Need help with algorithm analysis

Please help me to understand the attached questions.

Proof by Contradiction

Prove the following fact (give a proof by contradiction): There do not exist constants N > 0 and C > 0 such that ∀n ≥ N ,n^2 ≤ C*n

Prove that the big-O relationship is transitive

Prove that the big-O relationship is transitive (give a direct proof). That is, if f(n), g(n) and h(n) are positive-valued functions: if f(n) is Ο(g(n)) and g(n) is Ο(h(n)) then f (n) is Ο(h(n))

Child/Sibling implementation

Child/sibling implementation for following tree/graph!

Divide and Conquer Binary Tree

Consider an n-node complete binary tree T, where n=2^d - 1 for some d. Each node v of T is labeled with a real number x_v. You may assume that the real numbers labeling the nodes are all distinct. A node v of T is a local minimum if the label x_v is less than the label x_w for all nodes w that are joined to v by an edge. You ...continues

C++ reverse integer using recursion

I need a recursive function that accepts an integer and returns its reverse. for example int reverse( int n ); int main() { int n; n = reverse (123) ; // this returns 321 } I can do this easily without recursion but I have to use recursion. Thank you.

Data structures C++

The free newString() takes string objects strA and strB as arguments. For its action, newString() compares the string by using < and returns the concatenation of the arguments, with the lesser sring coming first. a) give a function prototype for newString() b)Give the implementation for newString() c) The main program has the ...continues

Data Structures C++

Write a program that generates an array of 10 random integers in the range from 0 to 999. Output array using the template function writeArray(), and then call the function bubbleSort() to sort the list. Output the sorted list.

Software Algorithms and Implementation

Please see the attached file. Give the order of each of the following functions. TA(n) = 200(n +4)3 TB(n)= n4 + 300n3log2(n) TC(n)=(2n +3)2log3(n) Suppose that each is the time efficiency function of an implementation of the same function (TA(n) for implementation A, and so on). Which of the implementations (A, B or C) ...continues

Data Structures + C++ STL

Give the value of v.size() after executing each of the following statements: (Be sure to include the code used to execute the statements. One program will be fine to execute all statements, no need to write multiple programs.) vector v(25); v.push_back(-4); v.resize(40); m = v.back(); v.pop_back();