Mathematical Algorithms are fundamentally important as several real-life problems can be modeled as a Mathematical problem. Solving such problems require mathematical insights.These problems are a fundamental part of Interviews as it illustrates the thinking process of the candidate clearly. By going through the problems in this book, you will be well prepared to tackle any Mathematical problem.Following are some of the problems we have explored which involve ideas to solve a wider range of problems.• Smallest number with multiplesThis is a unique problem where we learn key insights regarding Prime factorization, role of primes in multiples and much more.We improve the time complexity of this problem starting from O(N^3 * log N) to O(N * log N * log N) to O(N * log log N).• Largest palindromeIn this problem, we have reduced 810000 comparisons to 362 comparisons based on three deep insights. This is a dramatic improvement and demonstrates that even if time complexity cannot be improved, the performance can be improved significantly.• GCD of sub-partsThis problem brings up key insights involving GCD (a common and important topic) and in the process, we have explored several standard algorithms like Euclidean’ s GCD Algorithm in the path of developing our custom algorithm for the given problem.• Next PermutationThis problem demonstrates a significant improvement from O(N^N x N x logN) time to O(N) time complexity. Moreover, it illustrates that improving time complexity does not necessarily mean increasing space complexity as it reduces space complexity from O(N^N) to O(1).This brings in idea of Greedy Algorithms to Mathematical Algorithm and in the process, we have explored several standard algorithms like Heap’s Algorithm.With these problems and the thought process to solve them, you will be fully prepared.This book has been carefully prepared and reviewed by Top programmers and Algorithmic researchers and members of OpenGenus. We would like to thank Aditya Chatterjee and Ue Kiao for their expertise in this domain and reviews from professors at The University of Tokyo and Tokyo Institute of Technology.Read this book now and ace your upcoming coding interview. This is a must read for everyone preparing for Coding Interviews at top companies.Books in this series ("Day before coding Interview"):• Problems for the day before your coding interview• Greedy Algorithms for the day before your Coding Interview• Dynamic Programming for the day before your coding interview• String Algorithms for the day before your Coding Interview• Mathematical Algorithms for the day before your Coding Interview
Aditya Chatterjee is an Independent Algorithmic Researcher, Software Developer and Author. He is the founding member of OPENGENUS, an organization focus on changing Internet consumption.
He is based out of Japan and has collaborated with over 500 researchers. He has mentored over 3000 learners across the Globe through the Internship program at OPENGENUS.
Ue Kiao is a Japanese Software Developer and has worked at top Software development companies across China, Singapore and Japan. She is a leading program manager at OpenGenus.
She is, originally, from Taiwan and has been living in Japan for the last decade. Her academic interests range from Algorithms to System Design and has played key role in designing systems like TaoBao, AliPay and many more.
She has completed her B. Sc in Mathematics and Computing Science at National Taiwan University and PhD at Tokyo Institute of Technology.
We would like to thank reviews from Professors at Tokyo Institute of Technology and members at OpenGenus.
