| 10.1-10.7 | KMP + RMQ + suffix array Three knowledge questions assurance 70+ |
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| 10.8-10.14 | Dictionary tree automata + + AC sequence 60+ title guarantee |
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| 10.15-10.23 | ST+Treap+Lcp 60+ title guarantee |
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| 10.24-10.30 | Split Partition chain + + tree root algorithm 50+ title guarantee |
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Knowledge of each scenario
Disjoint-set:
Circle of friends question
Connectivity graph
Other optimization algorithm acceleration, you can try this
Family property issues, problems and relatives
Fenwick tree
The most basic point range and single query modification
Interval modify Fenwick tree using the differential thoughts
Tree-dimensional array, the more difficult, and some may also be combined theorem of inclusion-exclusion
Fenwick tree seeking to reverse: reverse the general thought of using merge sort, but discrete plus Fenwick tree is a more efficient way
Tree tree arrays, collections Fenwick tree to tree, a common method for the renumbering, and record number of new jurisdictions node. When solving the sub-tree weights and still quite practical. However, this application requires the construction side, front to use the chain to star in the game experience can skip.
Fenwick tree seeking monotone sequences specified length, the monotonous upgrade request queue in reverse order. We need to exclude two equal numbers, and multiple interval is calculated in line with the number of
More often, Fenwick tree to be combined with other algorithms (such as dichotomous answers, like prefixes and optimization) in order to play the greatest power
Segment tree
The most basic single-point update, a single point of inquiry
Then is the update interval, the interval query
The maximum range of the sub-segments and a maximum prefix, suffix largest, the largest sub-segment and
Range of two-dimensional matrix using a two-dimensional tree line, you can do basic template title
There are a large range of data consolidation problems, then use the tree line
Interval coloring problem can be used to maintain the tree line
Scanning line problem
Different trees and tree line array is an array tree can only maintain the prefix "operations and" (prefix and prefix plot, prefix max-min), while the segment tree can range operation and maintenance.
RMQ
Maximum Minimum Interval problem
There are two-dimensional and one-dimensional thinking, like
RMQ also be used in conjunction with other algorithms
The diameter of the tree using a tree DP problem or may DFS
KMP
Find the smallest circulation section
Looking for the number of cycles Festival
Find longest common subsequence
There are a variety of string match
Whether the subtree binary A binary tree is a B
Suffix array
It issues a single string, the first suffix array configuration and array seek Height
The maximum value of the longest substring may overlap repeated questions seeking array Height
May not overlap the longest substring repeated problems, the nature of master array Height
The idea is common in sub-suffix array-related issues
Superimposable repeated k times the longest substring, generally half do, just suffix k is determined whether the current segment can occur.
Repeated substring count problem, relatively simple SA title
Ans=∑max(Height[i]−Height[i−1],0)
Not counting the same substring problem is n-sa [k] + 1-height [k] substrings.
K lexicographically first substring problem, to find half
Continuously repeated substrings problems enumerated length string S k, if Rank [1] and Rank [k + 1] is Height = | L | -k then the current legal answers.
Most of repetitions is repeated continuously substrings problems enumerated substring length k, corresponding to the length of the look LCP between each position is equal to the maximum energy spread where k is the number of times repeated.
A string occurrences problem in all string
String substring repeated k times the issue, SA + segment tree maintenance
Strings of different types of continuous sub-string problem, this should be regarded as "prefix array" it. Specifically, while SA request is to flip the string, then the resulting array is the original prefix string.
Suffix array has been my nightmare, I hope the game never quite found it.
Trie
String retrieval problems
Word frequency statistics problem
Longest common prefix string problem
Search prefix string matching problem
As another structure of auxiliary data structures and algorithms, such as the suffix tree, the AC automatic machine
AC automaton
L gives a pattern string (summed length N), large text and a length of M, the position of each pattern string extraction requirements arise from a large text. KMP complexity than the lower
N give you a template string and a text string, you ask these template strings appear in the text string up to the number of times
AC automatic machine with weights generally combined and DP.
You now infer a length S = n string composed of lowercase letters how many ways the composition, and DP binding
Treap
I feel that this word is used in a large number of queries on K, delete, modify, and other operations other uses have not seen
There are a large range of queries on K
Tree chain split
Modify the path in a tree, seeking extreme value, sum, this time should immediately think of tree chain split
Tree chain split sub-tree problem solving
Tree cross + segment tree can maintain that point right section of the tree, if it is the right side of the interval, then we must turn point edge.
