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 235 / 275 1400
Tree query 223 / 230 1500
Inversions query 139 / 156 1500
Nearest vertex 129 / 139 1600
Dominating color 94 / 109 1700
String occurences 3 87 / 98 1700
Inversions query 2 67 / 75 1700
Pair 55 / 64 1700
Sparse update 53 / 57 1800
Tree 40 / 41 1900
Range query 53 / 61 1900
String concatenation 91 / 126 1900
Subarray distance 15 / 30 2000
Chameleon 42 / 50 2000
Knapsack 77 / 103 2000
Bit counting 10 / 11 2000
Subsequence queries 24 / 30 2100
Sub-subsequence 7 / 12 2100
Delete numbers 14 / 18 2200
Mode 53 / 64 2200
Marisa is happy 14 / 55 2200
Inversions query 3 8 / 12 2300
Upperbound 4 / 6 2300
23 path 11 / 15 2300
Yet another square root decomposition problem 24 / 27 2400
Marisa plays poker 38 / 41 2400
Wonderful world 23 / 27 2400