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 269 / 314 1400
Tree query 244 / 252 1500
Inversions query 159 / 177 1500
Nearest vertex 150 / 164 1600
Dominating color 105 / 122 1700
String occurences 3 96 / 109 1700
Inversions query 2 81 / 91 1700
Pair 67 / 79 1700
Sparse update 60 / 67 1800
Tree 48 / 50 1900
Range query 61 / 71 1900
String concatenation 107 / 149 1900
Subarray distance 16 / 36 2000
Chameleon 47 / 56 2000
Knapsack 88 / 117 2000
Bit counting 13 / 14 2000
Subsequence queries 24 / 31 2100
Sub-subsequence 7 / 12 2100
Delete numbers 15 / 19 2200
Mode 60 / 76 2200
Marisa is happy 17 / 60 2200
Inversions query 3 8 / 13 2300
Upperbound 4 / 7 2300
23 path 11 / 16 2300
Yet another square root decomposition problem 26 / 29 2400
Marisa plays poker 40 / 44 2400
Wonderful world 23 / 28 2400