T(1) = 1 T(n)= T(n - 1) + n² , n > 1
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Find the recursive equation. use telescoping method, transformations and Verify your answer
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- def sum ( lst ): """ Sums a list of numbers .""" if len ( lst ) == 0: return 0 return lst [0] + sum ( lst [1:]) def factorial ( number ): """ Returns the factorial value of any number """ if (( number == 0) or ( number == 1)): return 1 else : return number * factorial ( number - 1) Write down a tail recursive implementation of the function sum in python language. You can use the helper function in your solution. Write down a tail recursive implementation of the function factorial in python language.Using C language, trace this: void trace(int x, int *y, int z) {x = 1; *y=2;z=4;printf("%2d %2d %2d\n", x, *y, z);}main() {int x=1, y=3,z=4;clrscr();printf("%2d %2d %2d\n",x,y,z);trace(y,&x,z);printf("%2d %2d %2d\n",x,y,z);trace(x,&z,y);printf("%2d %2d %2d\n",x,y,z);trace(z,&y,x);printf("%2d %2d %2d\n",x,y,z);getch();return 0; }(c)#include<sFactorial of a number is defined as: n! = n(n-1)(n-2)(n-3)...(2)(1) For example, 4! = 4*3*2*1 The n! can be written in terms of (n-1)! as: n! = n* (n-1)! (n-1)! = (n-1)*(n-2) ! and so forth. Thus, in order to compute n!, we need (n-1)!, to have (n-1)!, we need (n-2)! and so forth. As you may immediately notice, the base case for factorial is 1 because 1! = 1. Write a program that uses a recursive function called factorial that takes an integer n as its argument and returns n! to the main. C++ PLEASE
- Analyze the below code carefully and figure out what each fragment is doing.i)public void func (Tree root){func(root.left);func(root.right);cout<< root.data;}ii)public void func(Tree root){cout <<root.data;func(root.left);func(root.right);}Full explan pleaseComplete the following recursive method for computing the factorial of an integer. Assume that n is greater than or equal to 0. a. result = n * factorial(n - 1)b. result = n * factorial(n)c. result = factorial(n - 1)d. result = (n - 1) * factorial(n)e. result = (n - 1) * factorial(n - 1)
- In a contrapositive statement, a user implements a line mentioning values with a correlation of Q -> P, if Q is always P then what is -Q always equivalent to?Example: Enter an integer = 75 Smallest divisor is = 3Celebrity problem A celebrity among a group of n people is a person who knows nobody but is known by everybody else. The task is to identify a celebrity by only asking questions to people of the form: ”Do you know him/her?” Solution Select two people from the group given, say, A and B, and ask A whether A knows B. If A knows B, remove A from the remaining people who can be a celebrity; if A doesn’t know B, remove B from this group. Solve the problem recursively for the remaining group of people who can be a celebrity Which design strategy does the following solution use? A-)Decrease-by-a-constant factor algorithm B-)Variable-size-decrease algorithm C-)Decrease-by-a-constant algorithm D-)Divide-and-Conquer
- Explain the flow of the code. See attached photo for the problem. (This is not graded) int skip(int n, int start_pos, int end_pos) { node* currnode = head; node* prevnode = NULL; int delpos = 0; int count = 0; int pos = start_pos; while (currnode != NULL) { count++; if (pos > end_pos){ return delpos; } if (count == pos){ delpos++; if (prevnode == NULL){ currnode = currnode->next; removeHead(); head = currnode; } else{ prevnode->next = currnode->next; if (currnode == tail) { tail = prevnode; } node* rem = currnode; currnode = currnode->next;…Algorithm design with sorting. Each of n users spends some time on a social media site. For each i = 1, . . . , n, user i enters the site at time ai and leaves at time bi ≥ ai. You are interested in the question: how many distinct pairs of users are ever on the site at the same time? (Here, the pair (i, j) is the same as the pair (j, i)).Example: Suppose there are 5 users with the following entering and leaving times: Then, the number of distinct pairs of users who are on the site at the same time is five: these pairs are (1, 2), (1, 3), (2, 3), (4, 6), (5, 6). (Drawing the intervals on a number line may make this easier to see).(a) Given input (a1 , b1),(a2 , b2), . . . ,(an, bn) as above in no particular order (i.e., not sorted in any way), describe a straightforward algorithm that takes Θ(n2)-time to compute the number of pairs of users who are ever on the site at the same time, and explain why it takes Θ(n2)-time. [We are expecting pseudocode and a brief justification for its…What happens when a programmer attempts to access a node's data fields when the node variable refers to None? How do you guard against it? *PYTHON