const std = @import("std.zig");
const assert = std.debug.assert;
const testing = std.testing;
const mem = std.mem;
const math = std.math;
pub fn binarySearch(
comptime T: type,
key: T,
items: []const T,
context: anytype,
comptime compareFn: fn (context: @TypeOf(context), lhs: T, rhs: T) math.Order,
) ?usize {
var left: usize = 0;
var right: usize = items.len;
while (left < right) {
const mid = left + (right - left) / 2;
switch (compareFn(context, key, items[mid])) {
.eq => return mid,
.gt => left = mid + 1,
.lt => right = mid,
}
}
return null;
}
test "binarySearch" {
const S = struct {
fn order_u32(context: void, lhs: u32, rhs: u32) math.Order {
_ = context;
return math.order(lhs, rhs);
}
fn order_i32(context: void, lhs: i32, rhs: i32) math.Order {
_ = context;
return math.order(lhs, rhs);
}
};
try testing.expectEqual(
@as(?usize, null),
binarySearch(u32, 1, &[_]u32{}, {}, S.order_u32),
);
try testing.expectEqual(
@as(?usize, 0),
binarySearch(u32, 1, &[_]u32{1}, {}, S.order_u32),
);
try testing.expectEqual(
@as(?usize, null),
binarySearch(u32, 1, &[_]u32{0}, {}, S.order_u32),
);
try testing.expectEqual(
@as(?usize, null),
binarySearch(u32, 0, &[_]u32{1}, {}, S.order_u32),
);
try testing.expectEqual(
@as(?usize, 4),
binarySearch(u32, 5, &[_]u32{ 1, 2, 3, 4, 5 }, {}, S.order_u32),
);
try testing.expectEqual(
@as(?usize, 0),
binarySearch(u32, 2, &[_]u32{ 2, 4, 8, 16, 32, 64 }, {}, S.order_u32),
);
try testing.expectEqual(
@as(?usize, 1),
binarySearch(i32, -4, &[_]i32{ -7, -4, 0, 9, 10 }, {}, S.order_i32),
);
try testing.expectEqual(
@as(?usize, 3),
binarySearch(i32, 98, &[_]i32{ -100, -25, 2, 98, 99, 100 }, {}, S.order_i32),
);
}
pub fn insertionSort(
comptime T: type,
items: []T,
context: anytype,
comptime lessThan: fn (context: @TypeOf(context), lhs: T, rhs: T) bool,
) void {
var i: usize = 1;
while (i < items.len) : (i += 1) {
const x = items[i];
var j: usize = i;
while (j > 0 and lessThan(context, x, items[j - 1])) : (j -= 1) {
items[j] = items[j - 1];
}
items[j] = x;
}
}
pub fn insertionSortContext(len: usize, context: anytype) void {
var i: usize = 1;
while (i < len) : (i += 1) {
var j: usize = i;
while (j > 0 and context.lessThan(j, j - 1)) : (j -= 1) {
context.swap(j, j - 1);
}
}
}
const Range = struct {
start: usize,
end: usize,
fn init(start: usize, end: usize) Range {
return Range{
.start = start,
.end = end,
};
}
fn length(self: Range) usize {
return self.end - self.start;
}
};
const Iterator = struct {
size: usize,
power_of_two: usize,
numerator: usize,
decimal: usize,
denominator: usize,
decimal_step: usize,
numerator_step: usize,
fn init(size2: usize, min_level: usize) Iterator {
const power_of_two = math.floorPowerOfTwo(usize, size2);
const denominator = power_of_two / min_level;
return Iterator{
.numerator = 0,
.decimal = 0,
.size = size2,
.power_of_two = power_of_two,
.denominator = denominator,
.decimal_step = size2 / denominator,
.numerator_step = size2 % denominator,
};
}
fn begin(self: *Iterator) void {
self.numerator = 0;
self.decimal = 0;
}
fn nextRange(self: *Iterator) Range {
const start = self.decimal;
self.decimal += self.decimal_step;
self.numerator += self.numerator_step;
if (self.numerator >= self.denominator) {
self.numerator -= self.denominator;
self.decimal += 1;
}
return Range{
.start = start,
.end = self.decimal,
};
}
fn finished(self: *Iterator) bool {
return self.decimal >= self.size;
}
fn nextLevel(self: *Iterator) bool {
self.decimal_step += self.decimal_step;
self.numerator_step += self.numerator_step;
if (self.numerator_step >= self.denominator) {
self.numerator_step -= self.denominator;
self.decimal_step += 1;
}
return (self.decimal_step < self.size);
}
fn length(self: *Iterator) usize {
return self.decimal_step;
}
};
const Pull = struct {
from: usize,
to: usize,
count: usize,
range: Range,
};
pub fn sort(
comptime T: type,
items: []T,
context: anytype,
comptime lessThan: fn (context: @TypeOf(context), lhs: T, rhs: T) bool,
) void {
var cache: [512]T = undefined;
if (items.len < 4) {
if (items.len == 3) {
if (lessThan(context, items[1], items[0])) mem.swap(T, &items[0], &items[1]);
if (lessThan(context, items[2], items[1])) {
mem.swap(T, &items[1], &items[2]);
if (lessThan(context, items[1], items[0])) mem.swap(T, &items[0], &items[1]);
}
} else if (items.len == 2) {
if (lessThan(context, items[1], items[0])) mem.swap(T, &items[0], &items[1]);
}
return;
}
var iterator = Iterator.init(items.len, 4);
while (!iterator.finished()) {
var order = [_]u8{ 0, 1, 2, 3, 4, 5, 6, 7 };
const range = iterator.nextRange();
