You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
207 lines
6.5 KiB
207 lines
6.5 KiB
/*
|
|
* UCW Library -- Universal Heap Macros
|
|
*
|
|
* (c) 2001--2012 Martin Mares <mj@ucw.cz>
|
|
* (c) 2005--2012 Tomas Valla <tom@ucw.cz>
|
|
*
|
|
* This software may be freely distributed and used according to the terms
|
|
* of the GNU Lesser General Public License.
|
|
*/
|
|
|
|
/***
|
|
* [[intro]]
|
|
* Introduction
|
|
* ------------
|
|
*
|
|
* Binary heap is a simple data structure, which for example supports efficient insertions, deletions
|
|
* and access to the minimal inserted item. We define several macros for such operations.
|
|
* Note that because of simplicity of heaps, we have decided to define direct macros instead
|
|
* of a <<generic:,macro generator>> as for several other data structures in the Libucw.
|
|
*
|
|
* A heap is represented by a number of elements and by an array of values. Beware that we
|
|
* index this array from one, not from zero as do the standard C arrays.
|
|
*
|
|
* Most macros use these parameters:
|
|
*
|
|
* - @type - the type of elements
|
|
* - @num - a variable (signed or unsigned integer) with the number of elements
|
|
* - @heap - a C array of type @type; the heap is stored in `heap[1] .. heap[num]`; `heap[0]` is unused
|
|
* - @less - a callback to compare two element values; `less(x, y)` shall return a non-zero value iff @x is lower than @y
|
|
* - @swap - a callback to swap two array elements; `swap(heap, i, j, t)` must swap `heap[i]` with `heap[j]` with possible help of temporary variable @t (type @type).
|
|
*
|
|
* A valid heap must follow these rules:
|
|
*
|
|
* - `num >= 0`
|
|
* - `heap[i] >= heap[i / 2]` for each `i` in `[2, num]`
|
|
*
|
|
* The first element `heap[1]` is always lower or equal to all other elements.
|
|
*
|
|
* Position tracking
|
|
* -----------------
|
|
*
|
|
* As a heap does not support efficient lookup of an element by value, all functions
|
|
* acting on existing heap elements need to obtain the position of the element in the
|
|
* heap. This position has to be tracked by the caller, usually in the supplied swap
|
|
* callback.
|
|
*
|
|
* However, there are some caveats noted in the descriptions of individual functions.
|
|
*
|
|
* [[macros]]
|
|
* Macros
|
|
* ------
|
|
***/
|
|
|
|
/* For internal use. */
|
|
#define HEAP_BUBBLE_DOWN_J(heap,num,less,swap) \
|
|
for (;;) \
|
|
{ \
|
|
_l = 2*_j; \
|
|
if (_l > num) \
|
|
break; \
|
|
if (less(heap[_j],heap[_l]) && (_l == num || less(heap[_j],heap[_l+1]))) \
|
|
break; \
|
|
if (_l != num && less(heap[_l+1],heap[_l])) \
|
|
_l++; \
|
|
swap(heap,_j,_l,x); \
|
|
_j = _l; \
|
|
}
|
|
|
|
/* For internal use. */
|
|
#define HEAP_BUBBLE_UP_J(heap,num,less,swap) \
|
|
while (_j > 1) \
|
|
{ \
|
|
_u = _j/2; \
|
|
if (less(heap[_u], heap[_j])) \
|
|
break; \
|
|
swap(heap,_u,_j,x); \
|
|
_j = _u; \
|
|
}
|
|
|
|
/**
|
|
* Shuffle the items `heap[1]`, ..., `heap[num]` to get a valid heap.
|
|
* This operation takes linear time.
|
|
*
|
|
* Position tracking: Position of `heap[i]` must be initialized to `i` before calling.
|
|
**/
|
|
#define HEAP_INIT(type,heap,num,less,swap) \
|
|
do { \
|
|
uint _i = num; \
|
|
uint _j, _l; \
|
|
type x; \
|
|
while (_i >= 1) \
|
|
{ \
|
|
_j = _i; \
|
|
HEAP_BUBBLE_DOWN_J(heap,num,less,swap) \
|
|
_i--; \
|
|
} \
|
|
} while(0)
|
|
|
|
/**
|
|
* Delete the minimum element `heap[1]` in `O(log(n))` time. The @num variable is decremented.
|
|
* The removed value is moved just after the resulting heap (`heap[num + 1]`).
|
|
*
|
|
* Position tracking: Fully automatic.
