Lowest common ancestor P49809


Statement
 

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The lowest common ancestor (LCA) of two nodes x and y in a tree is the lowest (i.e. deepest) node that has both x and y as descendants, where we define each node to be a descendant of itself.

For instance, in the following tree, 5 is the LCA of 1 and 9, and 6 is the LCA of 1 and 0:

Write a function Tree lowest_common_ancestor (Tree t, int x, int y); that returns the node that corresponds to the LCA of x and y in a binary tree of integers. You can assume that t contains both x and y and that t does not contain repeated elements.

Most of the program is already writen for you. Download it! It reads several trees in preorder with leaves marked with −1 and, for each of these, reads severals pairs of values and prints their LCA. You just have to specify and implement the lowest_common_ancestor() function (and other helper functions, should you need them). Also, write a comment with the time efficiency of your algorithm.

Public test cases
  • Input

    2
    
    5 6 1 -1 -1 7 2 -1 -1 0 -1 -1 3 9 -1 -1 4 -1 -1
    
        1 9
        1 0
        6 3
        3 6
        5 5
        3 3
        5 0
        -1 -1
    
    5 2 3 -1 -1 8 -1 -1 -1
    
        3 8
        3 2
        3 5
        2 5
        8 5
        -1 -1
    

    Output

    5
    6
    5
    5
    5
    3
    5
    
    2
    2
    5
    5
    5
    
    
  • Information
    Author
    Jordi Petit
    Language
    English
    Official solutions
    C++
    User solutions
    C++ Python