const sliced_items = items[range.start..];
switch (range.length()) {
8 => {
swap(T, sliced_items, context, lessThan, &order, 0, 1);
swap(T, sliced_items, context, lessThan, &order, 2, 3);
swap(T, sliced_items, context, lessThan, &order, 4, 5);
swap(T, sliced_items, context, lessThan, &order, 6, 7);
swap(T, sliced_items, context, lessThan, &order, 0, 2);
swap(T, sliced_items, context, lessThan, &order, 1, 3);
swap(T, sliced_items, context, lessThan, &order, 4, 6);
swap(T, sliced_items, context, lessThan, &order, 5, 7);
swap(T, sliced_items, context, lessThan, &order, 1, 2);
swap(T, sliced_items, context, lessThan, &order, 5, 6);
swap(T, sliced_items, context, lessThan, &order, 0, 4);
swap(T, sliced_items, context, lessThan, &order, 3, 7);
swap(T, sliced_items, context, lessThan, &order, 1, 5);
swap(T, sliced_items, context, lessThan, &order, 2, 6);
swap(T, sliced_items, context, lessThan, &order, 1, 4);
swap(T, sliced_items, context, lessThan, &order, 3, 6);
swap(T, sliced_items, context, lessThan, &order, 2, 4);
swap(T, sliced_items, context, lessThan, &order, 3, 5);
swap(T, sliced_items, context, lessThan, &order, 3, 4);
},
7 => {
swap(T, sliced_items, context, lessThan, &order, 1, 2);
swap(T, sliced_items, context, lessThan, &order, 3, 4);
swap(T, sliced_items, context, lessThan, &order, 5, 6);
swap(T, sliced_items, context, lessThan, &order, 0, 2);
swap(T, sliced_items, context, lessThan, &order, 3, 5);
swap(T, sliced_items, context, lessThan, &order, 4, 6);
swap(T, sliced_items, context, lessThan, &order, 0, 1);
swap(T, sliced_items, context, lessThan, &order, 4, 5);
swap(T, sliced_items, context, lessThan, &order, 2, 6);
swap(T, sliced_items, context, lessThan, &order, 0, 4);
swap(T, sliced_items, context, lessThan, &order, 1, 5);
swap(T, sliced_items, context, lessThan, &order, 0, 3);
swap(T, sliced_items, context, lessThan, &order, 2, 5);
swap(T, sliced_items, context, lessThan, &order, 1, 3);
swap(T, sliced_items, context, lessThan, &order, 2, 4);
swap(T, sliced_items, context, lessThan, &order, 2, 3);
},
6 => {
swap(T, sliced_items, context, lessThan, &order, 1, 2);
swap(T, sliced_items, context, lessThan, &order, 4, 5);
swap(T, sliced_items, context, lessThan, &order, 0, 2);
swap(T, sliced_items, context, lessThan, &order, 3, 5);
swap(T, sliced_items, context, lessThan, &order, 0, 1);
swap(T, sliced_items, context, lessThan, &order, 3, 4);
swap(T, sliced_items, context, lessThan, &order, 2, 5);
swap(T, sliced_items, context, lessThan, &order, 0, 3);
swap(T, sliced_items, context, lessThan, &order, 1, 4);
swap(T, sliced_items, context, lessThan, &order, 2, 4);
swap(T, sliced_items, context, lessThan, &order, 1, 3);
swap(T, sliced_items, context, lessThan, &order, 2, 3);
},
5 => {
swap(T, sliced_items, context, lessThan, &order, 0, 1);
swap(T, sliced_items, context, lessThan, &order, 3, 4);
swap(T, sliced_items, context, lessThan, &order, 2, 4);
swap(T, sliced_items, context, lessThan, &order, 2, 3);
swap(T, sliced_items, context, lessThan, &order, 1, 4);
swap(T, sliced_items, context, lessThan, &order, 0, 3);
swap(T, sliced_items, context, lessThan, &order, 0, 2);
swap(T, sliced_items, context, lessThan, &order, 1, 3);
swap(T, sliced_items, context, lessThan, &order, 1, 2);
},
4 => {
swap(T, sliced_items, context, lessThan, &order, 0, 1);
swap(T, sliced_items, context, lessThan, &order, 2, 3);
swap(T, sliced_items, context, lessThan, &order, 0, 2);
swap(T, sliced_items, context, lessThan, &order, 1, 3);
swap(T, sliced_items, context, lessThan, &order, 1, 2);
},
else => {},
}
}
if (items.len < 8) return;
while (true) {
if (iterator.length() < cache.len) {
if ((iterator.length() + 1) * 4 <= cache.len and iterator.length() * 4 <= items.len) {
iterator.begin();
while (!iterator.finished()) {
var A1 = iterator.nextRange();
var B1 = iterator.nextRange();
var A2 = iterator.nextRange();
var B2 = iterator.nextRange();
if (lessThan(context, items[B1.end - 1], items[A1.start])) {
mem.copy(T, cache[B1.length()..], items[A1.start..A1.end]);
mem.copy(T, cache[0..], items[B1.start..B1.end]);
} else if (lessThan(context, items[B1.start], items[A1.end - 1])) {
mergeInto(T, items, A1, B1, context, lessThan, cache[0..]);
} else {
if (!lessThan(context, items[B2.start], items[A2.end - 1]) and !lessThan(context, items[A2.start], items[B1.end - 1])) continue;
mem.copy(T, cache[0..], items[A1.start..A1.end]);
mem.copy(T, cache[A1.length()..], items[B1.start..B1.end]);
}
A1 = Range.init(A1.start, B1.end);
if (lessThan(context, items[B2.end - 1], items[A2.start])) {
