CSCI 675 - P3

What is the worst case time complexity for search, insert and delete operations in a general Binary Search Tree? Answers: O(log n) for search ; O(n) for delete and insert O(n) for all O(log n) for all O(log n) for search and insert; O(n) for delete Response Feedback: Students shall be able to trace a binary search tree, do insert, delete algorithms, and their run time. May study at http://www.geeksforgeeks.org/binary-search-tree-data-structure/

O(n) for all

Suppose we run Dijkstra's single source shortest-path algorithm on the following edge weighted directed graph with vertex P as the source. In what order do the nodes get included into the set of vertices for which the shortest path distances are finalized? Answers: P, Q, T, R, U, S P, Q, R, U, S, T P, Q, R, S, T, U P, Q, R, U, T, S Response Feedback: Student needs to know types of graph, the representation of a graph, the algorithms related to the graph. May study at http://www.geeksforgeeks.org/graph-data-structure-and-algorithms/

P, Q, R, U, S, T

Which of the following should be virtual if a base class uses dynamic memory allocation? Answers: The destructor The copy constructor all public functions The constructor Response Feedback: Students shall understand the destructor, constructor, and the call order when create an object and when destroy an object

The destructor

Which of the following is True about AVL tree? Answers: The worst time for insert is O(n) The worst time for delete is O(n) The worst time for insert and delete are both O(log n) The worst time for insert and delete are both O(n) Response Feedback: Student shall know AVL insertion, rotation, and property. May study at http://www.geeksforgeeks.org/avl-tree-set-1-insertion/ May use to https://www.cs.usfca.edu/~galles/visualization/AVLtree.html visualize.

The worst time for insert and delete are both O(log n)

Let G be a weighted undirected graph and e be an edge with maximum weight in G. Suppose there is a minimum weight spanning tree in G containing the edge e. Which of the following statements is always TRUE? Answers: There exists a cycle in G having all edges of maximum weight All edges in G have the same weight Edge e cannot be contained in a cycle. There exists a cutset in G having all edges of maximum weight. Response Feedback: Student needs to know types of graph, the representation of a graph, the algorithms related to the graph. May study at http://www.geeksforgeeks.org/graph-data-structure-and-algorithms/

There exists a cutset in G having all edges of maximum weight.

What is the output of the following code if user typed: 1 2 3 then hit Enter Key? (there are spaces between numbers) Scanner input = new Scanner(System.in); int x = input.next(); System.out.println(x); Answers: There is a syntax error 1 There is run time error 123

There is a syntax error

What is the output of the following piece of code? int i = 0; do{ cout << i << ", "; }while (++i <= 5) Answers: 6, 5, This is an infinity loop, nothing output There is a syntax error 1, 2, 3, 4, 5, Response Feedback: Students shall know the syntax and semantics of for loop, while loop, and do while loop.

There is a syntax error

What will be the output after the execution of the following piece of code? char grade = 'a'; switch(grade){ case 'A', case 'a': cout <<"Excellent"; break; case 'B', case 'b': cout << "Good"; break; case 'C', case 'c': cout << "Average"; break; default: cout << "Work harder"; break; } Answers: Excellent Good Average Work harder There is a syntax error Response Feedback: Students shall pay attention to the syntax of if, if-else, if-esel if -else, and switch structure

There is a syntax error

Which of the following is the negation of [∀ x, α → (∃y, β → (∀ u, ∃v, y))]? Answers: [∀ x, ¬α → (∃y, ¬β → (∀u, ∃ v, ¬y))] [∃ x, α → (∀y, β → (∃u, ∀ v, y))] [∃ x, α → (∀y, β → (∃u, ∀ v, ¬y))] [∃ x, α ʌ (∀y, β ʌ (∃u, ∀ v, ¬y))] Response Feedback: Study the Quiz questions and understand the answers http://www.geeksforgeeks.org/propositional-and-first-order-logic-gq/

[∃ x, α ʌ (∀y, β ʌ (∃u, ∀ v, ¬y))]

Which of the following method is NOT a method in Double class? Answers: static Diouble valueOf(double) static Diouble valueOf(String) double valueOf(String) String toString()

double valueOf(String)

Which of the following doesn't have 5 as output? Answers: int x = 5; cout << ++x; cout << 40%7; int x = 5; cout << x++; cout << 40/7; Response Feedback: The students shall know operators +, -, *, /, %, ++, --, and their precedence.

