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 398 / 451 1400
Tree query 361 / 369 1500
Inversions query 244 / 273 1500
Nearest vertex 225 / 248 1600
Dominating color 167 / 190 1700
String occurences 3 145 / 162 1700
Inversions query 2 120 / 135 1700
Pair 105 / 123 1700
Sparse update 86 / 96 1800
Tree 74 / 76 1900
Range query 97 / 111 1900
String concatenation 145 / 198 1900
Subarray distance 25 / 68 2000
Chameleon 72 / 82 2000
Knapsack 132 / 171 2000
Bit counting 25 / 28 2000
Subsequence queries 28 / 38 2100
Sub-subsequence 15 / 23 2100
Delete numbers 19 / 26 2200
Mode 81 / 106 2200
Marisa is happy 20 / 64 2200
Inversions query 3 12 / 22 2300
Upperbound 6 / 12 2300
23 path 13 / 19 2300
Yet another square root decomposition problem 33 / 39 2400
Marisa plays poker 53 / 62 2400
Wonderful world 31 / 36 2400