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 117 / 140 1400
Tree query 104 / 109 1500
Inversions query 67 / 82 1500
Nearest vertex 59 / 63 1600
Dominating color 43 / 48 1700
String occurences 3 41 / 43 1700
Inversions query 2 34 / 37 1700
Pair 30 / 38 1700
Sparse update 19 / 20 1800
Tree 11 / 11 1900
Range query 19 / 26 1900
String concatenation 28 / 37 1900
Subarray distance 8 / 8 2000
Chameleon 20 / 23 2000
Knapsack 13 / 24 2000
Subsequence queries 18 / 24 2100
Sub-subsequence 3 / 5 2100
Delete numbers 11 / 13 2200
Mode 20 / 22 2200
Inversions query 3 5 / 5 2300
Upperbound 3 / 4 2300
Yet another square root decomposition problem 14 / 16 2400
Marisa plays poker 18 / 19 2400
Wonderful world 12 / 12 2400