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 193 / 226 1400
Tree query 181 / 188 1500
Inversions query 108 / 126 1500
Nearest vertex 102 / 109 1600
Dominating color 76 / 88 1700
String occurences 3 70 / 75 1700
Inversions query 2 53 / 57 1700
Pair 45 / 54 1700
Sparse update 42 / 43 1800
Tree 29 / 29 1900
Range query 38 / 45 1900
String concatenation 69 / 98 1900
23 path 8 / 10 1900
Subarray distance 12 / 21 2000
Chameleon 38 / 45 2000
Knapsack 57 / 80 2000
Bit counting 4 / 6 2000
Subsequence queries 23 / 29 2100
Sub-subsequence 6 / 10 2100
Delete numbers 14 / 17 2200
Mode 41 / 51 2200
Marisa is happy 11 / 51 2200
Inversions query 3 7 / 10 2300
Upperbound 3 / 4 2300
Yet another square root decomposition problem 20 / 23 2400
Marisa plays poker 32 / 34 2400
Wonderful world 17 / 20 2400