mem.copy(T, cache[A1.length() + B2.length() ..], items[A2.start..A2.end]);
mem.copy(T, cache[A1.length()..], items[B2.start..B2.end]);
} else if (lessThan(context, items[B2.start], items[A2.end - 1])) {
mergeInto(T, items, A2, B2, context, lessThan, cache[A1.length()..]);
} else {
mem.copy(T, cache[A1.length()..], items[A2.start..A2.end]);
mem.copy(T, cache[A1.length() + A2.length() ..], items[B2.start..B2.end]);
}
A2 = Range.init(A2.start, B2.end);
const A3 = Range.init(0, A1.length());
const B3 = Range.init(A1.length(), A1.length() + A2.length());
if (lessThan(context, cache[B3.end - 1], cache[A3.start])) {
mem.copy(T, items[A1.start + A2.length() ..], cache[A3.start..A3.end]);
mem.copy(T, items[A1.start..], cache[B3.start..B3.end]);
} else if (lessThan(context, cache[B3.start], cache[A3.end - 1])) {
mergeInto(T, cache[0..], A3, B3, context, lessThan, items[A1.start..]);
} else {
mem.copy(T, items[A1.start..], cache[A3.start..A3.end]);
mem.copy(T, items[A1.start + A1.length() ..], cache[B3.start..B3.end]);
}
}
_ = iterator.nextLevel();
} else {
iterator.begin();
while (!iterator.finished()) {
var A = iterator.nextRange();
var B = iterator.nextRange();
if (lessThan(context, items[B.end - 1], items[A.start])) {
mem.rotate(T, items[A.start..B.end], A.length());
} else if (lessThan(context, items[B.start], items[A.end - 1])) {
mem.copy(T, cache[0..], items[A.start..A.end]);
mergeExternal(T, items, A, B, context, lessThan, cache[0..]);
}
}
}
} else {
var block_size: usize = math.sqrt(iterator.length());
var buffer_size = iterator.length() / block_size + 1;
var A: Range = undefined;
var B: Range = undefined;
var index: usize = 0;
var last: usize = 0;
var count: usize = 0;
var find: usize = 0;
var start: usize = 0;
var pull_index: usize = 0;
var pull = [_]Pull{
Pull{
.from = 0,
.to = 0,
.count = 0,
.range = Range.init(0, 0),
},
Pull{
.from = 0,
.to = 0,
.count = 0,
.range = Range.init(0, 0),
},
};
var buffer1 = Range.init(0, 0);
var buffer2 = Range.init(0, 0);
find = buffer_size + buffer_size;
var find_separately = false;
if (block_size <= cache.len) {
find = buffer_size;
} else if (find > iterator.length()) {
find = buffer_size;
find_separately = true;
}
iterator.begin();
while (!iterator.finished()) {
A = iterator.nextRange();
B = iterator.nextRange();
last = A.start;
count = 1;
while (count < find) : ({
last = index;
count += 1;
}) {
index = findLastForward(T, items, items[last], Range.init(last + 1, A.end), context, lessThan, find - count);
if (index == A.end) break;
}
index = last;
if (count >= buffer_size) {
pull[pull_index] = Pull{
.range = Range.init(A.start, B.end),
.count = count,
.from = index,
.to = A.start,
};
pull_index = 1;
if (count == buffer_size + buffer_size) {
buffer1 = Range.init(A.start, A.start + buffer_size);
buffer2 = Range.init(A.start + buffer_size, A.start + count);
break;
} else if (find == buffer_size + buffer_size) {
buffer1 = Range.init(A.start, A.start + count);
find = buffer_size;
} else if (block_size <= cache.len) {
buffer1 = Range.init(A.start, A.start + count);
break;
} else if (find_separately) {
buffer1 = Range.init(A.start, A.start + count);
find_separately = false;
} else {
buffer2 = Range.init(A.start, A.start + count);
break;
}
} else if (pull_index == 0 and count > buffer1.length()) {
buffer1 = Range.init(A.start, A.start + count);
pull[pull_index] = Pull{
.range = Range.init(A.start, B.end),
.count = count,
.from = index,
.to = A.start,
};
}
last = B.end - 1;
count = 1;
while (count < find) : ({
last = index - 1;
count += 1;
}) {
index = findFirstBackward(T, items, items[last], Range.init(B.start, last), context, lessThan, find - count);
if (index == B.start) break;
}
index = last;
if (count >= buffer_size) {
pull[pull_index] = Pull{
.range = Range.init(A.start, B.end),
.count = count,
.from = index,
.to = B.end,
};
pull_index = 1;
if (count == buffer_size + buffer_size) {
buffer1 = Range.init(B.end - count, B.end - buffer_size);
buffer2 = Range.init(B.end - buffer_size, B.end);
break;
} else if (find == buffer_size + buffer_size) {
buffer1 = Range.init(B.end - count, B.end);
find = buffer_size;
} else if (block_size <= cache.len) {
buffer1 = Range.init(B.end - count, B.end);
break;
} else if (find_separately) {
buffer1 = Range.init(B.end - count, B.end);
find_separately = false;
} else {
if (pull[0].range.start == A.start) pull[0].range.end -= pull[1].count;
buffer2 = Range.init(B.end - count, B.end);
break;
}
} else if (pull_index == 0 and count > buffer1.length()) {
buffer1 = Range.init(B.end - count, B.end);
pull[pull_index] = Pull{
