Asterix and the Maagic Potion - Suffix tree problem
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Asterix needs to solve a problem to find the secret ingredients for the Magic Potion. Getafix provided each villager with a string and said to find all substrings that appear at least twice, as these would reveal the ingredients. To solve this, Asterix must build a suffix tree to efficiently find all repeated substrings in O(N^3) time before the writing disappears. The document then explains the node structure of a suffix tree and provides examples and functions to output the intermediate and final suffix trees and repeated substrings.
![Node Structure Of Suffix Tree:
Each node of the tree should contain at least:
● Node number (root is 0)
● An array of children
● An array of start and end positions of the substring in the string
For example let us take the word BOOK as input
B O O K
0 1 2 3
The tree will be as shown above and the node information will be as follows.
Node 0:
Child[0] is Node 1
Child[1] is Node 2
Child[2] is Node 3
Start[0] is 0 and End[0] is 3
Start[1] is 3 and End[1] is 3
Start[2] is 1 and End[2] is 1
Node 3:
Child[0] is Node 4
Child[1] is Node 5
Start[0] is 3 and End[0] is 3
Start[1] is 2 and End[1] is 3
Input:
A string of length N](https://image.slidesharecdn.com/assg5-160420122500/85/Asterix-and-the-Maagic-Potion-Suffix-tree-problem-2-320.jpg)
Asterix and the Maagic Potion - Suffix tree problem
- 2. Node Structure Of Suffix Tree: Each node of the tree should contain at least: ● Node number (root is 0) ● An array of children ● An array of start and end positions of the substring in the string For example let us take the word BOOK as input B O O K 0 1 2 3 The tree will be as shown above and the node information will be as follows. Node 0: Child[0] is Node 1 Child[1] is Node 2 Child[2] is Node 3 Start[0] is 0 and End[0] is 3 Start[1] is 3 and End[1] is 3 Start[2] is 1 and End[2] is 1 Node 3: Child[0] is Node 4 Child[1] is Node 5 Start[0] is 3 and End[0] is 3 Start[1] is 2 and End[1] is 3 Input: A string of length N
- 3. Functions and Outputs: ● print_suffix_intermediate_tree(i) Show all the paths in the Intermediate Suffix Tree, from the root to the leaves (printing tabs between the edges along the same path) for index i < N For i=3, the output should be: BOOK K O K O OK ● print_bfs_intermediate_tree(i) Show BFS (Level Ordering) of the Intermediate Suffix Trees for index i < N For i=3, the output should be: 0 BOOK 1 0 K 2 0 O 3 3 K 4 3 OK 5 ● print_suffix_final_tree(N) All the Suffixes of the Final Suffix Tree For the given input, the output should be: BOOK OOK OK K ● print_final_substrings(N) All the substrings as mentioned in the problem For the input ABABAB, the output should be: A B AB BA ABA BAB ABAB