Kmp algorithm

Uncategorized/KMP string-searching algorithm/README.md

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+# Knuth–Morris–Pratt string-searching algorithm
+KMP algorithm finds all occurrences of a string P (pattern) in another string (T).
+
+The main idea is reading T char-by-char, and keep tracking on the largest prefix of P which is also a suffix of the part of T we have read, while fallbacking to shorter prefixes of P if necessary.
+
+We pre-process P, using a very similar method, to get the correct fallback prefix for any case.
+
+## Complexity
+* **Time**:  ![](https://latex.codecogs.com/svg.latex?O(m+n))  where ![](https://latex.codecogs.com/svg.latex?m) is the length of P and ![](https://latex.codecogs.com/svg.latex?n) is the length of the T
+* **Space**:  ![](https://latex.codecogs.com/svg.latex?O(m))
+
+## References
+* [Wikipedia](https://en.wikipedia.org/wiki/Knuth%E2%80%93Morris%E2%80%93Pratt_algorithm)

Uncategorized/code.js

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+	// import visualization libraries {
+	const { Array2DTracer, Layout, LogTracer, Tracer, VerticalLayout } = require('algorithm-visualizer');
+	// }
+
+	// define tracer variables {
+	const patternTracer = new Array2DTracer('Pattern')
+	const textTracer = new Array2DTracer('Text')
+	// }
+
+	// define input variables
+	const pattern = 'abacabab';
+	const text = 'ababacabacababacabad'
+
+	// define KMP array
+	let KMP = [];
+
+	// calculate KMP table for pattern
+	function build_table() {
+		KMP.push(0);
+		// visualize {
+		patternTracer.patch(2,0,0);
+		Tracer.delay();
+		patternTracer.depatch(2,0);
+		// }
+		let n = 0;
+		for (let i=2; i <= pattern.length; i++) {
+			// visualize {
+			patternTracer.patch(0,n,pattern[n]);
+			patternTracer.patch(1,i-1,pattern[i-1]);
+			Tracer.delay();
+			// }
+			while (n > 0 && pattern[i-1] != pattern[n]) {
+				// visualize {
+				patternTracer.patch(2,n-1,KMP[n-1]);
+				Tracer.delay();
+				patternTracer.depatch(2,n-1);
+				patternTracer.depatch(0,n);
+				patternTracer.deselectRow(0,KMP[n-1],n-1);
+				patternTracer.deselectRow(1,i-1-n,i-2-KMP[n-1]);
+				// }
+				n = KMP[n-1];
+				// visualize {
+				patternTracer.patch(0,n,pattern[n]);
+				Tracer.delay();
+				// }
+			}
+			// visualize {
+			patternTracer.depatch(0,n);
+			patternTracer.depatch(1,i-1);
+			// }
+			if (pattern[i-1] == pattern[n]) {
+				// visualize {
+				patternTracer.select(0,n);
+				patternTracer.select(1,i-1);
+				// }
+				n++;
+			}
+			KMP.push(n);
+			// visualize {
+			patternTracer.patch(2,i-1,n);
+			Tracer.delay();
+			patternTracer.depatch(2,i-1);
+			// }
+		}
+		// visualize {
+		patternTracer.deselect(0,0,1,pattern.length-1);
+		// }
+	}
+
+	// search pattern in text
+	function search_pattern() {
+		let n = 0;
+		for (let i=1; i <= text.length; i++) {
+			// visualize {
+			if (n < pattern.length) {
+				patternTracer.patch(0,n,pattern[n]);
+			}
+			textTracer.patch(0,i-1,text[i-1]);
+			Tracer.delay();
+			// }
+			while (n > 0 && text[i-1] != pattern[n]) {
+				// visualize {
+				patternTracer.patch(1,n-1,KMP[n-1]);
+				Tracer.delay();
+				patternTracer.depatch(1,n-1);
+				if (n < pattern.length) {
+					patternTracer.depatch(0,n);
+				}
+				patternTracer.deselectRow(0,KMP[n-1],n-1);
+				textTracer.deselectRow(0,i-1-n,i-2-KMP[n-1]);
+				// }
+				n = KMP[n-1];
+				// visualize {
+				patternTracer.patch(0,n,pattern[n]);
+				Tracer.delay();
+				// }
+			}
+			// visualize {
+			patternTracer.depatch(0,n);
+			textTracer.depatch(0,i-1);
+			// }
+			if (text[i-1] == pattern[n]) {
+				// visualize {
+				patternTracer.select(0,n);
+				textTracer.select(0,i-1);
+				// }
+				n++;
+			}
+			// visualize {
+			textTracer.patch(1,i-1,n);
+			Tracer.delay();
+			textTracer.depatch(1,i-1);
+			if (n == pattern.length) {
+				textTracer.select(1,i-1);
+			}
+			// }
+		}
+		// visualize {
+		patternTracer.deselectRow(0,0,pattern.length-1);
+		textTracer.deselectRow(0,0,text.length-1);
+		// }
+	}
+
+
+
+	(function main() {
+	  // visualize {
+	  Layout.setRoot(new VerticalLayout([patternTracer,textTracer]));
+	  patternTracer.set([pattern,pattern,[]]);
+	  textTracer.set([text,[]]);
+	  Tracer.delay();
+	  // }
+	  build_table();
+	  // visualize {
+	  patternTracer.set([pattern,KMP]);
+	  Tracer.delay();
+	  // }
+	  search_pattern();
+	})();