# CWU Algorithm Analysis Worksheet

question 1) For the set I of intervals below, determine the smallest set S of intervals such that each interval in I overlaps with at least one interval in S. Two intervals [x, y] and [k, l] overlap if x ≤ k ≤ y, or x ≤ l ≤ y, or k ≤ x ≤ l, or k ≤ y ≤ l.I = { a: [9, 10], b: [7, 10], c: [7, 8], d: [0, 3], e: [0, 2], f: [4, 5], g: [3, 7], h: [1, 2], i: [6, 9], j: [9, 10] }

question 2)You are given the problem below. Describe a simple brute force or backtracking algorithm that solves it. State the runtime of your algorithm. Problem: You are given a string of length n. Find the longest palindrome in S.

question 3)You are given an instance of the Maximum Sub-Array Sum problem below. Solve the problem using dynamic programming as discussed in class. State each subproblem and the solution calculated for it. State the base case.arr = [ -6, 3, 1, -10, -9, 6, -5, 9, 5, -3 ]

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