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 366 / 417 1400
Tree query 331 / 339 1500
Inversions query 220 / 247 1500
Nearest vertex 201 / 220 1600
Dominating color 146 / 169 1700
String occurences 3 127 / 141 1700
Inversions query 2 103 / 118 1700
Pair 92 / 111 1700
Sparse update 75 / 83 1800
Tree 66 / 69 1900
Range query 84 / 98 1900
String concatenation 131 / 185 1900
Subarray distance 21 / 44 2000
Chameleon 61 / 71 2000
Knapsack 117 / 153 2000
Bit counting 19 / 21 2000
Subsequence queries 27 / 37 2100
Sub-subsequence 13 / 20 2100
Delete numbers 19 / 25 2200
Mode 73 / 98 2200
Marisa is happy 20 / 64 2200
Inversions query 3 11 / 20 2300
Upperbound 5 / 11 2300
23 path 13 / 18 2300
Yet another square root decomposition problem 29 / 34 2400
Marisa plays poker 49 / 57 2400
Wonderful world 29 / 34 2400