.range = Range.init(A.start, B.end),
.count = count,
.from = index,
.to = B.end,
};
}
}
pull_index = 0;
while (pull_index < 2) : (pull_index += 1) {
const length = pull[pull_index].count;
if (pull[pull_index].to < pull[pull_index].from) {
index = pull[pull_index].from;
count = 1;
while (count < length) : (count += 1) {
index = findFirstBackward(T, items, items[index - 1], Range.init(pull[pull_index].to, pull[pull_index].from - (count - 1)), context, lessThan, length - count);
const range = Range.init(index + 1, pull[pull_index].from + 1);
mem.rotate(T, items[range.start..range.end], range.length() - count);
pull[pull_index].from = index + count;
}
} else if (pull[pull_index].to > pull[pull_index].from) {
index = pull[pull_index].from + 1;
count = 1;
while (count < length) : (count += 1) {
index = findLastForward(T, items, items[index], Range.init(index, pull[pull_index].to), context, lessThan, length - count);
const range = Range.init(pull[pull_index].from, index - 1);
mem.rotate(T, items[range.start..range.end], count);
pull[pull_index].from = index - 1 - count;
}
}
}
buffer_size = buffer1.length();
block_size = iterator.length() / buffer_size + 1;
iterator.begin();
while (!iterator.finished()) {
A = iterator.nextRange();
B = iterator.nextRange();
start = A.start;
if (start == pull[0].range.start) {
if (pull[0].from > pull[0].to) {
A.start += pull[0].count;
if (A.length() == 0) continue;
} else if (pull[0].from < pull[0].to) {
B.end -= pull[0].count;
if (B.length() == 0) continue;
}
}
if (start == pull[1].range.start) {
if (pull[1].from > pull[1].to) {
A.start += pull[1].count;
if (A.length() == 0) continue;
} else if (pull[1].from < pull[1].to) {
B.end -= pull[1].count;
if (B.length() == 0) continue;
}
}
if (lessThan(context, items[B.end - 1], items[A.start])) {
mem.rotate(T, items[A.start..B.end], A.length());
} else if (lessThan(context, items[A.end], items[A.end - 1])) {
var findA: usize = undefined;
var blockA = Range.init(A.start, A.end);
var firstA = Range.init(A.start, A.start + blockA.length() % block_size);
var indexA = buffer1.start;
index = firstA.end;
while (index < blockA.end) : ({
indexA += 1;
index += block_size;
}) {
mem.swap(T, &items[indexA], &items[index]);
}
var lastA = firstA;
var lastB = Range.init(0, 0);
var blockB = Range.init(B.start, B.start + math.min(block_size, B.length()));
blockA.start += firstA.length();
indexA = buffer1.start;
if (lastA.length() <= cache.len) {
mem.copy(T, cache[0..], items[lastA.start..lastA.end]);
} else if (buffer2.length() > 0) {
blockSwap(T, items, lastA.start, buffer2.start, lastA.length());
}
if (blockA.length() > 0) {
while (true) {
if ((lastB.length() > 0 and !lessThan(context, items[lastB.end - 1], items[indexA])) or blockB.length() == 0) {
const B_split = binaryFirst(T, items, items[indexA], lastB, context, lessThan);
const B_remaining = lastB.end - B_split;
var minA = blockA.start;
findA = minA + block_size;
while (findA < blockA.end) : (findA += block_size) {
if (lessThan(context, items[findA], items[minA])) {
minA = findA;
}
}
blockSwap(T, items, blockA.start, minA, block_size);
mem.swap(T, &items[blockA.start], &items[indexA]);
indexA += 1;
if (lastA.length() <= cache.len) {
mergeExternal(T, items, lastA, Range.init(lastA.end, B_split), context, lessThan, cache[0..]);
} else if (buffer2.length() > 0) {
mergeInternal(T, items, lastA, Range.init(lastA.end, B_split), context, lessThan, buffer2);
} else {
mergeInPlace(T, items, lastA, Range.init(lastA.end, B_split), context, lessThan);
}
if (buffer2.length() > 0 or block_size <= cache.len) {
if (block_size <= cache.len) {
mem.copy(T, cache[0..], items[blockA.start .. blockA.start + block_size]);
} else {
blockSwap(T, items, blockA.start, buffer2.start, block_size);
}
blockSwap(T, items, B_split, blockA.start + block_size - B_remaining, B_remaining);
} else {
mem.rotate(T, items[B_split .. blockA.start + block_size], blockA.start - B_split);
}
lastA = Range.init(blockA.start - B_remaining, blockA.start - B_remaining + block_size);
lastB = Range.init(lastA.end, lastA.end + B_remaining);
blockA.start += block_size;
if (blockA.length() == 0) break;
} else if (blockB.length() < block_size) {
mem.rotate(T, items[blockA.start..blockB.end], blockB.start - blockA.start);
lastB = Range.init(blockA.start, blockA.start + blockB.length());
blockA.start += blockB.length();
blockA.end += blockB.length();
blockB.end = blockB.start;
} else {
blockSwap(T, items, blockA.start, blockB.start, block_size);
lastB = Range.init(blockA.start, blockA.start + block_size);
blockA.start += block_size;
