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 197 / 233 1400
Tree query 187 / 194 1500
Inversions query 110 / 128 1500
Nearest vertex 104 / 111 1600
Dominating color 77 / 90 1700
String occurences 3 71 / 76 1700
Inversions query 2 53 / 57 1700
Pair 46 / 55 1700
Sparse update 42 / 43 1800
Tree 30 / 30 1900
Range query 39 / 46 1900
String concatenation 70 / 99 1900
23 path 8 / 10 1900
Subarray distance 12 / 22 2000
Chameleon 39 / 46 2000
Knapsack 60 / 83 2000
Bit counting 4 / 6 2000
Subsequence queries 23 / 29 2100
Sub-subsequence 7 / 11 2100
Delete numbers 14 / 17 2200
Mode 42 / 52 2200
Marisa is happy 12 / 51 2200
Inversions query 3 7 / 10 2300
Upperbound 4 / 5 2300
Yet another square root decomposition problem 20 / 23 2400
Marisa plays poker 33 / 35 2400
Wonderful world 18 / 21 2400