**Question:** Write a Python function to find the longest increasing subsequence of a given list of integers. The subsequence should be non-consecutive, meaning the elements should not be adjacent in the original list. For example, for the input [1, 5, 3, 2, 6, 4, 8], the longest increasing subsequence is `[1, 3, 6, 8]. Your function should return this subsequence.
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- In Clojure In the following expression, there are three missing symbols (marked with underscores). (defn length [l] (if (empty? l) _ ( _ 1 ( _ (rest l))))) We want length to be a function which returns the number of elements in a list. Assume we are writing this function definition using recursion, what should be filled in in each of these underlined blanks?Complete the below function which takes the coefficients of a polynomial P(x) as a tuple, and a list of values, and returns a list of computed values of P(x). Note that P() can be of any order. For example, P((2,-1,1), [1,2,3]) shall compute P(x) for x=1,2,3P(x)=2x^2 -x +1where x^2 denotes the square of x. Hence, the function must return [2,7,16], because P(1) is 2, P(2) is 7, and P(3) is 16.Python Please Define a function max_run(lst: list) -> int to find the maximum run in a list. A run is a subsequence with identifical values. For example, in [1, 1, 2, 2, 3, 4, 4, 4, 2, 4, 4], the runs are [1, 1], [2, 2], [3], [4, 4, 4], [2], and [4, 4]. The longest run is [4, 4, 4], which has 3 elements. max_run([1, 1, 2, 2, 3, 4, 4, 4, 2, 4, 4]) should return 3. max_run([]) == 0, max_run([1, 2, 3]) = 1, and max_run([1, 2, 1, 1]) = 2.
- Provide an explanation that justifies the running time of each function in terms of n, where n is the number of students in the list. You can assume the name of each student is of length O(1). HERE ARE THE FUNCTIONS FOR YOU TO EXPLAIN THE RUNNING TIME OF: FUNCTION 1: bool insert_student(int id, char name[], struct slist* lst) { char* studentName = find_student(id, lst); if (studentName == NULL) { // no student with the given id is found, // so we can perform insertion here // creating a new student node struct snode* new_node = (struct snode*) malloc(sizeof(struct snode*)); new_node->id = id; new_node->name = (char*) malloc(strlen(name)*sizeof(char)); strcpy(new_node->name, name); new_node->next = NULL; // if the first node is null if (lst->front == NULL) { lst->front = new_node; } else { struct snode* prevNode = NULL; struct snode* nextNode = lst->front; bool is_node_inserted = false; do { if (id < nextNode->id) { if (prevNode == NULL) { // new…Consider the following problem: You are given a list of integers. Write a Python function that finds the longest increasing subsequence in the list. A subsequence is considered increasing if the elements are in ascending order, but they may not necessarily be contiguous. Your function should return the length of the longest increasing subsequence. For example, given the list [3, 4, 2, 8, 10, 5, 1], the longest increasing subsequence is [3, 4, 8, 10], so the function should return 4. Provide the implementation of the function step by step.Write a function verifsort that accepts a list as a parameter, check if the list elements are sorted and returns: 1 - if the list is sorted in ascending order, 2 – if the list is sorted in descending order, and 0 – if the list is not sorted. Write a function listsort which accepts a list as a parameter, and sorts it in ascending order. You can use any standard sorting algorithm, but don’t use built-in sort methods and functions. The function must sort and return the list. Write a script that asks user to enter 10 integer numbers, creates a list from those numbers, then calls verifsort function to detect if this list is sorted, prints message (list is sorted or list is not sorted) and if it’s not sorted then calls listsort function and prints the sorted list after listsort
- Question 2: Write a function that takes a list of distinct integers l, and an integer k. Your function then finds the index of the integer in l, whose removal from l results in a list whose sum is k. For example, given [3,6,4,1,5,2] and 18, your function should return index 0, which corresponds to 3 in the list. Because, when 3 is removed from the list, the sum of the remaining list [6,4,1,5,2] is 18. You can assume that the given problem is always solvable. """ def removeOne(l, k):write a Python function that takes in a list of integers and returns maximum and minimum values in the list as a tuple. Note (Your function MUST NOT do more than one pass on the list., you are not allowed to use built-in min and max functions.) What is the time complexity of your function (i.e., Big-oh)? max, min = find_max_min(my_list):Rewrite the Binary search function in the textbook to use a generic type for the array elements. Test the function with arrays of int, double, and string values. *When using test arrays make sure elements are stored in ascending sorted order*
- in F# (F sharp) Write an function findMatches that takes a string and a list of tuples as arguments. Each element of the list will be a tuple consisting of a string and an int. Find all of the tuples for which the string matches the first argument and collect all of the corresponding integers. Your final result should be the collected integers sorted in ascending order. For example, if the string argument is "A" and the list is [("A",5); ("BB",6); ("AA",9); ("A",0)], your function should return the list [0;5]. You may use the List.sort function to produce your final result.In F# (F sharp) Write an function findMatches that takes a string and a list of tuples as arguments. Each element of the list will be a tuple consisting of a string and an int. Find all of the tuples for which the string matches the first argument and collect all of the corresponding integers. Your final result should be the collected integers sorted in ascending order. For example, if the string argument is "A" and the list is [("A",5); ("BB",6); ("AA",9); ("A",0)], your function should return the list [0;5]. You may use the List.sort function to produce your final result. Important: Do not use F# system functions or methods (such as map, max or filter, etc). Examples in F# Interactive: > findMatches "A" [("A",5); ("BB",6); ("AA",9); ("A",0)];;val it : int list = [0; 5]> findMatches "BB" [("A",5); ("BB",6); ("AA",9); ("A",0)];;val it : int list = [6]> findMatches "X" [("A",5); ("BB",6); ("AA",9); ("A",0)];;val it : int list = []> findMatches "A" [];;val it : int list = []…Do not use 2d lists, sets, dicts, arrays or recursion. Code in Python. Write the function destructiveRemoveRepeats(L), whichtakes a list L and destructively returns a new list in which any repeating elements in L are removed. Thus, this function should directly modify the provided list to not have any repeating elements. Since this is a destructive function, it should not return any value at all (so, implicitly, it should return None). For example: L = [1, 3, 5, 3, 3, 2, 1, 7, 5] destructiveRemoveRepeats(L) assert(L == [1, 3, 5, 2, 7])