int x = 5;

BigInteger class belongs to which of the following package? Answers: java.lang java.math java.io java.util Response Feedback: Students shall know the often used classes and their packages. For instance, System, Math, String, Scanner, Integer (and other seven wrapper classes), BigInteger, BigDecimal.

java.math

Prove that 1 cross times 2 plus 2 cross times 3 plus... plus n cross times left parenthesis n plus 1 right parenthesis equals fraction numerator n left parenthesis n plus 1 right parenthesis left parenthesis n plus 2 right parenthesis over denominator 3 end fraction If we proof by mathematical induction, what will be the assumption for the inductive step? Answers: 1 cross times left parenthesis 1 plus 1 right parenthesis equals fraction numerator 1 left parenthesis 1 plus 1 right parenthesis left parenthesis 1 plus 2 right parenthesis over denominator 3 end fraction 1 cross times 2 plus 2 cross times 3 plus... plus k cross times left parenthesis k plus 1 right parenthesis plus left parenthesis k plus 1 right parenthesis cross times left parenthesis k plus 2 right parenthesis space equals space fraction numerator left parenthesis k plus 1 right parenthesis left parenthesis k plus 2 right parenthesis left parenthesis k plus 3 right parenthesis over denominator 3 end fraction k is positive integer and 1 cross times 2 plus 2 cross times 3 plus... plus k cross times left parenthesis k plus 1 right parenthesis equals fraction numerator k left parenthesis k plus 1 right parenthesis left parenthesis k plus 2 right parenthesis over denominator 3 end fraction 1 cross times 2 plus 2 cross times left parenthesis 2 plus 1 right parenthesis space equals space fraction numerator 2 left parenthesis 2 plus 1 right parenthesis left parenthesis 2 plus 2 right parenthesis over denominator 3 end fraction Response Feedback: Student shall know how to proof by mathematical induction and use mathematical induction to prove recurrence relation.

k is positive integer and 1 cross times 2 plus 2 cross times 3 plus... plus k cross times left parenthesis k plus 1 right parenthesis equals fraction numerator k left parenthesis k plus 1 right parenthesis left parenthesis k plus 2 right parenthesis over denominator 3 end fraction

A large union left parenthesis B large intersection C right parenthesis space equals Answers: left parenthesis A large intersection B right parenthesis space large union left parenthesis A large intersection C right parenthesis left parenthesis A large union B right parenthesis large intersection left parenthesis A large union C right parenthesis empty set B large union C large union A Response Feedback: Student shall know set operations and set identities

left parenthesis A large union B right parenthesis large intersection left parenthesis A large union C right parenthesis

In a depth-first traversal of a graph G with n vertices, k edges are marked as tree edges. The number of connected components in G is Answers: k k+1 n-k+1 n-k Response Feedback: Student needs to know types of graph, the representation of a graph, the algorithms related to the graph. May study at http://www.geeksforgeeks.org/graph-data-structure-and-algorithms/

n-k

What will the output in file data.txt after we execute the following Java program? Answers: nothing in file HelloWorld Compile error in line 5 Hello World

nothing in file

If x and y are both even, then x + y is even. Proof: Assume that x = 2m, y = 2n, then x + y = 2 (m + n) which is even. The above proof method is: Answers: direct proof proof by contrapositive proof by mathematical induction proof by contradiction Response Feedback: Student shall know five proof skills. Direct proof, proof by contradiction, proof by cases, proof by contrapositive, and proof by mathematical indcution

direct proof

Suppose we have the following definition: vector<int> vec, vec1; //use push_back to put 10 values into vec vector<int>::iterator p = vec.begin(); vector<int>::const_iterator q = vec.begin(); Which of the following expressions is NOT legal? Treat the effect of these as non-cumulative. Answers: *p = 1; *q = 1; q = vec1.end(); p = vec.end (); Response Feedback: Students shall know how to use iterators

*q = 1;

Suppose that outFile is an ofstream connected to file named "output.txt". What will be output to output.txt file due to following code? int x = 5; outFile.setf(ios::showpos); outFile << x; Answers: 5 +5 -5 5.0 Response Feedback: students shall know how to use iomanip library. The ofstream can use setf with argument ios::fixed, ios::showpos, ios::showpoint. Also know that setprecision function and precision member functon

