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// A generic in-place max heap on a slice for any type.
package heap
/*
Copyright 2022 Dale Weiler <weilercdale@gmail.com>.
Made available under Odin's BSD-3 license.
List of contributors:
Dale Weiler: Initial implementation
*/
/*
Constructs a max heap in slice given by data with comparator. A max heap is
a range of elements which has the following properties:
1. With N = len(data), for all 0 < i < N, data[(i - 1) / 2] does not compare
less than data[i].
2. A new element can be added using push in O(log n) time.
3. The first element can be removed using pop in O(log n) time.
The comparator compares elements of type T and can be used to construct a
max heap (less than) or min heap (greater than) for T.
*/
make :: proc(data: []$T, less: proc(a, b: T) -> bool) {
// amoritize length lookup
length := len(data)
if length <= 1 {
return
}
// start from data parent, no need to consider children
for start := (length - 2) / 2; start >= 0; start -= 1 {
sift_down(data, less, start)
}
}
/*
Inserts the element at the position len(data)-1 into the max heap with
comparator.
At most log(N) comparisons where N = len(data) will be performed.
*/
push :: proc(data: []$T, less: proc(a, b: T) -> bool) {
sift_up(data, less)
}
/*
Swaps the value in position data[0] and the value in data[len(data)-1] and
makes subrange [0, len(data)-1) into a heap. This has the effect of removing
the first element from the heap.
At most 2 * log(N) comparisons where N = len(data) will be performed.
*/
pop :: proc(data: []$T, less: proc(a, b: T) -> bool) {
length := len(data)
if length <= 1 {
return
}
last := length
// create a hole at 0
top := data[0]
hole := floyd_sift_down(data, less)
last -= 1
if hole == last {
data[hole] = top
} else {
data[hole] = data[last]
hole += 1
data[last] = top
sift_up(data[:hole], less)
}
}
/*
Converts the max heap into a sorted range in ascending order. The resulting
slice will no longer be a heap after this.
At most 2 * N * log(N) comparisons where N = len(data) will be performed.
*/
sort :: proc(data: []$T, less: proc(a, b: T) -> bool) {
for n := len(data); n >= 1; n -= 1 {
pop(data[:n], less)
}
}
/*
Examines the slice and finds the largest range which is a max-heap. Elements
are compared with user-supplied comparison procedure.
This returns the upper bound of the largest range in the slice which is a
max heap. That is, the last index for which data is a max heap.
At most O(n) comparisons where N = len(data) will be performed.
*/
is_heap_until :: proc(data: []$T, less: proc(a, b: T) -> bool) -> int {
length := len(data)
a := 0
b := 1
for b < length {
if less(data[a], data[b]) {
return b
}
b += 1
if b == length || less(data[a], data[b]) {
return b
}
a += 1
b = 2 * a + 1
}
return length
}
/*
Checks if a given slice is a max heap.
At most O(n) comparisons where N = len(data) will be performed.
*/
is_heap :: #force_inline proc(data: []$T, less: proc(a, b: T) -> bool) -> bool {
return is_heap_until(data, less) == len(data)
}
@(private="file")
floyd_sift_down :: proc(data: []$T, less: proc(a, b: T) -> bool) -> int {
length := len(data)
assert(length >= 2)
hole := 0
child := 0
index := 0
for {
index += child + 1
child = 2 * child + 1
if child + 1 < length && less(data[index], data[index + 1]) {
child += 1
index += 1
}
data[hole] = data[index]
hole = index
if child > (length - 2) / 2 {
return hole
}
}
unreachable()
}
@(private="file")
sift_down :: proc(data: []$T, less: proc(a, b: T) -> bool, start: int) {
start := start
child := start
// amoritize length lookup
length := len(data)
// left child of start is at 2 * start + 1
// right child of start is at 2 * start + 2
if length < 2 || (length - 2) / 2 < child {
return
}
child = 2 * child + 1
if child + 1 < length && less(data[child], data[child + 1]) {
// right child exists and is greater than left child
child += 1
}
// check if in heap order
if less(data[child], data[start]) {
// start is larger than its largest child
return
}
top := data[start]
for {
// not in heap order, swap parent with its largest child
data[start] = data[child]
start = child
if (length - 2) / 2 < child {
break
}
// recompute child based off updated parent
child = 2 * child + 1
if child + 1 < length && less(data[child], data[child + 1]) {
// right child exists and is greater than left child
child += 1
}
// check if we are in heap order
if less(data[child], top) {
break
}
}
data[start] = top
}
@(private="file")
sift_up :: proc(data: []$T, less: proc(a, b: T) -> bool) {
// amoritize length lookup
length := len(data)
if length <= 1 {
return
}
last := length
length = (length - 2) / 2
index := length
last -= 1
if less(data[index], data[last]) {
top := data[last]
for {
data[last] = data[index]
last = index
if length == 0 {
break
}
length = (length - 1) / 2
index = length
if !less(data[index], top) {
break
}
}
data[last] = top
}
}
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