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sorting.d
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sorting.d
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// Written in the D programming language.
/**
This is a submodule of $(MREF std, algorithm).
It contains generic _sorting algorithms.
$(BOOKTABLE Cheat Sheet,
$(TR $(TH Function Name) $(TH Description))
$(T2 completeSort,
If $(D a = [10, 20, 30]) and $(D b = [40, 6, 15]), then
$(D completeSort(a, b)) leaves $(D a = [6, 10, 15]) and $(D b = [20,
30, 40]).
The range $(D a) must be sorted prior to the call, and as a result the
combination $(D $(REF chain, std,range)(a, b)) is sorted.)
$(T2 isPartitioned,
$(D isPartitioned!"a < 0"([-1, -2, 1, 0, 2])) returns $(D true) because
the predicate is $(D true) for a portion of the range and $(D false)
afterwards.)
$(T2 isSorted,
$(D isSorted([1, 1, 2, 3])) returns $(D true).)
$(T2 isStrictlyMonotonic,
$(D isStrictlyMonotonic([1, 1, 2, 3])) returns $(D false).)
$(T2 ordered,
$(D ordered(1, 1, 2, 3)) returns $(D true).)
$(T2 strictlyOrdered,
$(D strictlyOrdered(1, 1, 2, 3)) returns $(D false).)
$(T2 makeIndex,
Creates a separate index for a range.)
$(T2 merge,
Lazily merges two or more sorted ranges.)
$(T2 multiSort,
Sorts by multiple keys.)
$(T2 nextEvenPermutation,
Computes the next lexicographically greater even permutation of a range
in-place.)
$(T2 nextPermutation,
Computes the next lexicographically greater permutation of a range
in-place.)
$(T2 partialSort,
If $(D a = [5, 4, 3, 2, 1]), then $(D partialSort(a, 3)) leaves
$(D a[0 .. 3] = [1, 2, 3]).
The other elements of $(D a) are left in an unspecified order.)
$(T2 partition,
Partitions a range according to a unary predicate.)
$(T2 partition3,
Partitions a range according to a binary predicate in three parts (less
than, equal, greater than the given pivot). Pivot is not given as an
index, but instead as an element independent from the range's content.)
$(T2 pivotPartition,
Partitions a range according to a binary predicate in two parts: less
than or equal, and greater than or equal to the given pivot, passed as
an index in the range.)
$(T2 schwartzSort,
Sorts with the help of the $(LUCKY Schwartzian transform).)
$(T2 sort,
Sorts.)
$(T2 topN,
Separates the top elements in a range.)
$(T2 topNCopy,
Copies out the top elements of a range.)
$(T2 topNIndex,
Builds an index of the top elements of a range.)
)
Copyright: Andrei Alexandrescu 2008-.
License: $(HTTP boost.org/LICENSE_1_0.txt, Boost License 1.0).
Authors: $(HTTP erdani.com, Andrei Alexandrescu)
Source: $(PHOBOSSRC std/algorithm/_sorting.d)
Macros:
T2=$(TR $(TDNW $(LREF $1)) $(TD $+))
*/
module std.algorithm.sorting;
import std.typecons : Flag;
import std.algorithm.mutation : SwapStrategy;
import std.functional; // : unaryFun, binaryFun;
import std.range.primitives;
// FIXME
import std.range; // : SortedRange;
import std.traits;
import std.meta; // : allSatisfy;
/**
Specifies whether the output of certain algorithm is desired in sorted
format.
If set to $(D SortOutput.no), the output should not be sorted.
Otherwise if set to $(D SortOutput.yes), the output should be sorted.
*/
alias SortOutput = Flag!"sortOutput";
// completeSort
/**
Sorts the random-access range $(D chain(lhs, rhs)) according to
predicate $(D less). The left-hand side of the range $(D lhs) is
assumed to be already sorted; $(D rhs) is assumed to be unsorted. The
exact strategy chosen depends on the relative sizes of $(D lhs) and
$(D rhs). Performs $(BIGOH lhs.length + rhs.length * log(rhs.length))
(best case) to $(BIGOH (lhs.length + rhs.length) * log(lhs.length +
rhs.length)) (worst-case) evaluations of $(D swap).