blockA.end += block_size;
blockB.start += block_size;
if (blockB.end > B.end - block_size) {
blockB.end = B.end;
} else {
blockB.end += block_size;
}
}
}
}
if (lastA.length() <= cache.len) {
mergeExternal(T, items, lastA, Range.init(lastA.end, B.end), context, lessThan, cache[0..]);
} else if (buffer2.length() > 0) {
mergeInternal(T, items, lastA, Range.init(lastA.end, B.end), context, lessThan, buffer2);
} else {
mergeInPlace(T, items, lastA, Range.init(lastA.end, B.end), context, lessThan);
}
}
}
insertionSort(T, items[buffer2.start..buffer2.end], context, lessThan);
pull_index = 0;
while (pull_index < 2) : (pull_index += 1) {
var unique = pull[pull_index].count * 2;
if (pull[pull_index].from > pull[pull_index].to) {
var buffer = Range.init(pull[pull_index].range.start, pull[pull_index].range.start + pull[pull_index].count);
while (buffer.length() > 0) {
index = findFirstForward(T, items, items[buffer.start], Range.init(buffer.end, pull[pull_index].range.end), context, lessThan, unique);
const amount = index - buffer.end;
mem.rotate(T, items[buffer.start..index], buffer.length());
buffer.start += (amount + 1);
buffer.end += amount;
unique -= 2;
}
} else if (pull[pull_index].from < pull[pull_index].to) {
var buffer = Range.init(pull[pull_index].range.end - pull[pull_index].count, pull[pull_index].range.end);
while (buffer.length() > 0) {
index = findLastBackward(T, items, items[buffer.end - 1], Range.init(pull[pull_index].range.start, buffer.start), context, lessThan, unique);
const amount = buffer.start - index;
mem.rotate(T, items[index..buffer.end], amount);
buffer.start -= amount;
buffer.end -= (amount + 1);
unique -= 2;
}
}
}
}
if (!iterator.nextLevel()) break;
}
}
pub fn sortContext(len: usize, context: anytype) void {
return insertionSortContext(len, context);
}
fn mergeInPlace(
comptime T: type,
items: []T,
A_arg: Range,
B_arg: Range,
context: anytype,
comptime lessThan: fn (@TypeOf(context), T, T) bool,
) void {
if (A_arg.length() == 0 or B_arg.length() == 0) return;
var A = A_arg;
var B = B_arg;
while (true) {
const mid = binaryFirst(T, items, items[A.start], B, context, lessThan);
const amount = mid - A.end;
mem.rotate(T, items[A.start..mid], A.length());
if (B.end == mid) break;
B.start = mid;
A = Range.init(A.start + amount, B.start);
A.start = binaryLast(T, items, items[A.start], A, context, lessThan);
if (A.length() == 0) break;
}
}
fn mergeInternal(
comptime T: type,
items: []T,
A: Range,
B: Range,
context: anytype,
comptime lessThan: fn (@TypeOf(context), T, T) bool,
buffer: Range,
) void {
var A_count: usize = 0;
var B_count: usize = 0;
var insert: usize = 0;
if (B.length() > 0 and A.length() > 0) {
while (true) {
if (!lessThan(context, items[B.start + B_count], items[buffer.start + A_count])) {
mem.swap(T, &items[A.start + insert], &items[buffer.start + A_count]);
A_count += 1;
insert += 1;
if (A_count >= A.length()) break;
} else {
mem.swap(T, &items[A.start + insert], &items[B.start + B_count]);
B_count += 1;
insert += 1;
if (B_count >= B.length()) break;
}
}
}
blockSwap(T, items, buffer.start + A_count, A.start + insert, A.length() - A_count);
}
fn blockSwap(comptime T: type, items: []T, start1: usize, start2: usize, block_size: usize) void {
var index: usize = 0;
while (index < block_size) : (index += 1) {
mem.swap(T, &items[start1 + index], &items[start2 + index]);
}
}
fn findFirstForward(
comptime T: type,
items: []T,
value: T,
range: Range,
context: anytype,
comptime lessThan: fn (@TypeOf(context), T, T) bool,
unique: usize,
) usize {
if (range.length() == 0) return range.start;
const skip = math.max(range.length() / unique, @as(usize, 1));
var index = range.start + skip;
while (lessThan(context, items[index - 1], value)) : (index += skip) {
if (index >= range.end - skip) {
return binaryFirst(T, items, value, Range.init(index, range.end), context, lessThan);
}
}
return binaryFirst(T, items, value, Range.init(index - skip, index), context, lessThan);
}
fn findFirstBackward(
comptime T: type,
items: []T,
value: T,
range: Range,
context: anytype,
comptime lessThan: fn (@TypeOf(context), T, T) bool,
unique: usize,
) usize {
if (range.length() == 0) return range.start;
const skip = math.max(range.length() / unique, @as(usize, 1));
var index = range.end - skip;
while (index > range.start and !lessThan(context, items[index - 1], value)) : (index -= skip) {
if (index < range.start + skip) {
return binaryFirst(T, items, value, Range.init(range.start, index), context, lessThan);
}
}
return binaryFirst(T, items, value, Range.init(index, index + skip), context, lessThan);