+5

The two linear equations above can be used to express gcd(225, 60) as a linear combination of 225 and 60: 15 = C · 225 + D · 60 What is the correct value for C? Answers: 1 -4 4 -1 Response Feedback: Student needs to know Euclidean Algorithm, Extended Euclidean Algorithm, and how to calculate the multiplicative inverse

-1

What is the output of the following Java code? Answers: compile error at line 6 compile error at line 3 1 compile error at line 7

1

The preorder traversal sequence of a binary search tree is 30, 20, 10, 15, 25, 23, 39, 35, 42. Which one of the following is the postorder traversal sequence of the same tree? Answers: 15, 10, 25, 23, 20, 42, 35, 39, 30 10, 20 , 15, 23, 25, 35, 42, 39, 30 15, 20, 10, 23, 25, 42, 35, 39, 30 15, 10, 23, 25, 20, 35, 42, 39, 30 Response Feedback: Students shall be able to trace a binary search tree, do traversal, insert, delete algorithms, and their run time. May study at http://www.geeksforgeeks.org/binary-search-tree-data-structure/

15, 10, 23, 25, 20, 35, 42, 39, 30

Suppose that I have function void myswap(int& x, int& y){ int temp = x; x = y; y = temp; } what will be the output of the following code segment? int x = 5, y = 10; myswap(x, y); cout << x << ", " << y; Answers: There is a syntax error There is a run time error 10, 5 5, 10 Response Feedback: Students shall be able to write and use functions with pointer argument and can write and call functions that pass by reference

10, 5

What is the output of the following Java code? Answers: Compile error in line 6 Compile error in line 10 100 0

100

What is the output of the following Java progam? Answers: 2 Compile error in line 8 Run time except at line 8 99 Compile error in line 9

2

What is the output of the following code if user's input is 8? Answers: 2 There is a compile error in code 0 1

2

What is the output? Assume that the size of char is 1 byte and size of int is 4 bytes, and there is no alignment done by the compiler. #include<iostream> #include<stdlib.h> using namespace std; template<class T, class U> class A { T x; U y; static int count; }; int main() { A<char, char> a; A<int, int> b; cout << sizeof(a) << endl; cout << sizeof(b) << endl; return 0; } Answers: 6 12 2 8 8 8 There is a syntax error Response Feedback: Students shall know how to write and use template. Also know the size of each data type.

2

Solve each of the following recurrence equation with the given initial values. bn = bn−1 + 12bn−2. Initial values: b0 = −2, b1 = 20. Answers: a subscript 1 left parenthesis minus 4 right parenthesis to the power of n plus a subscript 2 3 to the power of n a subscript 1 4 to the power of n plus a subscript 2 left parenthesis minus 3 right parenthesis to the power of n 2 left parenthesis 4 right parenthesis to the power of n minus 4 left parenthesis minus 3 right parenthesis to the power of n 2 left parenthesis minus 4 right parenthesis to the power of n minus 4 left parenthesis 3 right parenthesis to the power of n Response Feedback: Student needs to know how to solve linear homogeneous recurrence relation

2 left parenthesis 4 right parenthesis to the power of n minus 4 left parenthesis minus 3 right parenthesis to the power of n

Assume that x has prime factorization 5 to the power of 4 cross times 11 squared cross times 13 cubed and y has prime factorization 3 cross times 7 cross times 11 cross times 13 cubed, what is the prime factorization of the product of x and y? Answers: 3 cross times 5 to the power of 4 cross times 7 cross times 11 squared cross times 13 cubed 3 cross times 5 cross times 7 cross times 11 cross times 13 3 cross times 5 to the power of 4 cross times 7 cross times 11 cubed cross times 13 to the power of 6 11 cross times 13 cubed Response Feedback: Student shall know the concept about prime factorization, greatest common divisor and least common multiple. Also know that factoring is a hard problem

3 cross times 5 to the power of 4 cross times 7 cross times 11 cubed cross times 13 to the power of 6

Breadth First Search (BFS) is started on a binary tree beginning from the root vertex. There is a vertex t at a distance four from the root. If t is the n-th vertex in this BFS traversal, then the maximum possible value of n is ___________ Answers: 31 32 16 15 Response Feedback: Students need to know all algorithms of a binary tree, including pre-order, in-order, and post order traverse, Bread first search and Depth first search. May study at http://www.geeksforgeeks.org/binary-tree-data-structure/

