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Update substring search to use the Two Way algorithm #26327

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merged 4 commits into from
Jun 30, 2015
Merged

Update substring search to use the Two Way algorithm #26327

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b890b7b
StrSearcher: Update substring search to use the Two Way algorithm
Jun 14, 2015
a6dd203
StrSearcher: Specialize is_prefix_of/is_suffix_of for &str
Jun 17, 2015
71006bd
StrSearcher: Use trait to specialize two way algorithm by case
Jun 21, 2015
274bb24
StrSearcher: Explicitly separate the long and short cases
Jun 24, 2015
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10 changes: 9 additions & 1 deletion src/libcollectionstest/str.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -705,7 +705,7 @@ fn test_split_at() {
#[should_panic]
fn test_split_at_boundscheck() {
let s = "ศไทย中华Việt Nam";
let (a, b) = s.split_at(1);
s.split_at(1);
}

#[test]
Expand Down Expand Up @@ -1820,6 +1820,14 @@ mod pattern {
Match (4, 6),
Reject(6, 7),
]);
make_test!(str_searcher_ascii_haystack_seq, "bb", "abbcbbbbd", [
Reject(0, 1),
Match (1, 3),
Reject(3, 4),
Match (4, 6),
Match (6, 8),
Reject(8, 9),
]);
make_test!(str_searcher_empty_needle_ascii_haystack, "", "abbcbbd", [
Match (0, 0),
Reject(0, 1),
Expand Down
299 changes: 1 addition & 298 deletions src/libcore/str/mod.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -15,13 +15,12 @@
#![doc(primitive = "str")]
#![stable(feature = "rust1", since = "1.0.0")]

use self::OldSearcher::{TwoWay, TwoWayLong};
use self::pattern::Pattern;
use self::pattern::{Searcher, ReverseSearcher, DoubleEndedSearcher};

use char::CharExt;
use clone::Clone;
use cmp::{self, Eq};
use cmp::Eq;
use convert::AsRef;
use default::Default;
use fmt;
Expand All @@ -33,7 +32,6 @@ use option::Option::{self, None, Some};
use raw::{Repr, Slice};
use result::Result::{self, Ok, Err};
use slice::{self, SliceExt};
use usize;

pub mod pattern;

Expand Down Expand Up @@ -870,301 +868,6 @@ impl<'a> DoubleEndedIterator for LinesAny<'a> {
}
}

/// The internal state of an iterator that searches for matches of a substring
/// within a larger string using two-way search
#[derive(Clone)]
struct TwoWaySearcher {
// constants
crit_pos: usize,
period: usize,
byteset: u64,

// variables
position: usize,
memory: usize
}

/*
This is the Two-Way search algorithm, which was introduced in the paper:
Crochemore, M., Perrin, D., 1991, Two-way string-matching, Journal of the ACM 38(3):651-675.

Here's some background information.

A *word* is a string of symbols. The *length* of a word should be a familiar
notion, and here we denote it for any word x by |x|.
(We also allow for the possibility of the *empty word*, a word of length zero).

If x is any non-empty word, then an integer p with 0 < p <= |x| is said to be a
*period* for x iff for all i with 0 <= i <= |x| - p - 1, we have x[i] == x[i+p].
For example, both 1 and 2 are periods for the string "aa". As another example,
the only period of the string "abcd" is 4.

We denote by period(x) the *smallest* period of x (provided that x is non-empty).
This is always well-defined since every non-empty word x has at least one period,
|x|. We sometimes call this *the period* of x.

If u, v and x are words such that x = uv, where uv is the concatenation of u and
v, then we say that (u, v) is a *factorization* of x.

Let (u, v) be a factorization for a word x. Then if w is a non-empty word such
that both of the following hold

- either w is a suffix of u or u is a suffix of w
- either w is a prefix of v or v is a prefix of w

then w is said to be a *repetition* for the factorization (u, v).

