From 8679a70c5567770c532e28e6c7342ffe5ea11779 Mon Sep 17 00:00:00 2001
From: lauraste1 <30854371+lauraste1@users.noreply.github.com>
Date: Sat, 2 Mar 2019 10:00:27 +1100
Subject: [PATCH] Add Boyer-Moore article to string algorithms section of guide
 (#34937)

* Add files via upload

* fix: corrected front matter

* fix: renamed to be index.md
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+---
+title: Boyer-Moore
+---
+
+## Boyer-Moore
+
+This algorithm has been shown to be more effective than the Knuth-Morris-Pratt algorithm and others for pattern matching in natural languages like English. It relies on the use of [two key heuristics][1], namely:
+* The looking-glass heuristic: where the pattern P is compared to a substring of the text T starting from P’s last letter
+* Character-jump heuristic: if there is a mismatch at T[i] = c then
+    - If P contains c, shift P to line up the last instance of c in P with T[i]
+    - Else move P to align P[0] with T[i+1]
+
+Before applying these heuristics however, the algorithm analyses pattern P and alphabet Σ to create a last occurrence function. This function ties the letters of the alphabet to the letters in P according to where they occur in P.
+
+So if the last occurence of the letter c in P is at index P[i] then at L(c) the index i of that letter will be stored. If the letter c does not occur in P, -1 will be stored there.
+
+#### Example:
+
+__Σ =__ {e, f, g, h}
+__P =__ egef
+
+|  	| 	|  	| 	| 	|
+|---	|---	|---	|---	|---	|
+|  __c__	| e 	| f 	| g 	| h 	|
+| __L(c)__  |  2 | 3  | 1  | -1  |
+
+The last occurrence function can be stored as an array indexed by the numeric codes of the characters. This function can be calculated in O(m+s) time where m is the length of the pattern and s the size of the alphabet.
+
+### Code of Boyer-Moore Algorithm in C++
+```c++
+#include<iostream>
+#define MAXCHAR 256 //there are 256 ASCII characters
+using namespace std;
+
+int min(int num1, int num2) {
+  if (num1 < num2) {
+     return num1;
+  }
+  return num2;
+}
+
+void makeLOFunction(string pattern, int LOFunction[MAXCHAR]) {
+    int n = pattern.size();
+    for (int c = 0; c < MAXCHAR; c++)
+        LOFunction[c] = -1;
+    for (int c = 0; c < n; c++)
+        LOFunction[(int)pattern[c]] = c;
+}
+
+int boyerMoore(string pattern, string text) {
+    int m = pattern.size();
+    int n = text.size();
+    int LOFunction[MAXCHAR];
+    makeLOFunction(pattern, LOFunction); //fill array of last occurrence function
+    int i = m-1;
+    int j = m-1;
+    do {
+       if (text[i] == pattern[j]) {
+           if (j == 0) {
+               cout << "Pattern starts at index " << i << "\n";
+               return 1; //match found at i
+           } else {
+               i--;
+               j--; //move backwards through pattern
+           }
+       } else {
+           int leap = LOFunction[(int)text[i]]; //character jump
+           i = i + m - min(j, leap+1);
+           j = m - 1;
+       }
+    }
+    while (i <= n-1); //while not reached end of text
+    cout << "Match not found\n";
+    return -1; //no match found
+}
+
+int main() {
+    string pattern = "abacab";
+    string text = "abacaabadcabacabaabb";
+    boyerMoore(pattern, text);
+}
+
+```
+#### References
+[1]: https://www.cs.purdue.edu/homes/aliaga/cs251-16/lectures/22-PatternMatching.pdf
+1. Aliaga, D (2016) *Strings and Pattern Matching*, lecture notes, Data Structures and Algorithms CS251, Purdue University, delivered 9 April 2016.
+2. Christine, S (2018) Bad Character Heuristic [Source code]. https://www.tutorialspoint.com/Bad-Character-Heuristic
+3. Buerger, H (2012) Boyer-Moore Algorithm [Source code].
+https://gist.github.com/obstschale/3060059