}
fn findLastForward(
comptime T: type,
items: []T,
value: T,
range: Range,
context: anytype,
comptime lessThan: fn (@TypeOf(context), T, T) bool,
unique: usize,
) usize {
if (range.length() == 0) return range.start;
const skip = math.max(range.length() / unique, @as(usize, 1));
var index = range.start + skip;
while (!lessThan(context, value, items[index - 1])) : (index += skip) {
if (index >= range.end - skip) {
return binaryLast(T, items, value, Range.init(index, range.end), context, lessThan);
}
}
return binaryLast(T, items, value, Range.init(index - skip, index), context, lessThan);
}
fn findLastBackward(
comptime T: type,
items: []T,
value: T,
range: Range,
context: anytype,
comptime lessThan: fn (@TypeOf(context), T, T) bool,
unique: usize,
) usize {
if (range.length() == 0) return range.start;
const skip = math.max(range.length() / unique, @as(usize, 1));
var index = range.end - skip;
while (index > range.start and lessThan(context, value, items[index - 1])) : (index -= skip) {
if (index < range.start + skip) {
return binaryLast(T, items, value, Range.init(range.start, index), context, lessThan);
}
}
return binaryLast(T, items, value, Range.init(index, index + skip), context, lessThan);
}
fn binaryFirst(
comptime T: type,
items: []T,
value: T,
range: Range,
context: anytype,
comptime lessThan: fn (@TypeOf(context), T, T) bool,
) usize {
var curr = range.start;
var size = range.length();
if (range.start >= range.end) return range.end;
while (size > 0) {
const offset = size % 2;
size /= 2;
const mid = items[curr + size];
if (lessThan(context, mid, value)) {
curr += size + offset;
}
}
return curr;
}
fn binaryLast(
comptime T: type,
items: []T,
value: T,
range: Range,
context: anytype,
comptime lessThan: fn (@TypeOf(context), T, T) bool,
) usize {
var curr = range.start;
var size = range.length();
if (range.start >= range.end) return range.end;
while (size > 0) {
const offset = size % 2;
size /= 2;
const mid = items[curr + size];
if (!lessThan(context, value, mid)) {
curr += size + offset;
}
}
return curr;
}
fn mergeInto(
comptime T: type,
from: []T,
A: Range,
B: Range,
context: anytype,
comptime lessThan: fn (@TypeOf(context), T, T) bool,
into: []T,
) void {
var A_index: usize = A.start;
var B_index: usize = B.start;
const A_last = A.end;
const B_last = B.end;
var insert_index: usize = 0;
while (true) {
if (!lessThan(context, from[B_index], from[A_index])) {
into[insert_index] = from[A_index];
A_index += 1;
insert_index += 1;
if (A_index == A_last) {
mem.copy(T, into[insert_index..], from[B_index..B_last]);
break;
}
} else {
into[insert_index] = from[B_index];
B_index += 1;
insert_index += 1;
if (B_index == B_last) {
mem.copy(T, into[insert_index..], from[A_index..A_last]);
break;
}
}
}
}
fn mergeExternal(
comptime T: type,
items: []T,
A: Range,
B: Range,
context: anytype,
comptime lessThan: fn (@TypeOf(context), T, T) bool,
cache: []T,
) void {
var A_index: usize = 0;
var B_index: usize = B.start;
var insert_index: usize = A.start;
const A_last = A.length();
const B_last = B.end;
if (B.length() > 0 and A.length() > 0) {
while (true) {
if (!lessThan(context, items[B_index], cache[A_index])) {
items[insert_index] = cache[A_index];
A_index += 1;
insert_index += 1;
if (A_index == A_last) break;
} else {
items[insert_index] = items[B_index];
B_index += 1;
insert_index += 1;
if (B_index == B_last) break;
}
}
}
mem.copy(T, items[insert_index..], cache[A_index..A_last]);
}
fn swap(
comptime T: type,
items: []T,
context: anytype,
comptime lessThan: fn (@TypeOf(context), lhs: T, rhs: T) bool,
order: *[8]u8,
x: usize,
y: usize,
) void {
if (lessThan(context, items[y], items[x]) or ((order.*)[x] > (order.*)[y] and !lessThan(context, items[x], items[y]))) {
mem.swap(T, &items[x], &items[y]);
mem.swap(u8, &(order.*)[x], &(order.*)[y]);
}
}
pub fn asc(comptime T: type) fn (void, T, T) bool {
const impl = struct {
fn inner(context: void, a: T, b: T) bool {
_ = context;
return a < b;
}
};
return impl.inner;
}
pub fn desc(comptime T: type) fn (void, T, T) bool {
const impl = struct {
fn inner(context: void, a: T, b: T) bool {
_ = context;
return a > b;
}
};
return impl.inner;
}
test "stable sort" {
try testStableSort();
comptime try testStableSort();
}
fn testStableSort() !void {
var expected = [_]IdAndValue{
IdAndValue{ .id = 0, .value = 0 },
IdAndValue{ .id = 1, .value = 0 },
IdAndValue{ .id = 2, .value = 0 },
IdAndValue{ .id = 0, .value = 1 },
IdAndValue{ .id = 1, .value = 1 },
IdAndValue{ .id = 2, .value = 1 },
IdAndValue{ .id = 0, .value = 2 },
