Algorithm Design: A palindrome is a nonempty string over some alphabet that reads the same forward and backward. Examples of palindromes include all strings of length 1, civic, racecar and aibohphobia (fear of palindrome). Design an efficient algorithm using dynamic programming strategy to find the longest palindrome that is a subsequence of a given input string. For example, given the input character, your algorithm should return carac. What is the running time of your algorithm?

Algorithm Binary Search Input: L = a1, a2, ... , an list of distinct integers; x integer Output: p integer i = 1; j = n; found = F; p = 0; while i ≤ j and found = F m = ⌊i+j2⌋; if am = x then found = T and p = m else if am < x then i = m + 1 else j = m - 1; return p; When performing Algorithm Binary Search with input L = 1,3,5,7,9,11,13 and x = 9, how many times is x compared to an element ai of the list L?

Write the pseudocode for an algorithm that determines if a function is injective, assuming that you can iterate through all the elements in the domain and the co-domain in a finite number of steps.

Problem: Substring Pattern Matching Input: A text string t and a pattern string p Output: Does t contain the pattern p as a substring, and if so, where? For example: with t= abaababbaba, p = abba, your function should return 5. int findmatch(char *p, char *t) { int plen = strlen(p); // len of string int tlen = strlen(t); // len of string t //TODO: your code } Analyze your algorithm: what is the big O?

SPIM simulator (QtSpim). Simulation: Write a MIPS program that computes the expression; y = A * B + C * D Where A, B, C, and D are integers

Given the following CFG S → OB A → 1AA|A B → OAA The following strings can be generated except i. 001 ii. 000 iii.0011 iv. 01 O A. i and iii O B. i and ii O C. iv only O D. ii only

Nested Loops with Addition Principle This algorithm lists the number of strings formed from the symbols in set D (defined below) of length 4 or less with repetitions allowed. Count the number of operations in each loop and determine the total number of operations. Let D = a set of distinct symbols where |D| = 12. for x = D do print x for x = D do for y ED do print xy for x ED do for y ED do for 2 ED do print xyz for a ED do for y ED do for z E D do for q E D do print xyzq

Design an algorithm to find the weighted average of four test scores. The four test scores and their respective weights are given in the following format: (9) test Scorel weight Test Scorel For example, sample data is as follows: 75 0.20 95 0.35 85 0.15 65 0.30

public boolean isprefix(String s1, String s2) {int i = 0;if(s1.length > s2.length) return false;while(i < s1.length) {if(s1[i] != s2[i])return false;i++;}return true;} Use the active operation approach and determine the exact number of times the active operation is executed in the worst case. Express your answer in terms of n, the length of the string s1. Hint: simplify your final answer as much as possible, and do not put spaces in your answer. Use juxtaposition for the multiplication operator, for example to write "nine times n" write "9n" not "9xn" or "9*n"; to write "four times (n+2)" write "4(n+2)", not "4x(n+2)" or "4*(n+2)". Do not write your answer in Big-O notation. Write the exact number of lines executed.

Given a string containing only parentheses (, ), {, }, [, and ], determine if the input string is valid. An input string is valid if: Open brackets must be closed by the same type of brackets. Open brackets must be closed in the correct order. Write a function isValidParentheses that takes in a string s and returns a boolean value indicating whether the parentheses in s are valid. Example: Input: s = "{[()]}" Output: true Input: s = "{[()]}" Output: false Input: s = "{[(])}" Output: false Input: s = "{[()]}()[]" Output: true Note: The input string will only contain the characters (, ), {, }, [, and ]. An empty string is considered valid.

TRUE OR FALSE Finding a matching string can be effectively solved using a divide-and-conquer algorithm.

%matplotlib inline import numpy as np from matplotlib import pyplot as plt import math