Params:
less = The predicate to sort by.
ss = The swapping strategy to use.
lhs = The sorted, left-hand side of the random access range to be sorted.
rhs = The unsorted, right-hand side of the random access range to be
sorted.
*/
void completeSort(alias less = "a < b", SwapStrategy ss = SwapStrategy.unstable,
RandomAccessRange1, RandomAccessRange2)(SortedRange!(RandomAccessRange1, less) lhs, RandomAccessRange2 rhs)
if (hasLength!(RandomAccessRange2) && hasSlicing!(RandomAccessRange2))
{
import std.algorithm.mutation : bringToFront;
import std.range : chain, assumeSorted;
// Probably this algorithm can be optimized by using in-place
// merge
auto lhsOriginal = lhs.release();
foreach (i; 0 .. rhs.length)
{
auto sortedSoFar = chain(lhsOriginal, rhs[0 .. i]);
auto ub = assumeSorted!less(sortedSoFar).upperBound(rhs[i]);
if (!ub.length) continue;
bringToFront(ub.release(), rhs[i .. i + 1]);
}
}
///
@safe unittest
{
import std.range : assumeSorted;
int[] a = [ 1, 2, 3 ];
int[] b = [ 4, 0, 6, 5 ];
completeSort(assumeSorted(a), b);
assert(a == [ 0, 1, 2 ]);
assert(b == [ 3, 4, 5, 6 ]);
}
// isSorted
/**
Checks whether a forward range is sorted according to the comparison
operation $(D less). Performs $(BIGOH r.length) evaluations of $(D
less).
Unlike $(LREF isSorted), $(LREF isStrictlyMonotonic) does not allow for equal values,
i.e. values for which both `less(a, b)` and `less(b, a)` are false.
With either function, the predicate must be a strict ordering just like with
$(LREF isSorted). For example, using `"a <= b"` instead of `"a < b"` is
incorrect and will cause failed assertions.
Params:
less = Predicate the range should be sorted by.
r = Forward range to check for sortedness.
Returns:
`true` if the range is sorted, false otherwise. $(LREF isSorted) allows
duplicates, $(LREF isStrictlyMonotonic) not.
*/
bool isSorted(alias less = "a < b", Range)(Range r) if (isForwardRange!(Range))
{
if (r.empty) return true;
static if (isRandomAccessRange!Range && hasLength!Range)
{
immutable limit = r.length - 1;
foreach (i; 0 .. limit)
{
if (!binaryFun!less(r[i + 1], r[i])) continue;
assert(
!binaryFun!less(r[i], r[i + 1]),
"Predicate for isSorted is not antisymmetric. Both" ~
" pred(a, b) and pred(b, a) are true for certain values.");
return false;
}
}
else
{
auto ahead = r.save;
ahead.popFront();
size_t i;
for (; !ahead.empty; ahead.popFront(), r.popFront(), ++i)
{
if (!binaryFun!less(ahead.front, r.front)) continue;
// Check for antisymmetric predicate
assert(
!binaryFun!less(r.front, ahead.front),
"Predicate for isSorted is not antisymmetric. Both" ~
" pred(a, b) and pred(b, a) are true for certain values.");
return false;
}
}
return true;
}
///
@safe unittest
{
assert([1, 1, 2].isSorted);
// strictly monotonic doesn't allow duplicates
assert(![1, 1, 2].isStrictlyMonotonic);
int[] arr = [4, 3, 2, 1];
assert(!isSorted(arr));
assert(!isStrictlyMonotonic(arr));
assert(isSorted!"a > b"(arr));
assert(isStrictlyMonotonic!"a > b"(arr));
sort(arr);
assert(isSorted(arr));
assert(isStrictlyMonotonic(arr));
}
@safe unittest
{
import std.conv : to;
// Issue 9457
auto x = "abcd";
assert(isSorted(x));
auto y = "acbd";
assert(!isSorted(y));
int[] a = [1, 2, 3];
assert(isSorted(a));
int[] b = [1, 3, 2];
assert(!isSorted(b));
// ignores duplicates
int[] c = [1, 1, 2];
assert(isSorted(c));
dchar[] ds = "コーヒーが好きです"d.dup;
sort(ds);