IdAndValue{ .id = 1, .value = 2 },
IdAndValue{ .id = 2, .value = 2 },
};
var cases = [_][9]IdAndValue{
[_]IdAndValue{
IdAndValue{ .id = 0, .value = 0 },
IdAndValue{ .id = 0, .value = 1 },
IdAndValue{ .id = 0, .value = 2 },
IdAndValue{ .id = 1, .value = 0 },
IdAndValue{ .id = 1, .value = 1 },
IdAndValue{ .id = 1, .value = 2 },
IdAndValue{ .id = 2, .value = 0 },
IdAndValue{ .id = 2, .value = 1 },
IdAndValue{ .id = 2, .value = 2 },
},
[_]IdAndValue{
IdAndValue{ .id = 0, .value = 2 },
IdAndValue{ .id = 0, .value = 1 },
IdAndValue{ .id = 0, .value = 0 },
IdAndValue{ .id = 1, .value = 2 },
IdAndValue{ .id = 1, .value = 1 },
IdAndValue{ .id = 1, .value = 0 },
IdAndValue{ .id = 2, .value = 2 },
IdAndValue{ .id = 2, .value = 1 },
IdAndValue{ .id = 2, .value = 0 },
},
};
for (cases) |*case| {
insertionSort(IdAndValue, (case.*)[0..], {}, cmpByValue);
for (case.*) |item, i| {
try testing.expect(item.id == expected[i].id);
try testing.expect(item.value == expected[i].value);
}
}
}
const IdAndValue = struct {
id: usize,
value: i32,
};
fn cmpByValue(context: void, a: IdAndValue, b: IdAndValue) bool {
return asc_i32(context, a.value, b.value);
}
const asc_u8 = asc(u8);
const asc_i32 = asc(i32);
const desc_u8 = desc(u8);
const desc_i32 = desc(i32);
test "sort" {
const u8cases = [_][]const []const u8{
&[_][]const u8{
"",
"",
},
&[_][]const u8{
"a",
"a",
},
&[_][]const u8{
"az",
"az",
},
&[_][]const u8{
"za",
"az",
},
&[_][]const u8{
"asdf",
"adfs",
},
&[_][]const u8{
"one",
"eno",
},
};
for (u8cases) |case| {
var buf: [8]u8 = undefined;
const slice = buf[0..case[0].len];
mem.copy(u8, slice, case[0]);
sort(u8, slice, {}, asc_u8);
try testing.expect(mem.eql(u8, slice, case[1]));
}
const i32cases = [_][]const []const i32{
&[_][]const i32{
&[_]i32{},
&[_]i32{},
},
&[_][]const i32{
&[_]i32{1},
&[_]i32{1},
},
&[_][]const i32{
&[_]i32{ 0, 1 },
&[_]i32{ 0, 1 },
},
&[_][]const i32{
&[_]i32{ 1, 0 },
&[_]i32{ 0, 1 },
},
&[_][]const i32{
&[_]i32{ 1, -1, 0 },
&[_]i32{ -1, 0, 1 },
},
&[_][]const i32{
&[_]i32{ 2, 1, 3 },
&[_]i32{ 1, 2, 3 },
},
};
for (i32cases) |case| {
var buf: [8]i32 = undefined;
const slice = buf[0..case[0].len];
mem.copy(i32, slice, case[0]);
sort(i32, slice, {}, asc_i32);
try testing.expect(mem.eql(i32, slice, case[1]));
}
}
test "sort descending" {
const rev_cases = [_][]const []const i32{
&[_][]const i32{
&[_]i32{},
&[_]i32{},
},
&[_][]const i32{
&[_]i32{1},
&[_]i32{1},
},
&[_][]const i32{
&[_]i32{ 0, 1 },
&[_]i32{ 1, 0 },
},
&[_][]const i32{
&[_]i32{ 1, 0 },
&[_]i32{ 1, 0 },
},
&[_][]const i32{
&[_]i32{ 1, -1, 0 },
&[_]i32{ 1, 0, -1 },
},
&[_][]const i32{
&[_]i32{ 2, 1, 3 },
&[_]i32{ 3, 2, 1 },
},
};
for (rev_cases) |case| {
var buf: [8]i32 = undefined;
const slice = buf[0..case[0].len];
mem.copy(i32, slice, case[0]);
sort(i32, slice, {}, desc_i32);
try testing.expect(mem.eql(i32, slice, case[1]));
}
}
test "another sort case" {
var arr = [_]i32{ 5, 3, 1, 2, 4 };
sort(i32, arr[0..], {}, asc_i32);
try testing.expect(mem.eql(i32, &arr, &[_]i32{ 1, 2, 3, 4, 5 }));
}
test "sort fuzz testing" {
var prng = std.rand.DefaultPrng.init(0x12345678);
const random = prng.random();
const test_case_count = 10;
var i: usize = 0;
while (i < test_case_count) : (i += 1) {
try fuzzTest(random);
}
}
var fixed_buffer_mem: [100 * 1024]u8 = undefined;
fn fuzzTest(rng: std.rand.Random) !void {
const array_size = rng.intRangeLessThan(usize, 0, 1000);
var array = try testing.allocator.alloc(IdAndValue, array_size);
defer testing.allocator.free(array);
for (array) |*item, index| {
item.id = index;
item.value = rng.intRangeLessThan(i32, 0, 100);
}
sort(IdAndValue, array, {}, cmpByValue);
var index: usize = 1;
while (index < array.len) : (index += 1) {
if (array[index].value == array[index - 1].value) {
try testing.expect(array[index].id > array[index - 1].id);
} else {
try testing.expect(array[index].value > array[index - 1].value);
}
}
}
pub fn argMin(
comptime T: type,
items: []const T,
context: anytype,
comptime lessThan: fn (@TypeOf(context), lhs: T, rhs: T) bool,
) ?usize {
if (items.len == 0) {
return null;
}
var smallest = items[0];
var smallest_index: usize = 0;
for (items[1..]) |item, i| {
if (lessThan(context, item, smallest)) {
smallest = item;
smallest_index = i + 1;
}
}
return smallest_index;
}
test "argMin" {
try testing.expectEqual(@as(?usize, null), argMin(i32, &[_]i32{}, {}, asc_i32));
try testing.expectEqual(@as(?usize, 0), argMin(i32, &[_]i32{1}, {}, asc_i32));
try testing.expectEqual(@as(?usize, 0), argMin(i32, &[_]i32{ 1, 2, 3, 4, 5 }, {}, asc_i32));
