Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 2: Problem 39

Write an efficient algorithm that searches for a value in an \(n \times m\) table (twodimensional array). This table is sorted along the rows and columns - that is \\[ \begin{array}{l} \text { Table }(i][j] \leq T a b l c[i][j+1] \\ \text { Table }[i][j] \leq T a b l e[i+1][j] \end{array} \\]

Short Answer

Expert verified
The search algorithm should start from the top-right corner of the table and move left or down at each step based on the comparison result with the target value, effectively eliminating a row or column in each step. It stops when the value is found or when it reaches the leftmost column or the bottom row. This approach utilizes the property that the table is sorted along the rows and columns.

Step by step solution

01

Understand the properties of the table

First, it's important to understand the properties of the table. Each entry is less than or equal to the entries to its right and below. This implies that the smallest value is at the top left and the largest value is at the bottom right.
02

Initiate the search from the top right

Start the search from the entry in the top-right corner of the table. This position is chosen because it has the maximum number of decreasing and minimum number of increasing neighbours - we only have to compare with one neighbour to descend or ascend.
03

Compare the target with the entry

If the target value is less than the entry value, move left to the next column. This is done because all the entries in the current column to the bottom are greater. If the target value is greater than the entry value, move down to the next row. This is done because all the entries in the current row to the left are smaller.
04

Repeat the comparison until the value is found or limits are reached

Repeat Step 3 until you find the target or reach the limits, i.e., the leftmost column or the bottommost row. The search is efficient because it eliminates an entire row or column at each step. The algorithm works correctly due to the properties of the table.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Implement both Exchange Sort and Quicksort algorithms on your computer to sort a list of \(n\) elements. Find the lower bound for \(n\) that justifies application of the Quicksort algorithm with its overhead.

Implement both the standard algorithm and Strassen's Algorithm on your computer to multiply two \(n \times n\) matrices \(\left(n=2^{h}\right) .\) Find the lower bound for \(n\) that justifies application of Strassen's Algorithm with its overhead.

Assuming that Quicksort uses the first item in the list as the pivot item: (a) Give a list of \(n\) items (for example, an array of 10 integers) representing the worst-case scenario. (b) Give a list of \(n\) items (for example, an array of 10 integers) representing the best-case scenario.

Use the divide-and-conquer approach to write a recursive algorithm that finds the maximum sum in any contiguous sublist of a given list of \(n\) real values. Analyze your algorithm, and show the results in order notation.

Consider procedure solve \((P, I, O)\) given below. This algorithm solves problem \(P\) by finding the output (solution) \(O\) corresponding to any input \(l\) Assume \(g(n)\) basic operations for partitioning and combining and no basic operations for an instance of size 1 (a) Write a recurrence equation \(T(n)\) for the number of basic operations needed to solve \(P\) when the input size is \(n\) (b) What is the solution to this recurrence equation if \(g(n) \in \Theta(n)\) (proof not required \() ?\) (c) Assuming that \(g(n)=n^{2},\) solve the recurrence equation exactly for \(n=\) 27 (d) Find the general solution for \(n\) a power of 3
See all solutions

Recommended explanations on Computer Science Textbooks

Computer Network

Read Explanation

Functional Programming

Read Explanation

Game Design in Computer Science

Read Explanation

Big Data

Read Explanation

Databases

Read Explanation

Algorithms in Computer Science

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free