string s = to!string(ds);
assert(isSorted(ds)); // random-access
assert(isSorted(s)); // bidirectional
}
@nogc @safe nothrow pure unittest
{
static immutable a = [1, 2, 3];
assert(a.isSorted);
}
/// ditto
bool isStrictlyMonotonic(alias less = "a < b", Range)(Range r)
if (isForwardRange!Range)
{
import std.algorithm.searching : findAdjacent;
return findAdjacent!((a,b) => !binaryFun!less(a,b))(r).empty;
}
@safe unittest
{
import std.conv : to;
assert("abcd".isStrictlyMonotonic);
assert(!"aacd".isStrictlyMonotonic);
assert(!"acb".isStrictlyMonotonic);
assert([1, 2, 3].isStrictlyMonotonic);
assert(![1, 3, 2].isStrictlyMonotonic);
assert(![1, 1, 2].isStrictlyMonotonic);
// ー occurs twice -> can't be strict
dchar[] ds = "コーヒーが好きです"d.dup;
sort(ds);
string s = to!string(ds);
assert(!isStrictlyMonotonic(ds)); // random-access
assert(!isStrictlyMonotonic(s)); // bidirectional
dchar[] ds2 = "コーヒが好きです"d.dup;
sort(ds2);
string s2 = to!string(ds2);
assert(isStrictlyMonotonic(ds2)); // random-access
assert(isStrictlyMonotonic(s2)); // bidirectional
}
@nogc @safe nothrow pure unittest
{
static immutable a = [1, 2, 3];
assert(a.isStrictlyMonotonic);
}
/**
Like $(D isSorted), returns $(D true) if the given $(D values) are ordered
according to the comparison operation $(D less). Unlike $(D isSorted), takes values
directly instead of structured in a range.
$(D ordered) allows repeated values, e.g. $(D ordered(1, 1, 2)) is $(D true). To verify
that the values are ordered strictly monotonically, use $(D strictlyOrdered);
$(D strictlyOrdered(1, 1, 2)) is $(D false).
With either function, the predicate must be a strict ordering. For example,
using $(D "a <= b") instead of $(D "a < b") is incorrect and will cause failed
assertions.
Params:
values = The tested value
less = The comparison predicate
Returns:
$(D true) if the values are ordered; $(D ordered) allows for duplicates,
$(D strictlyOrdered) does not.
*/
bool ordered(alias less = "a < b", T...)(T values)
if ((T.length == 2 && is(typeof(binaryFun!less(values[1], values[0])) : bool))
||
(T.length > 2 && is(typeof(ordered!less(values[0 .. 1 + $ / 2])))
&& is(typeof(ordered!less(values[$ / 2 .. $]))))
)
{
foreach (i, _; T[0 .. $ - 1])
{
if (binaryFun!less(values[i + 1], values[i]))
{
assert(!binaryFun!less(values[i], values[i + 1]),
__FUNCTION__ ~ ": incorrect non-strict predicate.");
return false;
}
}
return true;
}
/// ditto
bool strictlyOrdered(alias less = "a < b", T...)(T values)
if (is(typeof(ordered!less(values))))
{
foreach (i, _; T[0 .. $ - 1])
{
if (!binaryFun!less(values[i], values[i + 1]))
{
return false;
}
assert(!binaryFun!less(values[i + 1], values[i]),
__FUNCTION__ ~ ": incorrect non-strict predicate.");
}
return true;
}
///
@safe unittest
{
assert(ordered(42, 42, 43));
assert(!strictlyOrdered(43, 42, 45));
assert(ordered(42, 42, 43));
assert(!strictlyOrdered(42, 42, 43));
assert(!ordered(43, 42, 45));
// Ordered lexicographically
assert(ordered("Jane", "Jim", "Joe"));
assert(strictlyOrdered("Jane", "Jim", "Joe"));
// Incidentally also ordered by length decreasing
assert(ordered!((a, b) => a.length > b.length)("Jane", "Jim", "Joe"));
// ... but not strictly so: "Jim" and "Joe" have the same length
assert(!strictlyOrdered!((a, b) => a.length > b.length)("Jane", "Jim", "Joe"));
}
// partition
/**
Partitions a range in two using the given $(D predicate).
