 4
'''
1
/ \
2 3
/ \ / \
-4 -5 -2 -3
'''
# Correct result => 6 (2 -> 1 -> 3)
tree = TreeNode(1, TreeNode(2, TreeNode(-4), TreeNode(-5)), TreeNode(3, TreeNode(-2), TreeNode(-3)))
print(max_path_sum(tree))