suffixarray: a package for creating suffixarray-based indexes

This is a replacement for pending CL 2219042. It only contains
the raw suffixarray functionality with two methods:

- New       create a new index from some data
- Lookup    lookup occurences of a bytes slice in the data

Any other functionality (dealing with multiple data sets and
the corresponding position lists) is generic and doesn't have
to be part of this package.

Known performance bug: This implementation works fine for data sets
up to several megabytes as long as it doesn't contain very long
contiguous sequences of equal bytes. For instance, index creation for
all .go files under GOROOT (250KLOCs, approx. 9MB) takes ~50s on
2.66 GHz Intel Xeon as long as test/fixedbugs/257.go is excluded.
With that file, index creation times takes several days. 257.go contains
a string of 1M smiley faces.

There are more sophisticated suffixarray creation algorithms which
can handle very long common prefixes. The implementation can be
updated w/o the need to change the interface.

R=rsc, r, PeterGo
CC=golang-dev
https://golang.org/cl/2265041

src/pkg/Makefile

@@ -84,6 +84,7 @@ DIRS=\
 	image\
 	image/jpeg\
 	image/png\
+	index/suffixarray\
 	io\
 	io/ioutil\
 	json\

src/pkg/index/suffixarray/Makefile

@@ -0,0 +1,11 @@
+# Copyright 2010 The Go Authors. All rights reserved.
+# Use of this source code is governed by a BSD-style
+# license that can be found in the LICENSE file.
+
+include ../../../Make.inc
+
+TARG=index/suffixarray
+GOFILES=\
+	suffixarray.go\
+
+include ../../../Make.pkg

src/pkg/index/suffixarray/suffixarray.go

@@ -0,0 +1,117 @@
+// Copyright 2010 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// The suffixarray package implements substring search in logarithmic time
+// using an in-memory suffix array.
+//
+// Example use:
+//
+//	// create index for some data
+//	index := suffixarray.New(data)
+//
+//	// lookup byte slice s
+//	offsets1 := index.Lookup(s, -1) // the list of all indices where s occurs in data
+//	offsets2 := index.Lookup(s, 3)  // the list of at most 3 indices where s occurs in data
+//
+package suffixarray
+
+import (
+	"bytes"
+	"container/vector"
+	"sort"
+)
+
+// BUG(gri): For larger data (10MB) which contains very long (say 100000)
+// contiguous sequences of identical bytes, index creation time will be extremely slow.
+
+// TODO(gri): Use a more sophisticated algorithm to create the suffix array.
+
+
+// Index implements a suffix array for fast substring search.
+type Index struct {
+	data []byte
+	sa   []int // suffix array for data
+}
+
+
+// New creates a new Index for data.
+// Index creation time is approximately O(N*log(N)) for N = len(data).
+//
+func New(data []byte) *Index {
+	sa := make([]int, len(data))
+	for i, _ := range sa {
+		sa[i] = i
+	}
+	x := &index{data, sa}
+	sort.Sort(x)
+	return (*Index)(x)
+}
+
+
+func (x *Index) at(i int) []byte {
+	return x.data[x.sa[i]:]
+}
+
+
+// Binary search according to "A Method of Programming", E.W. Dijkstra.
+func (x *Index) search(s []byte) int {
+	i, j := 0, len(x.sa)
+	// i < j for non-empty x
+	for i+1 < j {
+		// 0 <= i < j <= len(x.sa) && (x.at(i) <= s < x.at(j) || (s is not in x))
+		h := i + (j-i)/2 // i < h < j
+		if bytes.Compare(x.at(h), s) <= 0 {
+			i = h
+		} else { // s < x.at(h)
+			j = h
+		}
+	}
+	// i+1 == j for non-empty x
+	return i
+}
+
+
+// Lookup returns an unsorted list of at most n indices where the byte string s
+// occurs in the indexed data. If n < 0, all occurrences are returned.
+// The result is nil if s is empty, s is not found, or n == 0.
+// Lookup time is O((log(N) + len(res))*len(s)) where N is the
+// size of the indexed data.
+//
+func (x *Index) Lookup(s []byte, n int) []int {
+	var res vector.IntVector
+
+	if len(s) > 0 && n != 0 {
+		// find matching suffix index i
+		i := x.search(s)
+		// x.at(i) <= s < x.at(i+1)
+
+		// ignore the first suffix if it is < s
+		if i < len(x.sa) && bytes.Compare(x.at(i), s) < 0 {
+			i++
+		}
+
+		// collect the following suffixes with matching prefixes
+		for (n < 0 || len(res) < n) && i < len(x.sa) && bytes.HasPrefix(x.at(i), s) {
+			res.Push(x.sa[i])
+			i++
+		}
+	}
+
+	return res
+}
+
+
+// index is like Index; it is only used to hide the sort.Interface methods
+type index struct {
+	data []byte
+	sa   []int
+}
+
+
+// index implements sort.Interface
+
+func (x *index) Len() int           { return len(x.sa) }
+func (x *index) Less(i, j int) bool { return bytes.Compare(x.at(i), x.at(j)) < 0 }
+func (x *index) Swap(i, j int)      { x.sa[i], x.sa[j] = x.sa[j], x.sa[i] }
+func (a *index) at(i int) []byte    { return a.data[a.sa[i]:] }

