Design and implement an algorithm that is given as input an integer value $k \geq 0$ and a list of k numbers $\mathrm{N}_{1}, \mathrm{N}_{2}, \ldots, \mathrm{N}_{\mathrm{k}}$ Your algorithm should reverse the order of the numbers in the list. That is, if the original list contained: $\mathrm{N}_{1}=5, \mathrm{N}_{2}=13, \mathrm{N}_{3}=8, \mathrm{N}_{4}=27, \mathrm{N}_{5}=10(\mathrm{k}=5)$ then when your algorithm has completed, the values stored in the list will be: $\mathrm{N}_{1}=10, \mathrm{N}_{2}=27, \mathrm{N}_{3}=8, \mathrm{N}_{4}=13, \mathrm{N}_{5}=5$

Design and implement an algorithm that gets as input a list of k integer values $\mathrm{N}_{1}, \mathrm{N}_{2}, \ldots, \mathrm{N}_{\mathrm{k}}$ as well as a special value SUM. Your algorithm must locate a pair of values in the list N that sum to the value SUM. For example, if your list of values is 3, 8, 13, 2, 17, 18, 10, and the value of SUM is 20, then your algorithm would output either the two values (2, 18) or (3, 17). If your algorithm cannot find any pair of values that sum to the value SUM, then it should print out the message ‘Sorry, there is no such pair of values.’

Use the Find Largest algorithm to help you develop an algorithm to find the median value in a list containing N unique numbers. The median of N numbers is defined as the value in the list in which approximately half the values are larger than it and half the values are smaller than it. For example, consider the following list of seven numbers. 26, 50, 83, 44, 91, 20, 55. The median value is 50 because three values (20, 26, and 44) are smaller and three values (55, 83, and 91) are larger. If N is an even value, then the number of values larger than the median will be one greater than the number of values smaller than the median. Get a value for n, the size of the list. Get values for $\mathrm{A}_{1}, \mathrm{A}_{\mathrm{2},} \ldots, \mathrm{A}_{n^{\prime}}$ the list to be searched. Set the value of largest so far to $A_{1}$ Set the value of location to 1.Set the value of i to 2. While $(i \leq n)$ do If $A_{i}>$ largest so far then. Set largest so far to $A_{i}.$ Set location to i. Add 1 to the value of i. End of the loop. print out the values of largest so far and location. Stop.

Refer to the pattern-matching algorithm. a. What is the output of the algorithm as it currently stands if our text is Text: We must band together and handle adversity and we search for the pattern “and”? b. How could we modify the algorithm so that it finds only the complete word and rather than the occurrence of the character sequence a, n, and d that is contained within another word, such as band? Get values for n and m, the size of the text and the pattern, respectively. Get values for both the text $T_{1} T_{2} \dots T_{n}$ and the pattern $P_{1} P_{2} \ldots P_{m}.$ Set k, the starting location for the attempted match, to 1. While $(k \leq(n-m+1))$ do. Set the value of i to 1. Set the value of Mismatch to NO. While both $(i \leq m)$ and (Mismatch = NO) do. If $P_{i} \neq T_{k+(j-1)}$ then. Set Mismatch to yes. Else. Increment i by 1 (to move to the next character). End of the loop. If Mismatch = NO then. Print the message 'There is a match at position'. Print the value of k. Increment k by 1. End of the loop. Stop, we are finished.

Write an algorithm that generates a Caesar cipher-a secret message in which each letter is replaced by the one that is k letters ahead of it in the alphabet, in a circular fashion. For example, if k = 5, then the letter a would be replaced by the letter f, and the letter x would be replaced by the letter c. (We’ll talk more about the Caesar cipher and other encryption algorithms in Chapter 8.) The input to your algorithm is the text to be encoded, ending with the special symbol “$”, and the value k. (You may assume that, except for the special ending character, the text contains only the 26 letters a . . . z.) The output of your algorithm is the encoded text.