31

Consider a max heap, represented by the array: 40, 30, 20, 10, 15, 16, 17, 8, 4. Now consider that a value 35 is inserted into this heap. After insertion, the new heap is Answers: 40, 30, 20, 10, 15, 16, 17, 8, 4, 35 40, 35, 20, 10, 30, 16, 17, 8, 4, 15 40, 30, 20, 10, 35, 16, 17, 8, 4, 15 40, 35, 20, 10, 15, 16, 17, 8, 4, 30 Response Feedback: Student shall know heap algorithms, properties, insert, and delete. May study at http://www.geeksforgeeks.org/heap-data-structure/

40, 35, 20, 10, 30, 16, 17, 8, 4, 15

What is the output of the following code segment? int x = (int) 5.6789; System.out.println(x); Answers: 6 5 There is a run time error There is a compile error

5

What is the output of the following code? int *p = new int[3]; *p = 1; *(p+1) = 2; *(p+2) = 3; int result = 0; int * q = p; for(int i = 0; i < 3; i++){ result += *q; q++; } cout << result; Answers: 1 6 0 There is a syntax error Response Feedback: Students shall know dynamic array. How to declare and initialize it.

6

6 people line up for a wedding picture, how many different ways to do this? Answers: 6! / 2 6! 5! 6 Response Feedback: Student shall know sum and product rules, permutation and combination, and the inclusive and exclusive rule

6!

What is the output of the following Java progam? Answers: Compile error in line 7 true false Compile error in main function

true

What is the output of the following code? Answers: 21 There is a syntax error 0 9

9

What is the value of x after the execution of the following line of code? int x = (int) (Math.random()*100); Answers: 1 Syntax Error A random integer between 0 and 99, inclusive A random integer between 1 and 100, inclusive Response Feedback: Student shall know the methods in Math class. For instance, sqrt, pow, floor, ceil, random, etc

A random integer between 0 and 99, inclusive

Copy of What is the output? #include <iostream> using namespace std; class Test { static int count; int id; public: Test() { count++; id = count; cout << "Constructing " << id << endl; if(id == 3) throw 3; } ~Test() { cout << "Destructing " << id << endl; } }; int Test::count = 0; int main() { try { Test array[3]; } catch(int i) { cout << "Caught " << i << endl; } } Answers: Constructing 1 Constructing 2 Constructing 3 Destructing 1 Destructing 2 Caught 3 Constructing 1 Constructing 2 Constructing 3 Destructing 3 Destructing 2 Destructing 1 Caught 2 There is a syntax error Constructing 1 Constructing 2 Constructing 3 Destructing 2 Destructing 1 Caught 3 Response Feedback: Students shall know how exception is handled and also know the order constructor and destructor are called

Constructing 1

What is the output of the following code? Answers: Compile error in line 16 Compile error in line 15 Base::fun() called Derived::fun() called

Derived::fun() called

What is the output of the following Java program? Answers: Divide by zero error inside the finally block Divide by zero error inside the finally block 0, Divide by zero error inside the finally block

Divide by zero error

Which of the following is the head of copy constructor of Employee class? Answers: void Employee(const Employee& other) Employee(Employee& other) void Employee() void Employee(Employee& other) Employee() Employee(const Employee& other) Response Feedback: Students are required to know how to write big three: Copy constructor, Destructor, and Assignment Operator for a class

Employee(const Employee& other)

What is the output of the following Java program? Answers: Compile error in line 4 Compile error in line 6 Good Morning Compile error in line 5

Good Morning

Give the following simplified classes and code, what is the output of the last statement? class Pet{ public: virtual void print(); string name; private: }; class Dog:public Pet{ public: void print(); string breed; }; void Pet::print(){ cout << "My name is " << name << endl; } void Dog::print(){ Pet::print(); cout << ", My breed is " << breed << endl; } Dog dPtr; Pet pPtr; dPtr.name = "rover"; dPtr.breed = "Collie"; pPtr = pDog; pPtr->print(); Answers: Nothing will be printed. The last statement has syntax error My name is rover, My breed is Collie My name is rover , My breed is Collie Response Feedback: Student shall understand the polymorphism and sliced problem

