Homework Assignment 4
Brute Force and Divide-and-Conquer Algorithms
Design and Analysis of Algorithms
Spring Semester 2014
Due: Thursday, March 13, at 12:30 PM
- Consider the common
brute-force string matching algorithm
below. How many comparisons, successful and unsuccessful,
will this algorithm make in searching a text consisting of
1000 zeroes for each of these patterns?
- Use the partitioning idea seen in binary search to design
an algorithm that finds a subrange of an sorted array.
- a sorted array, A[0..n-1]
- two integers, lower and upper
- output: the subrange of the array that contains all
values v such that lower ≤
v ≤ upper. That is:
If no such range exists, return -1.
- a pair [indexL, indexU] such that
- 0 ≤ indexL ≤ indexU ≤ n-1 and
- lower ≤ A[indexL] ≤ A[indexU] ≤
- Develop a divide-and-conquer algorithm that computes the
position of the largest element in an unsorted array of
n elements. What is the output of your algorithm
when several elements in the array are the same largest
- Consider the
the divide-and-conquer multiplication algorithm
we learned in Session 14.
- Demonstrate the algorithm by computing 1710 * 1011.
- Why does this algorithm not outperform conventional
multiplication algorithms until the numbers become
By the due date and time, submit a hardcopy of your solutions.
You may bring your solutions to class (preferred) and leave
them on the desk before class begins, or you may
leave them in my mailbox in the department office.
A Brute-Force String Matching Algorithm
// Input : Array S[0..n-1] of n characters (the string)
// Array P[0..m-1] of m characters (the pattern)
// Output: the index of the first character in the string
// that starts a substring that matches the pattern,
// or -1 if the search fails
for i ← 0 to n-m do
j ← 0
while j < m and P[j] == S[i+j] do
j ← j + 1
if j == m
Eugene Wallingford .....
March 11, 2014