[Leetcode] Binary tree-- 437. Path Sum III

Posted 2020-09-30 安新

You are given a binary tree in which each node contains an integer value.

Find the number of paths that sum to a given value.

The path does not need to start or end at the root or a leaf, but it must go downwards (traveling only from parent nodes to child nodes).

The tree has no more than 1,000 nodes and the values are in the range -1,000,000 to 1,000,000.

Example:

root = [10,5,-3,3,2,null,11,3,-2,null,1], sum = 8

      10
     /      5   -3
   / \      3   2   11
 / \   3  -2   1

Return 3. The paths that sum to 8 are:

1.  5 -> 3
2.  5 -> 2 -> 1
3. -3 -> 11

Solution:

1.use iterative way; BFS;  use hashmap to store each node‘s previous path sum and its number (each previous path start from the root to itself, and each children node to itself)

 1  if not root:
 2             return 0
 3     
 4         ans = 0
 5         innerHash= {root.val:1}
 6         d = []
 7         d.append((root, innerHash))
 8         
 9         while (len(d)):
10             nodeInfo = d.pop(0)
11             node = nodeInfo[0]
12             innerHash = nodeInfo[1]
13             
14             if sum in innerHash:
15                 ans += innerHash[sum]
16             #print ("get sum: ", node.val, innerHash)
17             if node.left:
18                 tmpHash = defaultdict(lambda: 0)
19                 for k in innerHash:
20                     tmpHash[k+node.left.val] =  innerHash[k]
21                 tmpHash[node.left.val] += 1
22                 d.append((node.left, tmpHash))
23             if node.right:
24                 tmpHash = defaultdict(lambda: 0)
25                 for k in innerHash:
26                     tmpHash[k+node.right.val] = innerHash[k]
27                     
28                 tmpHash[node.right.val] += 1   
29                 d.append((node.right, tmpHash))
30                 
31         return ans

 

2.  use recursive way 

1   def find_paths(root, target):
2             if root:
3                 return int(root.val == target) + find_paths(root.left, target-root.val) + find_paths(root.right, target-root.val)
4             return 0
5    
6         if root:
7             return find_paths(root, sum) + self.pathSum(root.left, sum) + self.pathSum(root.right, sum)
8         return 0

 

Extensions by myself: 

if we want to print all the paths.

#record each node path from "root", if current path sum is bigger than the given sum, pop the first element in the list ("root")
# get the continuous subsum; considering there is ‘0‘ element or negative element, so there is possible multiple indexes returned.

 

 1         def getSubSum(innerLst, s):
 2             tmpS = 0
 3             lstInd = []
 4             for i in range(len(innerLst)-1, -1, -1):
 5                 tmpS += innerLst[i]                    
 6                 if tmpS == s:
 7                     lstInd.append(i)          #return the start index that make the sum of element equal to s from start index to the end
 8             return lstInd
 9         
10         if root is None:
11             return 0
12         d = []
13         s = sum
14         innerLst = [root.val]
15         ansLst = []
16         d.append((root, innerLst))
17         
18         while (len(d)):
19             #pop
20             nodeInfo = d.pop(0)
21             node = nodeInfo[0]
22             innerLst = nodeInfo[1]
23             #print ("node: ", node.val, innerLst)
24             sumPath = 0
25             for e in innerLst:
26                 sumPath+=e
27 
28             lstInd = getSubSum(innerLst, s)
29             #print ("get sum: ", innerLst, lstInd)
30             for startInd in lstInd:
31                 ansLst.append(innerLst[startInd::])        
32 
33             #print ("updated: ", node.val, innerLst)
34             if node.left:
35                 d.append((node.left, innerLst + [node.left.val]))
36             if node.right:
37                 d.append((node.right, innerLst + [node.right.val]))
38         #print ("ans: ", ansLst)
39         #return ansLst
40         return len(ansLst)