Nothing will be printed. The last statement has syntax error

What is the worse case run time for following algorithm? CountDuplicatePairs This algorithm counts the number of duplicate pairs in a sequence. Input: a1, a2,...,an, where n is the length of the sequence. Output: count = the number of duplicate pairs. count := 0 For i = 1 to n For j = i+1 to n If ( ai = aj ), count := count +1 End-for End-for Return( count ) Answers: O left parenthesis n squared right parenthesis O left parenthesis n right parenthesis O left parenthesis n cubed right parenthesis O left parenthesis 1 right parenthesis Response Feedback: Student shall know big O notation. Also Big capital omega space a n d space B i g space capital theta. Be able to analyze the run time of a given algorithm.

O left parenthesis n squared right parenthesis

If we use binary search algorithm to search 5 4 8 9 21 15 19 20 25 28 32 35 36 48 52 for key 17, list the elements that will be compared with key in order of when the comparison happens Answers: cannot use binary search algorithm because the key is not in the array 20 9 15 19 cannot use binary search algorithm since the array to be searched is not sorted 1 8 15 Response Feedback: Students need to know how to apply linear search and binary search algorithms

cannot use binary search algorithm since the array to be searched is not sorted

Assume that I have a Student class, and I overloaded the operators >> and << for Student class. If I want to input a Student object from keyboard, which of the following code is correct? Assume the Student object variable name is s. Answers: cin >> s; cout << s; s >> info; Cannot do it Response Feedback: The student shall know how to oeverload operators +, -, *, /, >>, and <<. if it is needed

cin >> s;

Design a circuit from a description of the circuit in English. The output is 1 if all three inputs are 1 Answers: f left parenthesis x comma space y comma space z right parenthesis space equals space x y top enclose z space plus space top enclose x y z space plus space x top enclose y z f(x, y, z) = x + y + z f(x, y, z) = xy + yz + zx f(x, y, z) = xyz Response Feedback: Student shall be able to design a circuit

f(x, y, z) = xyz

Which one of the following hash functions on integers will distribute keys most uniformly over 10 buckets numbered 0 to 9 for i ranging from 0 to 2020? Answers: h left parenthesis i right parenthesis space identical to i squared space left parenthesis m o d space 10 right parenthesis h left parenthesis i right parenthesis space identical to i cubed space left parenthesis m o d space 10 right parenthesis h left parenthesis i right parenthesis space identical to left parenthesis 11 cross times i squared right parenthesis space left parenthesis m o d space 10 right parenthesis h left parenthesis i right parenthesis space identical to left parenthesis 12 cross times i squared right parenthesis space left parenthesis m o d space 10 right parenthesis Response Feedback: Students need to know hash with open addressing and separate chaining. May study at http://www.geeksforgeeks.org/data-structures/

h left parenthesis i right parenthesis space identical to i cubed space left parenthesis m o d space 10 right parenthesis

Consider the Node structure as following /* Node of a doubly linked list */ struct Node { int data; Node *next; // Pointer to next node in DLL Node *prev; // Pointer to previous node in DLL }; What will be the code for missing step in C++? // may need two lines of code /* Given a reference (pointer to pointer) to the head of a list and an int, inserts a new node on the front of the list. */ void push(struct Node** head_ref, int new_data) { /* 1. allocate new node */ /* 2. put in the data into new node */ /* 3. Make next of new node as head and previous as NULL */ /* 4. ____________________________ */ /* 5. move the head to point to the new node */ } Answers: (*head_ref)->prev = new_node; head_ref->prev = new_node; if(*head_ref != NULL) (*head_ref)->prev = new_node; if(head_ref != NULL) head_ref->prev = new_node; Response Feedback: Students shall know basic algorithms (insert after, insert in front, back, and delete) about double linked list. May Study at http://www.geeksforgeeks.org/doubly-linked-list/

if(*head_ref != NULL) (*head_ref)->prev = new_node;

/* Given a node prev_node, insert a new node after the given prev_node */ void insertAfter(Node* prev_node, int new_data) { if (prev_node == NULL) { cout << "the given previous node cannot be NULL" << endl; return; } Node* new_node =new Node; new_node->data = new_data; new_node->next = prev_node->next; ________________________ } Fill up the missing line Answers: prev_node->next = NULL; prev_node->next = new_node; prev_node = new_node -> next; prev_node = new_node; Response Feedback: Students shall know the linked list and how to implement it. May study at http://www.geeksforgeeks.org/data-structures/linked-list/

prev_node->next = new_node;