Specifically, reorders the range $(D r = [left, right$(RPAREN)) using $(D swap)
such that all elements $(D i) for which $(D predicate(i)) is $(D true) come
before all elements $(D j) for which $(D predicate(j)) returns $(D false).
Performs $(BIGOH r.length) (if unstable or semistable) or $(BIGOH
r.length * log(r.length)) (if stable) evaluations of $(D less) and $(D
swap). The unstable version computes the minimum possible evaluations
of $(D swap) (roughly half of those performed by the semistable
version).
Params:
predicate = The predicate to partition by.
ss = The swapping strategy to employ.
r = The random-access range to partition.
Returns:
The right part of $(D r) after partitioning.
If $(D ss == SwapStrategy.stable), $(D partition) preserves the relative
ordering of all elements $(D a), $(D b) in $(D r) for which $(D predicate(a) ==
predicate(b)). If $(D ss == SwapStrategy.semistable), $(D partition) preserves
the relative ordering of all elements $(D a), $(D b) in the left part of $(D r)
for which $(D predicate(a) == predicate(b)).
See_Also:
STL's $(HTTP sgi.com/tech/stl/_partition.html, _partition)$(BR)
STL's $(HTTP sgi.com/tech/stl/stable_partition.html, stable_partition)
*/
Range partition(alias predicate, SwapStrategy ss, Range)(Range r)
if (ss == SwapStrategy.stable && isRandomAccessRange!(Range) && hasLength!Range && hasSlicing!Range)
{
import std.algorithm.mutation : bringToFront;
alias pred = unaryFun!(predicate);
if (r.empty) return r;
if (r.length == 1)
{
if (pred(r.front)) r.popFront();
return r;
}
const middle = r.length / 2;
alias recurse = .partition!(pred, ss, Range);
auto lower = recurse(r[0 .. middle]);
auto upper = recurse(r[middle .. r.length]);
bringToFront(lower, r[middle .. r.length - upper.length]);
return r[r.length - lower.length - upper.length .. r.length];
}
///ditto
Range partition(alias predicate, SwapStrategy ss = SwapStrategy.unstable, Range)(Range r)
if (ss != SwapStrategy.stable && isInputRange!Range && hasSwappableElements!Range)
{
import std.algorithm.mutation : swap;
alias pred = unaryFun!(predicate);
static if (ss == SwapStrategy.semistable)
{
if (r.empty) return r;
for (; !r.empty; r.popFront())
{
// skip the initial portion of "correct" elements
if (pred(r.front)) continue;
// hit the first "bad" element
auto result = r;
for (r.popFront(); !r.empty; r.popFront())
{
if (!pred(r.front)) continue;
swap(result.front, r.front);
result.popFront();
}
return result;
}
return r;
}
else
{
// Inspired from www.stepanovpapers.com/PAM3-partition_notes.pdf,
// section "Bidirectional Partition Algorithm (Hoare)"
static if (isDynamicArray!Range)
{
import std.algorithm.mutation : swapAt;
// For dynamic arrays prefer index-based manipulation
if (!r.length) return r;
size_t lo = 0, hi = r.length - 1;
for (;;)
{
for (;;)
{
if (lo > hi) return r[lo .. r.length];
if (!pred(r[lo])) break;
++lo;
}
// found the left bound
assert(lo <= hi);
for (;;)
{
if (lo == hi) return r[lo .. r.length];
if (pred(r[hi])) break;
--hi;
}
// found the right bound, swap & make progress
r.swapAt(lo++, hi--);
}
}
else
{
import std.algorithm.mutation : swap;
auto result = r;
for (;;)
{
for (;;)
{
if (r.empty) return result;
if (!pred(r.front)) break;
r.popFront();
result.popFront();
}
// found the left bound
assert(!r.empty);
for (;;)
{
if (pred(r.back)) break;
r.popBack();
if (r.empty) return result;
}
// found the right bound, swap & make progress
static if (is(typeof(swap(r.front, r.back))))
{
swap(r.front, r.back);
}
else
{
auto t1 = r.moveFront(), t2 = r.moveBack();
r.front = t2;
r.back = t1;
}
r.popFront();
result.popFront();
r.popBack();
}
}
}
}
///
@safe unittest
{
import std.algorithm.searching : count, find;
import std.conv : text;
import std.range.primitives : empty;
import std.algorithm.mutation : SwapStrategy;
auto Arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10];
auto arr = Arr.dup;
static bool even(int a) { return (a & 1) == 0; }
// Partition arr such that even numbers come first
auto r = partition!(even)(arr);
// Now arr is separated in evens and odds.