src/pkg/index/suffixarray/suffixarray_test.go

@@ -0,0 +1,161 @@
+// Copyright 2010 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package suffixarray
+
+import (
+	"container/vector"
+	"sort"
+	"strings"
+	"testing"
+)
+
+
+type testCase struct {
+	name    string   // name of test case
+	source  string   // source to index
+	lookups []string // strings to lookup
+}
+
+
+var testCases = []testCase{
+	testCase{
+		"empty string",
+		"",
+		[]string{
+			"",
+			"foo",
+		},
+	},
+
+	testCase{
+		"all a's",
+		"aaaaaaaaaa", // 10 a's
+		[]string{
+			"",
+			"a",
+			"aa",
+			"aaa",
+			"aaaa",
+			"aaaaa",
+			"aaaaaa",
+			"aaaaaaa",
+			"aaaaaaaa",
+			"aaaaaaaaa",
+			"aaaaaaaaaa",
+			"aaaaaaaaaaa", // 11 a's
+		},
+	},
+
+	testCase{
+		"abc",
+		"abc",
+		[]string{
+			"a",
+			"b",
+			"c",
+			"ab",
+			"bc",
+			"abc",
+		},
+	},
+
+	testCase{
+		"barbara*3",
+		"barbarabarbarabarbara",
+		[]string{
+			"a",
+			"bar",
+			"rab",
+			"arab",
+			"barbar",
+		},
+	},
+
+	testCase{
+		"typing drill",
+		"Now is the time for all good men to come to the aid of their country.",
+		[]string{
+			"Now",
+			"the time",
+			"to come the aid",
+			"is the time for all good men to come to the aid of their",
+		},
+	},
+}
+
+
+// find all occurences of s in source; report at most n occurences
+func find(src, s string, n int) []int {
+	var res vector.IntVector
+	if s != "" && n != 0 {
+		// find at most n occurences of s in src
+		for i := -1; n < 0 || len(res) < n; {
+			j := strings.Index(src[i+1:], s)
+			if j < 0 {
+				break
+			}
+			i += j + 1
+			res.Push(i)
+		}
+	}
+	return res
+}
+
+
+func testLookups(t *testing.T, src string, x *Index, tc *testCase, n int) {
+	for _, s := range tc.lookups {
+		res := x.Lookup([]byte(s), n)
+		exp := find(tc.source, s, n)
+
+		// check that the lengths match
+		if len(res) != len(exp) {
+			t.Errorf("test %q, lookup %q (n = %d): expected %d results; got %d", tc.name, s, n, len(exp), len(res))
+		}
+
+		// if n >= 0 the number of results is limited --- unless n >= all results,
+		// we may obtain different positions from the Index and from find (because
+		// Index may not find the results in the same order as find) => in general
+		// we cannot simply check that the res and exp lists are equal
+
+		// check that there are no duplicates
+		sort.SortInts(res)
+		for i, r := range res {
+			if i > 0 && res[i-1] == r {
+				t.Errorf("test %q, lookup %q, result %d (n = %d): found duplicate index %d", tc.name, s, i, n, r)
+			}
+		}
+
+		// check that each result is in fact a correct match
+		for i, r := range res {
+			if r < 0 || len(src) <= r {
+				t.Errorf("test %q, lookup %q, result %d (n = %d): index %d out of range [0, %d[", tc.name, s, i, n, r, len(src))
+			} else if !strings.HasPrefix(src[r:], s) {
+				t.Errorf("test %q, lookup %q, result %d (n = %d): index %d not a match", tc.name, s, i, n, r)
+			}
+		}
+
+		if n < 0 {
+			// all results computed - sorted res and exp must be equal
+			for i, r := range res {
+				e := exp[i]
+				if r != e {
+					t.Errorf("test %q, lookup %q, result %d: expected index %d; got %d", tc.name, s, i, e, r)
+					continue
+				}
+			}
+		}
+	}
+}
+
+
+func TestIndex(t *testing.T) {
+	for _, tc := range testCases {
+		x := New([]byte(tc.source))
+		testLookups(t, tc.source, x, &tc, 0)
+		testLookups(t, tc.source, x, &tc, 1)
+		testLookups(t, tc.source, x, &tc, 10)
+		testLookups(t, tc.source, x, &tc, -1)
+	}
+}