try testing.expectEqual(@as(?usize, 3), argMin(i32, &[_]i32{ 9, 3, 8, 2, 5 }, {}, asc_i32));
try testing.expectEqual(@as(?usize, 0), argMin(i32, &[_]i32{ 1, 1, 1, 1, 1 }, {}, asc_i32));
try testing.expectEqual(@as(?usize, 0), argMin(i32, &[_]i32{ -10, 1, 10 }, {}, asc_i32));
try testing.expectEqual(@as(?usize, 3), argMin(i32, &[_]i32{ 6, 3, 5, 7, 6 }, {}, desc_i32));
}
pub fn min(
comptime T: type,
items: []const T,
context: anytype,
comptime lessThan: fn (context: @TypeOf(context), lhs: T, rhs: T) bool,
) ?T {
const i = argMin(T, items, context, lessThan) orelse return null;
return items[i];
}
test "min" {
try testing.expectEqual(@as(?i32, null), min(i32, &[_]i32{}, {}, asc_i32));
try testing.expectEqual(@as(?i32, 1), min(i32, &[_]i32{1}, {}, asc_i32));
try testing.expectEqual(@as(?i32, 1), min(i32, &[_]i32{ 1, 2, 3, 4, 5 }, {}, asc_i32));
try testing.expectEqual(@as(?i32, 2), min(i32, &[_]i32{ 9, 3, 8, 2, 5 }, {}, asc_i32));
try testing.expectEqual(@as(?i32, 1), min(i32, &[_]i32{ 1, 1, 1, 1, 1 }, {}, asc_i32));
try testing.expectEqual(@as(?i32, -10), min(i32, &[_]i32{ -10, 1, 10 }, {}, asc_i32));
try testing.expectEqual(@as(?i32, 7), min(i32, &[_]i32{ 6, 3, 5, 7, 6 }, {}, desc_i32));
}
pub fn argMax(
comptime T: type,
items: []const T,
context: anytype,
comptime lessThan: fn (context: @TypeOf(context), lhs: T, rhs: T) bool,
) ?usize {
if (items.len == 0) {
return null;
}
var biggest = items[0];
var biggest_index: usize = 0;
for (items[1..]) |item, i| {
if (lessThan(context, biggest, item)) {
biggest = item;
biggest_index = i + 1;
}
}
return biggest_index;
}
test "argMax" {
try testing.expectEqual(@as(?usize, null), argMax(i32, &[_]i32{}, {}, asc_i32));
try testing.expectEqual(@as(?usize, 0), argMax(i32, &[_]i32{1}, {}, asc_i32));
try testing.expectEqual(@as(?usize, 4), argMax(i32, &[_]i32{ 1, 2, 3, 4, 5 }, {}, asc_i32));
try testing.expectEqual(@as(?usize, 0), argMax(i32, &[_]i32{ 9, 3, 8, 2, 5 }, {}, asc_i32));
try testing.expectEqual(@as(?usize, 0), argMax(i32, &[_]i32{ 1, 1, 1, 1, 1 }, {}, asc_i32));
try testing.expectEqual(@as(?usize, 2), argMax(i32, &[_]i32{ -10, 1, 10 }, {}, asc_i32));
try testing.expectEqual(@as(?usize, 1), argMax(i32, &[_]i32{ 6, 3, 5, 7, 6 }, {}, desc_i32));
}
pub fn max(
comptime T: type,
items: []const T,
context: anytype,
comptime lessThan: fn (context: @TypeOf(context), lhs: T, rhs: T) bool,
) ?T {
const i = argMax(T, items, context, lessThan) orelse return null;
return items[i];
}
test "max" {
try testing.expectEqual(@as(?i32, null), max(i32, &[_]i32{}, {}, asc_i32));
try testing.expectEqual(@as(?i32, 1), max(i32, &[_]i32{1}, {}, asc_i32));
try testing.expectEqual(@as(?i32, 5), max(i32, &[_]i32{ 1, 2, 3, 4, 5 }, {}, asc_i32));
try testing.expectEqual(@as(?i32, 9), max(i32, &[_]i32{ 9, 3, 8, 2, 5 }, {}, asc_i32));
try testing.expectEqual(@as(?i32, 1), max(i32, &[_]i32{ 1, 1, 1, 1, 1 }, {}, asc_i32));
try testing.expectEqual(@as(?i32, 10), max(i32, &[_]i32{ -10, 1, 10 }, {}, asc_i32));
try testing.expectEqual(@as(?i32, 3), max(i32, &[_]i32{ 6, 3, 5, 7, 6 }, {}, desc_i32));
}
pub fn isSorted(
comptime T: type,
items: []const T,
context: anytype,
comptime lessThan: fn (context: @TypeOf(context), lhs: T, rhs: T) bool,
) bool {
var i: usize = 1;
while (i < items.len) : (i += 1) {
if (lessThan(context, items[i], items[i - 1])) {
return false;
}
}
return true;
}
test "isSorted" {
try testing.expect(isSorted(i32, &[_]i32{}, {}, asc_i32));
try testing.expect(isSorted(i32, &[_]i32{10}, {}, asc_i32));
try testing.expect(isSorted(i32, &[_]i32{ 1, 2, 3, 4, 5 }, {}, asc_i32));
try testing.expect(isSorted(i32, &[_]i32{ -10, 1, 1, 1, 10 }, {}, asc_i32));
try testing.expect(isSorted(i32, &[_]i32{}, {}, desc_i32));
try testing.expect(isSorted(i32, &[_]i32{-20}, {}, desc_i32));
try testing.expect(isSorted(i32, &[_]i32{ 3, 2, 1, 0, -1 }, {}, desc_i32));
try testing.expect(isSorted(i32, &[_]i32{ 10, -10 }, {}, desc_i32));
try testing.expect(isSorted(i32, &[_]i32{ 1, 1, 1, 1, 1 }, {}, asc_i32));
try testing.expect(isSorted(i32, &[_]i32{ 1, 1, 1, 1, 1 }, {}, desc_i32));
try testing.expectEqual(false, isSorted(i32, &[_]i32{ 5, 4, 3, 2, 1 }, {}, asc_i32));
try testing.expectEqual(false, isSorted(i32, &[_]i32{ 1, 2, 3, 4, 5 }, {}, desc_i32));
try testing.expect(isSorted(u8, "abcd", {}, asc_u8));
try testing.expect(isSorted(u8, "zyxw", {}, desc_u8));
try testing.expectEqual(false, isSorted(u8, "abcd", {}, desc_u8));
try testing.expectEqual(false, isSorted(u8, "zyxw", {}, asc_u8));
try testing.expect(isSorted(u8, "ffff", {}, asc_u8));
try testing.expect(isSorted(u8, "ffff", {}, desc_u8));
}