// Numbers may have become shuffled due to instability
assert(r == arr[5 .. $]);
assert(count!(even)(arr[0 .. 5]) == 5);
assert(find!(even)(r).empty);
// Can also specify the predicate as a string.
// Use 'a' as the predicate argument name
arr[] = Arr[];
r = partition!(q{(a & 1) == 0})(arr);
assert(r == arr[5 .. $]);
// Now for a stable partition:
arr[] = Arr[];
r = partition!(q{(a & 1) == 0}, SwapStrategy.stable)(arr);
// Now arr is [2 4 6 8 10 1 3 5 7 9], and r points to 1
assert(arr == [2, 4, 6, 8, 10, 1, 3, 5, 7, 9] && r == arr[5 .. $]);
// In case the predicate needs to hold its own state, use a delegate:
arr[] = Arr[];
int x = 3;
// Put stuff greater than 3 on the left
bool fun(int a) { return a > x; }
r = partition!(fun, SwapStrategy.semistable)(arr);
// Now arr is [4 5 6 7 8 9 10 2 3 1] and r points to 2
assert(arr == [4, 5, 6, 7, 8, 9, 10, 2, 3, 1] && r == arr[7 .. $]);
}
@safe unittest
{
import std.algorithm.internal : rndstuff;
static bool even(int a) { return (a & 1) == 0; }
// test with random data
auto a = rndstuff!int();
partition!even(a);
assert(isPartitioned!even(a));
auto b = rndstuff!string();
partition!`a.length < 5`(b);
assert(isPartitioned!`a.length < 5`(b));
}
// pivotPartition
/**
Partitions `r` around `pivot` using comparison function `less`, algorithm akin
to $(LUCKY Hoare partition). Specifically, permutes elements of `r` and returns
an index $(D k < r.length) such that:
$(UL
$(LI `r[pivot]` is swapped to `r[k]`)
$(LI All elements `e` in subrange $(D r[0 .. k]) satisfy $(D !less(r[k], e))
(i.e. `r[k]` is greater than or equal to each element to its left according to
predicate `less`))
$(LI All elements `e` in subrange $(D r[0 .. k]) satisfy $(D !less(e,
r[k])) (i.e. `r[k]` is less than or equal to each element to its right
according to predicate `less`)))
If `r` contains equivalent elements, multiple permutations of `r` satisfy these
constraints. In such cases, `pivotPartition` attempts to distribute equivalent
elements fairly to the left and right of `k` such that `k` stays close to $(D
r.length / 2).
Params:
less = The predicate used for comparison, modeled as a $(LUCKY strict weak
ordering) (irreflexive, antisymmetric, transitive, and implying a transitive
equivalence)
r = The range being partitioned
pivot = The index of the pivot for partitioning, must be less than `r.length` or
`0` is `r.length` is `0`
Returns:
The new position of the pivot
See_Also:
$(HTTP jgrcs.info/index.php/jgrcs/article/view/142, Engineering of a Quicksort
Partitioning Algorithm), D. Abhyankar, Journal of Global Research in Computer
Science, February 2011. $(HTTPS youtube.com/watch?v=AxnotgLql0k, ACCU 2016
Keynote), Andrei Alexandrescu.
