Module Square root decomposition

Square root decomposition

**Frequency: 7/10** In square root decomposition, there are generally four types of techniques that are commonly used: - Mo's algorithm. - Dividing the array into smaller blocks of size $\sqrt{n}$. - Partitioning the data into light and heavy sets. - Processing $\sqrt{q}$ queries at a time. If these concepts are not clear to you, don't worry! By completing the problems below, you will gain a thorough understanding of what each of these techniques entails. In some OI-style data structure problems, you may find that the second-to-last subtask can be efficiently solved using square root decomposition.

Resources

- [CP Algorithms: Sqrt decomposition](https://cp-algorithms.com/data_structures/sqrt_decomposition.html#:~:text=Sqrt%20Decomposition%20is%20a%20method,%2Fmaximal%20element%2C%20etc.)

Problems

Frequency 215 / 250 1400
Tree query 207 / 214 1500
Inversions query 123 / 141 1500
Nearest vertex 114 / 124 1600
Dominating color 84 / 97 1700
String occurences 3 82 / 90 1700
Inversions query 2 59 / 66 1700
Pair 50 / 59 1700
Sparse update 48 / 52 1800
Tree 34 / 35 1900
Range query 45 / 52 1900
String concatenation 81 / 117 1900
Subarray distance 14 / 26 2000
Chameleon 40 / 47 2000
Knapsack 71 / 97 2000
Bit counting 7 / 8 2000
Subsequence queries 23 / 29 2100
Sub-subsequence 7 / 11 2100
Delete numbers 14 / 17 2200
Mode 49 / 60 2200
Marisa is happy 14 / 55 2200
Inversions query 3 8 / 11 2300
Upperbound 4 / 5 2300
23 path 11 / 13 2300
Yet another square root decomposition problem 22 / 25 2400
Marisa plays poker 37 / 40 2400
Wonderful world 22 / 26 2400