# Data Structures and Algorithms Made Easy: Data Structures by Narasimha Karumanchi

By Narasimha Karumanchi

Peeling info buildings and Algorithms:

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"Data buildings And Algorithms Made effortless: information buildings and Algorithmic Puzzles" is a booklet that provides recommendations to complicated information buildings and algorithms. There are a number of strategies for every challenge and the publication is coded in C/C++, it comes convenient as an interview and examination advisor for machine scientists.

A convenient advisor of types for any laptop technological know-how specialist, information buildings And Algorithms Made effortless: info constructions and Algorithmic Puzzles is an answer financial institution for varied complicated difficulties on the topic of information constructions and algorithms. it may be used as a reference handbook by way of these readers within the desktop technological know-how undefined. This booklet serves as consultant to organize for interviews, checks, and campus paintings. briefly, this ebook deals suggestions to numerous complicated information constructions and algorithmic difficulties.

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**Sample text**

We start with the brute force solution and slowly move toward the best solution possible for that problem. For each problem, we endeavor to understand how much time the algorithm takes and how much memory the algorithm uses. It is recommended that the reader does at least one complete reading of this book to gain a full understanding of all the topics that are covered. Then, in subsequent readings you can skip directly to any chapter to refer to a specific topic. Even though many readings have been done for the purpose of correcting errors, there could still be some minor typos in the book.

Solution: The while loop will terminate once the value of ‘k’ is greater than or equal to the value of ‘n’. In each iteration the value of ‘k’ is multiplied by 3. If i is the number of iterations, then ‘k’ has the value of 3i after i iterations. The loop is terminated upon reaching i iterations when 3i ≥ n ↔ i ≥ log3 n, which shows that i = Ω(logn). Problem-33膕膕Solve the following recurrence. Solution: By iteration: Note: We can use the Subtraction and Conquer master theorem for this problem. Problem-34膕膕Consider the following program: Solution: The recurrence relation for the running time of this program is: T(n) = T(n – 1) + T(n – 2) + c.

Problem-59膕膕For Problem-58, can we improve the time complexity? Solution: Refer to the Divide and Conquer chapter. Problem-60膕膕Find the time complexity of recurrence . Solution: Let us solve this problem by method of guessing. The total size on each level of the recurrance tree is less than n, so we guess that f(n) = n will dominate. Assume for all i < n that c1n ≤ T(i) < c2n. Then, If c1 ≥ 8k and c2 ≤ 8k, then c1n = T(n) = c2n. So, T(n) = Θ(n). In general, if you have multiple recursive calls, the sum of the arguments to those calls is less than n (in this case ), and f(n) is reasonably large, a good guess is T(n) = Θ(f(n)).