*/
size_t pivotPartition(alias less = "a < b", Range)
(Range r, size_t pivot)
if (isRandomAccessRange!Range && hasLength!Range && hasSlicing!Range)
{
assert(pivot < r.length || r.length == 0 && pivot == 0);
if (r.length <= 1) return 0;
import std.algorithm.mutation : swapAt, move;
alias lt = binaryFun!less;
// Pivot at the front
r.swapAt(pivot, 0);
// Fork implementation depending on nothrow copy, assignment, and
// comparison. If all of these are nothrow, use the specialized
// implementation discussed at https://youtube.com/watch?v=AxnotgLql0k.
static if (is(typeof(
() nothrow { auto x = r.front; x = r.front; return lt(x, x); }
)))
{
auto p = r[0];
// Plant the pivot in the end as well as a sentinel
size_t lo = 0, hi = r.length - 1;
auto save = move(r[hi]);
r[hi] = p; // Vacancy is in r[$ - 1] now
// Start process
for (;;)
{
// Loop invariant
version(unittest)
{
import std.algorithm.searching;
assert(r[0 .. lo].all!(x => !lt(p, x)));
assert(r[hi + 1 .. r.length].all!(x => !lt(x, p)));
}
do ++lo; while (lt(r[lo], p));
r[hi] = r[lo];
// Vacancy is now in r[lo]
do --hi; while (lt(p, r[hi]));
if (lo >= hi) break;
r[lo] = r[hi];
// Vacancy is not in r[hi]
}
// Fixup
assert(lo - hi <= 2);
assert(!lt(p, r[hi]));
if (lo == hi + 2)
{
assert(!lt(r[hi + 1], p));
r[lo] = r[hi + 1];
--lo;
}
r[lo] = save;
if (lt(p, save)) --lo;
assert(!lt(p, r[lo]));
}
else
{
size_t lo = 1, hi = r.length - 1;
loop: for (;; lo++, hi--)
{
for (;; ++lo)
{
if (lo > hi) break loop;
if (!lt(r[lo], r[0])) break;
}
// found the left bound: r[lo] >= r[0]
assert(lo <= hi);
for (;; --hi)
{
if (lo >= hi) break loop;
if (!lt(r[0], r[hi])) break;
}
// found the right bound: r[hi] <= r[0], swap & make progress
assert(!lt(r[lo], r[hi]));
r.swapAt(lo, hi);
}
--lo;
}
r.swapAt(lo, 0);
return lo;
}
///
@safe nothrow unittest
{
int[] a = [5, 3, 2, 6, 4, 1, 3, 7];
size_t pivot = pivotPartition(a, a.length / 2);
import std.algorithm.searching : all;
assert(a[0 .. pivot].all!(x => x <= a[pivot]));
assert(a[pivot .. $].all!(x => x >= a[pivot]));
}
@safe unittest
{
void test(alias less)()
{
int[] a;
size_t pivot;
a = [-9, -4, -2, -2, 9];
pivot = pivotPartition!less(a, a.length / 2);
import std.algorithm.searching : all;
assert(a[0 .. pivot].all!(x => x <= a[pivot]));
assert(a[pivot .. $].all!(x => x >= a[pivot]));
a = [9, 2, 8, -5, 5, 4, -8, -4, 9];
pivot = pivotPartition!less(a, a.length / 2);
assert(a[0 .. pivot].all!(x => x <= a[pivot]));
assert(a[pivot .. $].all!(x => x >= a[pivot]));
a = [ 42 ];
pivot = pivotPartition!less(a, a.length / 2);
assert(pivot == 0);
assert(a == [ 42 ]);
a = [ 43, 42 ];
pivot = pivotPartition!less(a, 0);
assert(pivot == 1);
assert(a == [ 42, 43 ]);
a = [ 43, 42 ];
pivot = pivotPartition!less(a, 1);
assert(pivot == 0);
assert(a == [ 42, 43 ]);
a = [ 42, 42 ];
pivot = pivotPartition!less(a, 0);
assert(pivot == 0 || pivot == 1);
assert(a == [ 42, 42 ]);
pivot = pivotPartition!less(a, 1);
assert(pivot == 0 || pivot == 1);
assert(a == [ 42, 42 ]);
import std.random;
import std.algorithm.iteration : map;
import std.stdio;
auto s = unpredictableSeed;
auto g = Random(s);
a = iota(0, uniform(1, 1000, g))
.map!(_ => uniform(-1000, 1000, g))
.array;
scope(failure) writeln("RNG seed was ", s);
pivot = pivotPartition!less(a, a.length / 2);
assert(a[0 .. pivot].all!(x => x <= a[pivot]));
assert(a[pivot .. $].all!(x => x >= a[pivot]));
}
test!"a < b";
static bool myLess(int a, int b)
{
static bool bogus;
if (bogus) throw new Exception(""); // just to make it no-nothrow
return a < b;
}
test!myLess;
}
/**
Params:
pred = The predicate that the range should be partitioned by.
