Consider the worst-case scenario and for each questions: Feel free to use O(1) instead of specific constants when analyzing the algorithms a. State the size of the input in big-Oh. For example, if the input to an algorithm is an array of size k, then the input size is n E O(K) b. Derive the cost function for the algorithm. Be sure to show your work c. State the complexity of the algorithm in Big-Oh. The complexity MUST be stated in terms of input-size d. Prove that the derived cost function is in the stated order (big-Oh) Sample answers are given below in red: Example 1: input: M[k] [k] // A matrix (2D array) of size k x lk output: M x V Rarray [k new array of size n [2] for j -0 k Example 2: class List: class Node V[k] // A vector (1D array) of size k next // next pointer elem // data stored in node head tail size // pointer to head of list // pointer to tail of list // size of list 2[n] kIn n) input: L :Linked List output: if the 1ist is a palindrome for i- 0 . . k startL.head n = List, size for i 0 n 2 [2] I/ [1] is also fine here [2] I/ [1] is also fine here n/2] [n/2] [n-2i-1] return R curr start 1. From neO(K2+K), we get neO(K2) 2. See beside code 3. 9n2 3n +2 4.9n23n +2 V[t+1] break for h0... k for i-0... k for j-0 .. k if D[i] [j] > D[i] [D[h] [j] D[i] j]Di] [h D[h] [j.] return D return A Consider the worst-case scenario and for each questions: Feel free to use O(1) instead of specific constants when analyzing the algorithms a. State the size of the input in big-Oh. For example, if the input to an algorithm is an array of size k, then the input size is n E O(K) b. Derive the cost function for the algorithm. Be sure to show your work c. State the complexity of the algorithm in Big-Oh. The complexity MUST be stated in terms of input-size d. Prove that the derived cost function is in the stated order (big-Oh) Sample answers are given below in red: Example 1: input: M[k] [k] // A matrix (2D array) of size k x lk output: M x V Rarray [k new array of size n [2] for j -0 k Example 2: class List: class Node V[k] // A vector (1D array) of size k next // next pointer elem // data stored in node head tail size // pointer to head of list // pointer to tail of list // size of list 2[n] kIn n) input: L :Linked List output: if the 1ist is a palindrome for i- 0 . . k startL.head n = List, size for i 0 n 2 [2] I/ [1] is also fine here [2] I/ [1] is also fine here n/2] [n/2] [n-2i-1] return R curr start 1. From neO(K2+K), we get neO(K2) 2. See beside code 3. 9n2 3n +2 4.9n23n +2 V[t+1] break for h0... k for i-0... k for j-0 .. k if D[i] [j] > D[i] [D[h] [j] D[i] j]Di] [h D[h] [j.] return D return A