Just to unpack this, there are four possibilities here. Let w = "abc". Then we
might have:

- w is a suffix of u and w is a prefix of v. ex: ("lolabc", "abcde")
- w is a suffix of u and v is a prefix of w. ex: ("lolabc", "ab")
- u is a suffix of w and w is a prefix of v. ex: ("bc", "abchi")
- u is a suffix of w and v is a prefix of w. ex: ("bc", "a")

Note that the word vu is a repetition for any factorization (u,v) of x = uv,
so every factorization has at least one repetition.

If x is a string and (u, v) is a factorization for x, then a *local period* for
(u, v) is an integer r such that there is some word w such that |w| = r and w is
a repetition for (u, v).

We denote by local_period(u, v) the smallest local period of (u, v). We sometimes
call this *the local period* of (u, v). Provided that x = uv is non-empty, this
is well-defined (because each non-empty word has at least one factorization, as
noted above).

It can be proven that the following is an equivalent definition of a local period
for a factorization (u, v): any positive integer r such that x[i] == x[i+r] for
all i such that |u| - r <= i <= |u| - 1 and such that both x[i] and x[i+r] are
defined. (i.e. i > 0 and i + r < |x|).

Using the above reformulation, it is easy to prove that

1 <= local_period(u, v) <= period(uv)

A factorization (u, v) of x such that local_period(u,v) = period(x) is called a
*critical factorization*.

The algorithm hinges on the following theorem, which is stated without proof:

**Critical Factorization Theorem** Any word x has at least one critical
factorization (u, v) such that |u| < period(x).

The purpose of maximal_suffix is to find such a critical factorization.

*/
impl TwoWaySearcher {
#[allow(dead_code)]
fn new(needle: &[u8]) -> TwoWaySearcher {
let (crit_pos_false, period_false) = TwoWaySearcher::maximal_suffix(needle, false);
let (crit_pos_true, period_true) = TwoWaySearcher::maximal_suffix(needle, true);

let (crit_pos, period) =
if crit_pos_false > crit_pos_true {
(crit_pos_false, period_false)
} else {
(crit_pos_true, period_true)
};

// This isn't in the original algorithm, as far as I'm aware.
let byteset = needle.iter()
.fold(0, |a, &b| (1 << ((b & 0x3f) as usize)) | a);

// A particularly readable explanation of what's going on here can be found
// in Crochemore and Rytter's book "Text Algorithms", ch 13. Specifically
// see the code for "Algorithm CP" on p. 323.
//
// What's going on is we have some critical factorization (u, v) of the
// needle, and we want to determine whether u is a suffix of
// &v[..period]. If it is, we use "Algorithm CP1". Otherwise we use
// "Algorithm CP2", which is optimized for when the period of the needle
// is large.
if &needle[..crit_pos] == &needle[period.. period + crit_pos] {
TwoWaySearcher {
crit_pos: crit_pos,
period: period,
byteset: byteset,

position: 0,
memory: 0
}
} else {
TwoWaySearcher {
crit_pos: crit_pos,
period: cmp::max(crit_pos, needle.len() - crit_pos) + 1,
byteset: byteset,

position: 0,
memory: usize::MAX // Dummy value to signify that the period is long
}
}
}

// One of the main ideas of Two-Way is that we factorize the needle into
// two halves, (u, v), and begin trying to find v in the haystack by scanning
// left to right. If v matches, we try to match u by scanning right to left.
// How far we can jump when we encounter a mismatch is all based on the fact
// that (u, v) is a critical factorization for the needle.
#[inline]
fn next(&mut self, haystack: &[u8], needle: &[u8], long_period: bool)
-> Option<(usize, usize)> {
'search: loop {
// Check that we have room to search in
if self.position + needle.len() > haystack.len() {
return None;
}

// Quickly skip by large portions unrelated to our substring
if (self.byteset >>
((haystack[self.position + needle.len() - 1] & 0x3f)
as usize)) & 1 == 0 {
self.position += needle.len();
if !long_period {
self.memory = 0;
}
continue 'search;
}