r = The range to check.
Returns: $(D true) if $(D r) is partitioned according to predicate $(D pred).
*/
bool isPartitioned(alias pred, Range)(Range r)
if (isForwardRange!(Range))
{
for (; !r.empty; r.popFront())
{
if (unaryFun!(pred)(r.front)) continue;
for (r.popFront(); !r.empty; r.popFront())
{
if (unaryFun!(pred)(r.front)) return false;
}
break;
}
return true;
}
///
@safe unittest
{
int[] r = [ 1, 3, 5, 7, 8, 2, 4, ];
assert(isPartitioned!"a & 1"(r));
}
// partition3
/**
Rearranges elements in $(D r) in three adjacent ranges and returns
them. The first and leftmost range only contains elements in $(D r)
less than $(D pivot). The second and middle range only contains
elements in $(D r) that are equal to $(D pivot). Finally, the third
and rightmost range only contains elements in $(D r) that are greater
than $(D pivot). The less-than test is defined by the binary function
$(D less).
Params:
less = The predicate to use for the rearrangement.
ss = The swapping strategy to use.
r = The random-access range to rearrange.
pivot = The pivot element.
Returns:
A $(REF Tuple, std,typecons) of the three resulting ranges. These ranges are
slices of the original range.
BUGS: stable $(D partition3) has not been implemented yet.
*/
auto partition3(alias less = "a < b", SwapStrategy ss = SwapStrategy.unstable, Range, E)
(Range r, E pivot)
if (ss == SwapStrategy.unstable && isRandomAccessRange!Range
&& hasSwappableElements!Range && hasLength!Range && hasSlicing!Range
&& is(typeof(binaryFun!less(r.front, pivot)) == bool)
&& is(typeof(binaryFun!less(pivot, r.front)) == bool)
&& is(typeof(binaryFun!less(r.front, r.front)) == bool))
{
// The algorithm is described in "Engineering a sort function" by
// Jon Bentley et al, pp 1257.
import std.algorithm.mutation : swap, swapAt, swapRanges;
import std.algorithm.comparison : min;
import std.typecons : tuple;
alias lessFun = binaryFun!less;
size_t i, j, k = r.length, l = k;
bigloop:
for (;;)
{
for (;; ++j)
{
if (j == k) break bigloop;
assert(j < r.length);
if (lessFun(r[j], pivot)) continue;
if (lessFun(pivot, r[j])) break;
r.swapAt(i++, j);
}
assert(j < k);
for (;;)
{
assert(k > 0);
if (!lessFun(pivot, r[--k]))
{
if (lessFun(r[k], pivot)) break;
r.swapAt(k, --l);
}
if (j == k) break bigloop;
}
// Here we know r[j] > pivot && r[k] < pivot
r.swapAt(j++, k);
}
// Swap the equal ranges from the extremes into the middle
auto strictlyLess = j - i, strictlyGreater = l - k;
auto swapLen = min(i, strictlyLess);
swapRanges(r[0 .. swapLen], r[j - swapLen .. j]);
swapLen = min(r.length - l, strictlyGreater);
swapRanges(r[k .. k + swapLen], r[r.length - swapLen .. r.length]);
return tuple(r[0 .. strictlyLess],
r[strictlyLess .. r.length - strictlyGreater],
r[r.length - strictlyGreater .. r.length]);
}
///
@safe unittest
{
auto a = [ 8, 3, 4, 1, 4, 7, 4 ];
auto pieces = partition3(a, 4);
assert(pieces[0] == [ 1, 3 ]);
assert(pieces[1] == [ 4, 4, 4 ]);
assert(pieces[2] == [ 8, 7 ]);
}
@safe unittest
{
import std.random : uniform;
auto a = new int[](uniform(0, 100));
foreach (ref e; a)
{
e = uniform(0, 50);
}
auto pieces = partition3(a, 25);
assert(pieces[0].length + pieces[1].length + pieces[2].length == a.length);
foreach (e; pieces[0])
{
