Competitive Programming 4: The New Lower Bound of Programming Contests in the 2020s

Abstract

Seven years have passed since me and my brother Felix Halim released the 3rd edition of our Competitive Programming book (CP3) on 24 May 2013 that had influenced the competitive programming field in the past decade: 2010s. We have just released the 4th edition of our book (CP4) on 19 July 2020 – the original IOI 2020 arrival day where free preview copies should have been given to all invited delegations. In this short report, we address two groups of readers: those who have read/heard about CP3 and those who are new with this book.

Multidimensional segment trees can do range updates in poly-logarithmic time

“…Now, in the lazy propagation process of the classical 1D Segment Tree, updates that are to be performed on a number of adjacent segments are stored in an ancestor node of the tree, that represents a bigger segment covering the segments to be updated. During query time these updates are passed down and distributed properly such that the effects of the updates are fulfilled [17]. Unfortunately, following the classical Segment Tree algorithm, it is only possible to implement lazy propagation in the innermost dimension, i.e., y dimension [18].…”

“…Range query problems are one of the most frequent problems in computer science. For one dimensional variant, these problems can be solved efficiently and effortlessly using Segment trees [17]. In this section, we describe the relative suitability of the various algorithms and data structures in order to solve the two dimensional range sum query problem and present a comparison with our proposed algorithm.…”

“…Sparse tables, developed by using the ideas of dynamic programming [17], are capable of returning queries in constant time. However, the downfall of this data structure is that it is immutable; after initializing it in O(nm log n log m) time, the individual elements cannot be updated.…”

“…However, the downfall of this data structure is that it is immutable; after initializing it in O(nm log n log m) time, the individual elements cannot be updated. Square root decomposition, also known as Mo's algorithm, partitions the 2D array into p×q grids with p = √ n, q = √ m [17]. This data structure precomputes the sums of the elements of these grids.…”

“…In higher dimensions, it suffers greatly due to its inability to handle range updates efficiently therein. In one dimension, Segment Trees exploit the idea of Lazy Propagation that allows it to perform range updates in logarithmic time [17]. But unfortunately, this trick does not generalize to higher dimensions.…”