// See if the right part of the needle matches
let start = if long_period { self.crit_pos }
else { cmp::max(self.crit_pos, self.memory) };
for i in start..needle.len() {
if needle[i] != haystack[self.position + i] {
self.position += i - self.crit_pos + 1;
if !long_period {
self.memory = 0;
}
continue 'search;
}
}

// See if the left part of the needle matches
let start = if long_period { 0 } else { self.memory };
for i in (start..self.crit_pos).rev() {
if needle[i] != haystack[self.position + i] {
self.position += self.period;
if !long_period {
self.memory = needle.len() - self.period;
}
continue 'search;
}
}

// We have found a match!
let match_pos = self.position;
self.position += needle.len(); // add self.period for all matches
if !long_period {
self.memory = 0; // set to needle.len() - self.period for all matches
}
return Some((match_pos, match_pos + needle.len()));
}
}

// Computes a critical factorization (u, v) of `arr`.
// Specifically, returns (i, p), where i is the starting index of v in some
// critical factorization (u, v) and p = period(v)
#[inline]
#[allow(dead_code)]
#[allow(deprecated)]
fn maximal_suffix(arr: &[u8], reversed: bool) -> (usize, usize) {
let mut left: usize = !0; // Corresponds to i in the paper
let mut right = 0; // Corresponds to j in the paper
let mut offset = 1; // Corresponds to k in the paper
let mut period = 1; // Corresponds to p in the paper

while right + offset < arr.len() {
let a;
let b;
if reversed {
a = arr[left.wrapping_add(offset)];
b = arr[right + offset];
} else {
a = arr[right + offset];
b = arr[left.wrapping_add(offset)];
}
if a < b {
// Suffix is smaller, period is entire prefix so far.
right += offset;
offset = 1;
period = right.wrapping_sub(left);
} else if a == b {
// Advance through repetition of the current period.
if offset == period {
right += offset;
offset = 1;
} else {
offset += 1;
}
} else {
// Suffix is larger, start over from current location.
left = right;
right += 1;
offset = 1;
period = 1;
}
}
(left.wrapping_add(1), period)
}
}

/// The internal state of an iterator that searches for matches of a substring
/// within a larger string using a dynamically chosen search algorithm
#[derive(Clone)]
// NB: This is kept around for convenience because
// it is planned to be used again in the future
enum OldSearcher {
TwoWay(TwoWaySearcher),
TwoWayLong(TwoWaySearcher),
}

impl OldSearcher {
#[allow(dead_code)]
fn new(haystack: &[u8], needle: &[u8]) -> OldSearcher {
if needle.is_empty() {
// Handle specially
unimplemented!()
// FIXME: Tune this.
// FIXME(#16715): This unsigned integer addition will probably not
// overflow because that would mean that the memory almost solely
// consists of the needle. Needs #16715 to be formally fixed.
} else if needle.len() + 20 > haystack.len() {
// Use naive searcher
unimplemented!()
} else {
let searcher = TwoWaySearcher::new(needle);
if searcher.memory == usize::MAX { // If the period is long
TwoWayLong(searcher)
} else {
TwoWay(searcher)
}
}
}
}

#[derive(Clone)]
// NB: This is kept around for convenience because
// it is planned to be used again in the future
struct OldMatchIndices<'a, 'b> {
// constants
haystack: &'a str,
needle: &'b str,
searcher: OldSearcher
}

impl<'a, 'b> OldMatchIndices<'a, 'b> {
#[inline]
#[allow(dead_code)]
fn next(&mut self) -> Option<(usize, usize)> {
match self.searcher {
TwoWay(ref mut searcher)
=> searcher.next(self.haystack.as_bytes(), self.needle.as_bytes(), false),
TwoWayLong(ref mut searcher)
=> searcher.next(self.haystack.as_bytes(), self.needle.as_bytes(), true),
}
}
}

/*
Section: Comparing strings
*/
Expand Down
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