Created
November 14, 2013 20:02
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{ | |
"metadata": { | |
"name": "" | |
}, | |
"nbformat": 3, | |
"nbformat_minor": 0, | |
"worksheets": [ | |
{ | |
"cells": [ | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"def z(s):\n", | |
" ''' Use Z-algorithm to preprocess given string. See\n", | |
" Gusfield for complete description of algorithm. '''\n", | |
" \n", | |
" Z = [len(s)] + [0] * len(s)\n", | |
" assert len(s) > 1\n", | |
" \n", | |
" # Initial comparison of s[1:] with prefix\n", | |
" for i in xrange(1, len(s)):\n", | |
" if s[i] == s[i-1]:\n", | |
" Z[1] += 1\n", | |
" else:\n", | |
" break\n", | |
" \n", | |
" r, l = 0, 0\n", | |
" if Z[1] > 0:\n", | |
" r, l = Z[1], 1\n", | |
" \n", | |
" for k in xrange(2, len(s)):\n", | |
" assert Z[k] == 0\n", | |
" if k > r:\n", | |
" # Case 1\n", | |
" for i in xrange(k, len(s)):\n", | |
" if s[i] == s[i-k]:\n", | |
" Z[k] += 1\n", | |
" else:\n", | |
" break\n", | |
" r, l = k + Z[k] - 1, k\n", | |
" else:\n", | |
" # Case 2\n", | |
" # Calculate length of beta\n", | |
" nbeta = r - k + 1\n", | |
" Zkp = Z[k - l]\n", | |
" if nbeta > Zkp:\n", | |
" # Case 2a: Zkp wins\n", | |
" Z[k] = Zkp\n", | |
" else:\n", | |
" # Case 2b: Compare characters just past r\n", | |
" nmatch = 0\n", | |
" for i in xrange(r+1, len(s)):\n", | |
" if s[i] == s[i - k]:\n", | |
" nmatch += 1\n", | |
" else:\n", | |
" break\n", | |
" l, r = k, r + nmatch\n", | |
" Z[k] = r - k + 1\n", | |
" return Z" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [], | |
"prompt_number": 1 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"z('abracadabra')\n", | |
"# abracadabra (11)\n", | |
"# a (1)\n", | |
"# a (1)\n", | |
"# abra (4)\n", | |
"# a (1)" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"metadata": {}, | |
"output_type": "pyout", | |
"prompt_number": 2, | |
"text": [ | |
"[11, 0, 0, 1, 0, 1, 0, 4, 0, 0, 1, 0]" | |
] | |
} | |
], | |
"prompt_number": 2 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"z('aaaaa')" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"metadata": {}, | |
"output_type": "pyout", | |
"prompt_number": 3, | |
"text": [ | |
"[5, 4, 3, 2, 1, 0]" | |
] | |
} | |
], | |
"prompt_number": 3 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"def zMatch(p, t):\n", | |
" s = p + \"$\" + t\n", | |
" Z = z(s)\n", | |
" occurrences = []\n", | |
" for i in xrange(len(p) + 1, len(s)):\n", | |
" if Z[i] >= len(p):\n", | |
" occurrences.append(i - (len(p) + 1))\n", | |
" return occurrences" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [], | |
"prompt_number": 4 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"zMatch('needle', 'haystack needle haystack')\n", | |
"# 012345678901234567890123\n", | |
"# 1 2" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"metadata": {}, | |
"output_type": "pyout", | |
"prompt_number": 5, | |
"text": [ | |
"[9]" | |
] | |
} | |
], | |
"prompt_number": 5 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"zMatch('needle', 'haystack needle needle')\n", | |
"# 0123456789012345678901\n", | |
"# 1 2" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"metadata": {}, | |
"output_type": "pyout", | |
"prompt_number": 6, | |
"text": [ | |
"[9, 16]" | |
] | |
} | |
], | |
"prompt_number": 6 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [] | |
} | |
], | |
"metadata": {} | |
} | |
] | |
} |
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