Consider the following C++ function: void fun(int n){ stack<int> s; while(n > 0){ s.push(n%2); n = n/2; } while(!s.empty()){ cout << s.top(); s.pop(); } } what dose this function do in general? Answers: print the binary representation of n in reverse order print the value of square root of n print the value of square root of n in reverse order print the binary representation of n Response Feedback: Student need to know the algorithm, implementation, and application for stack and queue. May study at http://www.geeksforgeeks.org/data-structures/

print the binary representation of n

Fibonacci sequence is defined as following: f subscript 1 space equals space 1 comma space f subscript 2 equals 1 comma space f subscript n space end subscript equals space f subscript n minus 1 end subscript plus f subscript n minus 2 end subscript space w h e n space n space greater or equal than 3. Write a recursive function, take positive integer n as input, return nth Fibonacci number. What is placed in _____________ int fibonacci(int n){ if(n == 1 || n == 2) _____________ return fibonacci(n-1)+fibonacci(n-2); } Answers: int result = 1; return 0; return 1; return 2; Response Feedback: Students shall be able to write and trace recursive algorithm

return 1;

The following propositional statement (P → (Q v R)) → ((P ^ Q) → R) is: Answers: a contradiction valid satisfiable but not valid Response Feedback: Students may study logic and practice at http://www.geeksforgeeks.org/propositional-and-first-order-logic-gq/

satisfiable but not valid

Which assignment statements will copy the value " toaster" into a string variable (str1)? Answers: strcpy(str1,"toaster"); str1 += toaster; str1 = toaster; str1 = "toaster"; Response Feedback: Students shall know the difference between C-string and string. Shall study the class string and related examples at http://www.cplusplus.com/reference/string/string/

str1 = "toaster";

Assume that char name[80] = "John Doe"; char nameCopy[80]; Whihc of the following assign "John Doe" to nameCopy? Answers: strcpy(name, nameCopy); nameCopy = name; name = nameCopy; strcpy(nameCopy, name); Response Feedback: Students shall know how to do C-string assignment, copy, comparison, query length, and concatenate.

strcpy(nameCopy, name);

Assume that I have a structure: struct Student{ string name; int id; double gpa; Student* next; }; Student *student = new Student; How to I assign the student gpa as 3.85? Answers: student-gpa = 3.95; student'gpa = 3.95; student->gpa = 3.95; student.gpa = 3.95; Response Feedback: Know how to write and use struct

student->gpa = 3.95;

By the law of Boolean Algebra, x top enclose y plus x y space equals Answers: top enclose x y y xy x Response Feedback: Student shall know basic Boolean operations, Boolean functions, and gates

x

Use the following selection sort to sort int array {2, 5, 3, 6, 4, 1}, Right after i is increased to 3, before the next outer loop, what is the array? void selectionSort(int arr[], int n) { int i, j, min_idx; // One by one move boundary of unsorted subarray for (i = 0; i < n-1; i++) { // Find the minimum element in unsorted array min_idx = i; for (j = i+1; j < n; j++) if (arr[j] < arr[min_idx]) min_idx = j; // Swap the found minimum element with the first element swap(&arr[min_idx], &arr[i]); } } Answers: {1, 5, 3, 6, 4, 1} {1, 2, 3, 4, 6, 5} {1, 2, 3, 6, 4, 5} {2, 5, 3, 6, 4, 1} Response Feedback: Student shall be able to trace and implement insertion sort and selection sort algorithm. May study at http://www.geeksforgeeks.org/

{1, 2, 3, 6, 4, 5}

Suppose that we use merge sort algorithm to sort the following array: {3, 6, 1, 7, 2, 8, 5, 4}. What will be the array right before the last call of merge? Answers: {1, 3, 6, 7, 2, 4, 5, 8} {2, 4, 5, 8, 1, 3, 6, 7} {3, 6, 1, 7, 2, 8, 4, 5} {1, 2, 3, 4, 5, 6, 7, 8} Response Feedback: Students shall understand the quick sort, merge sort, insertion sort, and selection sort. Also know their run time and the stability. May study at http://www.geeksforgeeks.org/

{1, 3, 6, 7, 2, 4, 5, 8}