Category: Technology

Binary Tree is the most often used Data structure in the programming world and is also the basis of other complex data structures. So as a Computer Science student, it is very important to understand it thoroughly. The following paragraph is quoted by Standford Univ.’s Website explaining Binary Tree:

A binary tree is made of nodes, where each node contains a “left” pointer, a “right” pointer, and a data element. The “root” pointer points to the topmost node in the tree. The left and right pointers recursively point to smaller “subtrees” on either side. A null pointer represents a binary tree with no elements — the empty tree. The formal recursive definition is: a binary tree is either empty (represented by a null pointer), or is made of a single node, where the left and right pointers (recursive definition ahead) each point to a binary tree.

Continue reading “Basic Operations on Binary Tree”

The problem is:
Describe a Θ(n lg n)-time algorithm that, given a set S of n integers and another integer x, determines whether or not there exist two elements in S whose sum is exactly x.
Solution:
1.Sort the elements in S using merge sort.
2.Remove the last element from S. Let y be the value of the removed element.
3.If S is nonempty, look for z= x – y in S using binary search.
4.If S contains such an element z, then STOP, since we have found y and z such that x= y+ z. Otherwise, repeat Step 2.
5.If S is empty, then no two elements in S sum to x.
Step 1 takesΘ(n lg n) time. Step 2 takes Θ(1) time. Step 3 requires at most lg n time. Steps 2–4 are repeated at most n times. Thus, the total running time of this algorithm isΘ(n lg n). The following is my implement code:

Continue reading “Notes of Introduction to Algorithm(Exercise 2.3.7)”