assert(e < 25);
}
foreach (e; pieces[1])
{
assert(e == 25);
}
foreach (e; pieces[2])
{
assert(e > 25);
}
}
// makeIndex
/**
Computes an index for $(D r) based on the comparison $(D less). The
index is a sorted array of pointers or indices into the original
range. This technique is similar to sorting, but it is more flexible
because (1) it allows "sorting" of immutable collections, (2) allows
binary search even if the original collection does not offer random
access, (3) allows multiple indexes, each on a different predicate,
and (4) may be faster when dealing with large objects. However, using
an index may also be slower under certain circumstances due to the
extra indirection, and is always larger than a sorting-based solution
because it needs space for the index in addition to the original
collection. The complexity is the same as $(D sort)'s.
The first overload of $(D makeIndex) writes to a range containing
pointers, and the second writes to a range containing offsets. The
first overload requires $(D Range) to be a forward range, and the
latter requires it to be a random-access range.
$(D makeIndex) overwrites its second argument with the result, but
never reallocates it.
Params:
less = The comparison to use.
ss = The swapping strategy.
r = The range to index.
index = The resulting index.
Returns: The pointer-based version returns a $(D SortedRange) wrapper
over index, of type $(D SortedRange!(RangeIndex, (a, b) =>
binaryFun!less(*a, *b))) thus reflecting the ordering of the
index. The index-based version returns $(D void) because the ordering
relation involves not only $(D index) but also $(D r).
Throws: If the second argument's length is less than that of the range
indexed, an exception is thrown.
*/
SortedRange!(RangeIndex, (a, b) => binaryFun!less(*a, *b))
makeIndex(
alias less = "a < b",
SwapStrategy ss = SwapStrategy.unstable,
Range,
RangeIndex)
(Range r, RangeIndex index)
if (isForwardRange!(Range) && isRandomAccessRange!(RangeIndex)
&& is(ElementType!(RangeIndex) : ElementType!(Range)*))
{
import std.algorithm.internal : addressOf;
import std.exception : enforce;
// assume collection already ordered
size_t i;
for (; !r.empty; r.popFront(), ++i)
index[i] = addressOf(r.front);
enforce(index.length == i);
// sort the index
sort!((a, b) => binaryFun!less(*a, *b), ss)(index);
return typeof(return)(index);
}
/// Ditto
void makeIndex(
alias less = "a < b",
SwapStrategy ss = SwapStrategy.unstable,
Range,
RangeIndex)
(Range r, RangeIndex index)
if (isRandomAccessRange!Range && !isInfinite!Range &&
isRandomAccessRange!RangeIndex && !isInfinite!RangeIndex &&
isIntegral!(ElementType!RangeIndex))
{
import std.exception : enforce;
import std.conv : to;
alias IndexType = Unqual!(ElementType!RangeIndex);
enforce(r.length == index.length,
"r and index must be same length for makeIndex.");
static if (IndexType.sizeof < size_t.sizeof)
{
enforce(r.length <= IndexType.max, "Cannot create an index with " ~
"element type " ~ IndexType.stringof ~ " with length " ~
to!string(r.length) ~ ".");
}
for (IndexType i = 0; i < r.length; ++i)
{
index[cast(size_t) i] = i;
}
// sort the index
sort!((a, b) => binaryFun!less(r[cast(size_t) a], r[cast(size_t) b]), ss)
(index);
}