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 259 / 301 1400
Tree query 241 / 249 1500
Inversions query 154 / 171 1500
Nearest vertex 143 / 157 1600
Dominating color 102 / 119 1700
String occurences 3 93 / 105 1700
Inversions query 2 79 / 88 1700
Pair 65 / 75 1700
Sparse update 59 / 65 1800
Tree 47 / 48 1900
Range query 60 / 69 1900
String concatenation 102 / 142 1900
Subarray distance 16 / 34 2000
Chameleon 46 / 53 2000
Knapsack 86 / 113 2000
Bit counting 12 / 13 2000
Subsequence queries 24 / 30 2100
Sub-subsequence 7 / 12 2100
Delete numbers 15 / 18 2200
Mode 59 / 73 2200
Marisa is happy 16 / 58 2200
Inversions query 3 8 / 13 2300
Upperbound 4 / 6 2300
23 path 11 / 16 2300
Yet another square root decomposition problem 26 / 29 2400
Marisa plays poker 40 / 44 2400
Wonderful world 23 / 27 2400