|
|
**/
|
|
#define HEAP_DELETE_MIN(type,heap,num,less,swap) \
|
|
do { \
|
|
uint _j, _l; \
|
|
type x; \
|
|
swap(heap,1,num,x); \
|
|
num--; \
|
|
_j = 1; \
|
|
HEAP_BUBBLE_DOWN_J(heap,num,less,swap); \
|
|
} while(0)
|
|
|
|
/**
|
|
* Insert a new element @elt to the heap. The @num variable is incremented.
|
|
* This operation takes `O(log(n))` time.
|
|
*
|
|
* Position tracking: The position of the new element must be initialized to @num+1
|
|
* before calling this macro.
|
|
**/
|
|
#define HEAP_INSERT(type,heap,num,less,swap,elt) \
|
|
do { \
|
|
uint _j, _u; \
|
|
type x; \
|
|
heap[++num] = elt; \
|
|
_j = num; \
|
|
HEAP_BUBBLE_UP_J(heap,num,less,swap); \
|
|
} while(0)
|
|
|
|
/**
|
|
* Increase `heap[pos]` to a new value @elt (greater or equal to the previous value).
|
|
* The time complexity is `O(log(n))`.
|
|
*
|
|
* Position tracking: Fully automatic.
|
|
**/
|
|
#define HEAP_INCREASE(type,heap,num,less,swap,pos,elt) \
|
|
do { \
|
|
uint _j, _l; \
|
|
type x; \
|
|
heap[pos] = elt; \
|
|
_j = pos; \
|
|
HEAP_BUBBLE_DOWN_J(heap,num,less,swap); \
|
|
} while(0)
|
|
|
|
/**
|
|
* Decrease `heap[pos]` to a new value @elt (less or equal to the previous value).
|
|
* The time complexity is `O(log(n))`.
|
|
*
|
|
* Position tracking: Fully automatic.
|
|
**/
|
|
#define HEAP_DECREASE(type,heap,num,less,swap,pos,elt) \
|
|
do { \
|
|
uint _j, _u; \
|
|
type x; \
|
|
heap[pos] = elt; \
|
|
_j = pos; \
|
|
HEAP_BUBBLE_UP_J(heap,num,less,swap); \
|
|
} while(0)
|
|
|
|
/**
|
|
* Change `heap[pos]` to a new value @elt. The time complexity is `O(log(n))`.
|
|
* If you know that the new value is always smaller or always greater, it is faster
|
|
* to use `HEAP_DECREASE` or `HEAP_INCREASE` respectively.
|
|
*
|
|
* Position tracking: Fully automatic.
|
|
**/
|
|
#define HEAP_REPLACE(type,heap,num,less,swap,pos,elt) \
|
|
do { \
|
|
type _elt = elt; \
|
|
if (less(heap[pos], _elt)) \
|
|
HEAP_INCREASE(type,heap,num,less,swap,pos,_elt); \
|
|
else \
|
|
HEAP_DECREASE(type,heap,num,less,swap,pos,_elt); \
|
|
} while(0)
|
|
|
|
/**
|
|
* Replace the minimum `heap[pos]` by a new value @elt. The time complexity is `O(log(n))`.
|
|
*
|
|
* Position tracking: Fully automatic.
|
|
**/
|
|
#define HEAP_REPLACE_MIN(type,heap,num,less,swap,elt) \
|
|
HEAP_INCREASE(type,heap,num,less,swap,1,elt)
|
|
|
|
/**
|
|
* Delete an arbitrary element, given by its position. The @num variable is decremented.
|
|
* The operation takes `O(log(n))` time.
|
|
*
|
|
* Position tracking: Fully automatic.
|
|
**/
|
|
#define HEAP_DELETE(type,heap,num,less,swap,pos) \
|
|
do { \
|
|
uint _j, _l, _u; \
|
|
type x; \
|
|
_j = pos; \
|
|
swap(heap,_j,num,x); \
|
|
num--; \
|
|
if (less(heap[_j], heap[num+1])) \
|
|
HEAP_BUBBLE_UP_J(heap,num,less,swap) \
|
|
else \
|
|
HEAP_BUBBLE_DOWN_J(heap,num,less,swap); \
|
|
} while(0)
|
|
|
|
/**
|
|
* Default swapping macro.
|
|
**/
|
|
#define HEAP_SWAP(heap,a,b,t) (t=heap[a], heap[a]=heap[b], heap[b]=t)
|
|
|