Smallest String Starting From Leaf in Python

Suppose we have the root of a binary tree, each node is containing a value from 0 to 25 , which are representing the letters 'a' to 'z': a value of 0 represents 'a', a value of 1 represents 'b', and so on. We have to search the lexicographically smallest string that starts at a leaf of this tree and finishes at the root. So if the tree is like −

Then the output will be “adz” as the sequence is [0,3,25]

To solve this, we will follow these steps −

• Define a dfs traversal method as follows

• if node is not null, then

  • insert node value as a character into A

  • if node has no left and right child, then

    • ans := minimum of ans and A elements as string in reversed form

    • delete the last element from A

    • return

  • perform dfs(left of node, A)

  • perform dfs(right of node, A)

  • Delete last element from A

  • return

• The actual method will be like −

• ans := “~”

• call dfs(root, an empty array as A)

• return ans

Let us see the following implementation to get better understanding −

Example

 Live Demo

class TreeNode:
   def __init__(self, data, left = None, right = None):
      self.data = data
      self.left = left
      self.right = right
def insert(temp,data):
   que = []
   que.append(temp)
   while (len(que)):
      temp = que[0]
      que.pop(0)
      if (not temp.left):
         if data is not None:
            temp.left = TreeNode(data)
         else:
            temp.left = TreeNode(0)
         break
      else:
         que.append(temp.left)
      if (not temp.right):
         if data is not None:
            temp.right = TreeNode(data)
         else:
            temp.right = TreeNode(0)
         break
      else:
         que.append(temp.right)
def make_tree(elements):
   Tree = TreeNode(elements[0])
   for element in elements[1:]:
      insert(Tree, element)
   return Tree
class Solution(object):
   def smallestFromLeaf(self, root):
      self.ans = "~"
      self.dfs(root,[])
      return self.ans
   def dfs(self, node, A):
      if node:
         A.append(chr(node.data + ord('a')))
         if not node.left and not node.right:
            self.ans = min(self.ans, ''.join(reversed(A)))
            A.pop()
            return
      self.dfs(node.left,A)
      self.dfs(node.right,A)
      A.pop()
      return
root = make_tree([25,1,3,1,3,0,2])
ob = Solution()
print(ob.smallestFromLeaf(root))

Input

[25,1,3,1,3,0,2]

Output

adz