1, given your understanding of the big oh notation and how it can be applied to the different sorting algorithms, discuss how this knowledge will affect your choice for the most appropriate algorithm for a given problem. if two algorithms have the same complexity in terms of the big oh notation, does that mean they both will perform the same for all problems. support your answers with examples
2 ,compare the two implementations for binary trees: linked lists vs. arrays. discuss the pros and cons for each approach considering the key operations you need to perform for these trees including the different types of traversals.
3 four of the most commonly used sorting algorithms, the selection sort, the bubble sort, the merge sort, and the quick sort, have been presented to you. do some research and post three other sorting algorithms along with detailed analysis in terms of the key operations performed in these algorithms, the time efficiency, the space efficiency and perform a quick comparison among these algorithms identifying when you should pick which algorithm for a particular problem.

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We as humans write math expression in infix notation, e. g. 5 + 2 (the operators are written in-between the operands). in a computer’s language, however, it is preferred to have the operators on the right side of the operands, i. e. 5 2 +. for more complex expressions that include parenthesis and multiple operators, a compiler has to convert the expression into postfix first and then evaluate the resulting postfix. write a program that takes an “infix” expression as input, uses stacks to convert it into postfix expression, and finally evaluates it. it must support the following operations: + - / * ^ % (example infix expression: (7 - 3) / (2 + 2)postfix expression: 7 3 - 2 2 + /result: 1guidelines: 1. you will need to use stacks in three placesa. one for the parenthesis check [char stack]b. one during infix to postfix [char stack]c. one during evaluation [int stack]for a and b above, you can use same array and same push, pop method as both ofthem are char. but for evaluation you have int stack and you might consider to createanother push pop method to handle it. maybe push_int, pop_int, etc. or find otherstrategy to utilize existing push pop method2. you can create a function for obtaining operator priority. that function should take anoperator as input and return its priority as an integer. this function will you a lot andreduce repeated code3. during evaluation you will need to convert char into integer. example for single digit: char c = '5'; int x = c - '0';

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