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Practice Problems

This document contains 10 practice problems related to data structures and algorithms. The problems cover topics such as finding a k-majority element in an array, finding the subarray of an array with a sum closest to a given input, finding the row with the most 0s in a binary matrix, efficiently finding the maximum and minimum of an array, finding the closest pair of points on a line, finding the peak entry in a unimodal array, counting significant inversions in an array, checking if a tree is a red-black tree, finding the missing value range to make a BST valid, and designing algorithms for problems on BSTs.

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206 views1 page

Practice Problems

This document contains 10 practice problems related to data structures and algorithms. The problems cover topics such as finding a k-majority element in an array, finding the subarray of an array with a sum closest to a given input, finding the row with the most 0s in a binary matrix, efficiently finding the maximum and minimum of an array, finding the closest pair of points on a line, finding the peak entry in a unimodal array, counting significant inversions in an array, checking if a tree is a red-black tree, finding the missing value range to make a BST valid, and designing algorithms for problems on BSTs.

Uploaded by

yogendra
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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ESO207: Data Structures and Algorithms (Practice Problems)

Question 1: Finding k-majority Element


Given an array A with n elements and a number 1 ≤ k ≤ n, an element of A is said to be k-majority
of A if it appears more than n/k times in A. Design an O(nk) time and O(k) space algorithm which
computes a k-majority element, if one exists, in an array A.
Question 2: Sub-array with sum closest to input
Given an array A storing n numbers and a number x, determine the subarray of A whose sum is closest
to x in O(n log n) time.
Question 3: Row with most 0s
Given a n × n matrix of 0s and 1s such that in each row no 0 comes before a 1, design an O(n) time
algorithm to find the row with the most 0s.
Question 4: Finding maximum and minimum efficiently
Design an algorithm that takes an array A having n distinct numbers and outputs the maximum and
minimum element of the array using at most d3n/2e comparisons.
Question 5: Closest pair of points on a line
Given the x-coordinates of n points on the real line, design an O(n log n) time algorithm to find the
closest pair of points.
Question 6: Finding the peak entry in an array
An array A having n distinct elements is said to be unimodular if for some index p between 0 and n − 1,
the values in the array entries increase up to position p in A (also known as the peak) and then decrease
the remainder of the way until position n − 1.
Design an O(log n) time algorithm that given a unimodular array A finds the the peak position p of A.
Question 7: Counting number of significant inversions
A pair (i, j) is called a significant inversion if i < j and A[i] > 2A[j]. Design an O(n log n) time algorithm
to count the number of significant inversions in an array.
Question 8: Check if red-black tree
Given a binary tree T on n nodes where each node is colored red or black, design an O(n) time algorithm
to determine if T is a red-black tree.
Question 9: Missing value in BST
Given a BST T having a node with a missing value, find the exact range from which you can select a
value and get back a valid BST in O(n) time.
Question 10: Problems on BSTs
Design an O(h) time algorithm for the following problems on BSTs having n nodes and height h:
(a) Given a BST T and an index 1 ≤ i ≤ n, output the i-th element in T .
(b) Compute the successor of an element in a BST.
(c) Compute the predecessor of an element in a BST.
Credits: Thanks to Prof. Surender Baswana for sharing many of the above questions from earlier offerings
of this course.

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