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KMP classic algorithm and unit tests #125
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100 changes: 100 additions & 0 deletions
src/_Classics_/knuth-morris-pratt/index.js
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| /* * | ||
| * The time complexity of KMP algorithm is O(n) in the worst case | ||
| * Example use case: Pattern = ABCABCACA Text = AAABCBAABCABCACACABBCA | ||
| * LPSArray = [ 0, 0, 0, 1, 2, 3, 4, 0, 1 ] | ||
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There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. It should be LPSArray = [ 0, 1, 0, 0, 1, 0 ] There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. Hi @TheSTL the pattern had been updated to ABCABCACA. I feel this is a more intuitive example. I believe [ 0, 0, 0, 1, 2, 3, 4, 0, 1 ] to be the correct LPS, if there are any more queries or amendments you would like to be made, I’ll updage the PR as appropriate. Cheers. There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. I think this example is more understandable from previous one to compute LPS. |
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| * Found = true, at index 7 | ||
| * */ | ||
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| // Longest prefix suffix - generate an array of the lps for each pattern array value | ||
| const createLPS = (pattern, patternLength) => { | ||
| // initialise the current longest prefix suffix length and iterator index values | ||
| const lps = [patternLength]; | ||
| lps[0] = 0; | ||
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| let length = 0; | ||
| let i = 1; | ||
| // while there is still pattern to iterate over - calculate the lps for i = 1 to patternLength - 1 | ||
| while (i < patternLength) { | ||
| /* * | ||
| * if the pattern character at position i matches the pattern character at position length, | ||
| * then increment length, update | ||
| * the lps to the incremted length value and iterate to the next index i. | ||
| * */ | ||
| if (pattern.charAt(i) === pattern.charAt(length)) { | ||
| length += 1; | ||
| lps[i] = length; | ||
| i += 1; | ||
| // if not matching | ||
| } else if (length !== 0) { | ||
| // if the length value is not 0, then set the length to be the lps value of index length - 1 | ||
| length = lps[length - 1]; | ||
| } else { | ||
| // else if length is 0, then set the lps at position i to length, i.e. 0 and increment i. | ||
| lps[i] = length; | ||
| i += 1; | ||
| } | ||
| } | ||
| return lps; | ||
| }; | ||
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| /* * | ||
| * Invoke the Knuth-Morris-Pratt pattern matching algorithm to find a Pattern with a Text - this | ||
| * uses a precomputed prefix-suffix array/table to essentially skip chunks of the text that we | ||
| * know will match the pattern. This algorithm will return true if the pattern is a subset of | ||
| * the text, else it will return false. | ||
| * This algorithm accepts two strings, the pattern and text. | ||
| * The time complexity of the KMP algorithm is O(n) in the worst case. | ||
| * */ | ||
| const KMPSearch = (pattern, text) => { | ||
| const patternLength = pattern.length; // Often referred to as M | ||
| const textLength = text.length; // Often referred to as N | ||
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| // Longest Pattern Suffix - array containing the lps for all pattern value positions | ||
| const lps = createLPS(pattern, patternLength); // This is preprocessed. | ||
| // console.log({ lpsArray: lps }) | ||
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| let patternIndex = 0; // Referred to as P | ||
| let textIndex = 0; // Referred to as T | ||
| let found = false; | ||
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| // While there is still text left to iterate over and the pattern has not yet been found | ||
| while (textIndex < textLength && found === false) { | ||
| // if the pattern char at index pos P equals the text char at text pos T, then increment indexes | ||
| if (pattern.charAt(patternIndex) === text.charAt(textIndex)) { | ||
| textIndex += 1; | ||
| patternIndex += 1; | ||
| } | ||
| /* * | ||
| * if the pattern index equals the pattern length then the pattern has been successfully | ||
| * found, as such the pattern is a subset of the text the pattern index is set to the longest | ||
| * pattern suffix value (the index is decremented due to being zero indexed). | ||
| * */ | ||
| if (patternIndex === patternLength) { | ||
| // console.log(`Pattern found at index ${textIndex-patternIndex}`); | ||
| patternIndex = lps[patternIndex - 1]; | ||
| found = true; | ||
| } else if (textIndex < textLength && pattern.charAt(patternIndex) !== text.charAt(textIndex)) { | ||
| /* * | ||
| * else if there is still text left to iterate over and the pattern character does not match | ||
| * the text characterat their respective index positions, then check of the pattern Index is 0, | ||
| * i.e. if it is the first pattern position. If so then jump to the next text character, else | ||
| * (this is not the first pattern position), then update the pattern index using the generated | ||
| * longest prefix suffix, to skip ahead of matching values. This logic will only be encountered | ||
| * after T number of mismatches. | ||
| * */ | ||
| if (patternIndex === 0) textIndex += 1; | ||
| else patternIndex = lps[patternIndex - 1]; | ||
| } | ||
| } | ||
| // Pattern has not been found, return false. Else return true. | ||
| if (!found) { | ||
| // console.log('The pattern was not found!') | ||
| return false; | ||
| } | ||
| return true; | ||
| }; | ||
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| module.exports = { | ||
| KMPSearch, | ||
| }; | ||
39 changes: 39 additions & 0 deletions
src/_Classics_/knuth-morris-pratt/knuth-morris-pratt.test.js
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| const { KMPSearch } = require('.'); | ||
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| describe('Pattern Matching Classic Algorithm: Knuth-Morris-Pratt', () => { | ||
| describe('KMPSearch', () => { | ||
| it('Should return true when the pattern equals the text', () => { | ||
| expect(KMPSearch('A', 'A')).toEqual(true); | ||
| }); | ||
| it('Should return true when the pattern is a single character and is contained within the text', () => { | ||
| expect(KMPSearch('S', 'TEST')).toEqual(true); | ||
| }); | ||
| it('Should return true when the pattern is multiple characters and in the middle of the text', () => { | ||
| expect(KMPSearch('WORLD', 'TESTWORLDTEST')).toEqual(true); | ||
| }); | ||
| it('Should return true when the pattern is present multiple times within the text', () => { | ||
| expect(KMPSearch('ST', 'TESTWORLDTEST')).toEqual(true); | ||
| }); | ||
| it('Should return true when the pattern is a single character and is present at the start of the text', () => { | ||
| expect(KMPSearch('A', 'ABABABAABCABCABC')).toEqual(true); | ||
| }); | ||
| it('Should return true when the pattern is multiple characters and is present at the start of the text', () => { | ||
| expect(KMPSearch('AB', 'ABABABAABCABCABC')).toEqual(true); | ||
| }); | ||
| it('Should return true when the pattern contains repeating characters, and is present in the middle of the text', () => { | ||
| expect(KMPSearch('AAABAAAA', 'AAAAAAAAAAABAAAAAA')).toEqual(true); | ||
| }); | ||
| it('Should return true when the pattern is contained within the text and the pattern contains non alphabetic characters', () => { | ||
| expect(KMPSearch('AAA123! ', 'AAAAAA123! AAAAABAAAAAA')).toEqual(true); | ||
| }); | ||
| it('Should return false when the pattern does not equal the text', () => { | ||
| expect(KMPSearch('A', 'B')).toEqual(false); | ||
| }); | ||
| it('Should return false when the pattern is not contained within the text', () => { | ||
| expect(KMPSearch('AD', 'ABABABAABCABCABC')).toEqual(false); | ||
| }); | ||
| it('Should return false when the pattern is longer than the text', () => { | ||
| expect(KMPSearch('AAAAAAAA', 'AAAAAA')).toEqual(false); | ||
| }); | ||
| }); | ||
| }); |
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