/*
* UCW Library -- Universal Heap Macros
*
* (c) 2001 Martin Mares
* (c) 2005 Tomas Valla
*
* 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 <> 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.
*
* [[macros]]
* Macros
* ------
*/
/* For internal usage. */
#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 usage. */
#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 unordered array @heap of @num elements to become a valid heap. The time complexity is linear.
**/
#define HEAP_INIT(heap,num,type,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 removed value is moved just after the resulting heap (`heap[num + 1]`).
**/
#define HEAP_DELMIN(heap,num,type,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 `heap[num]` in `O(log(n))` time. The value of @num must be increased before.
**/
#define HEAP_INSERT(heap,num,type,less,swap) \
do { \
uint _j, _u; \
type x; \
_j = num; \
HEAP_BUBBLE_UP_J(heap,num,less,swap); \
} while(0)
/**
* If you need to increase the value of `heap[pos]`, just do it and then call this macro to rebuild the heap.
* Only `heap[pos]` can be changed, the rest of the array must form a valid heap.
* The time complexity is `O(log(n))`.
**/
#define HEAP_INCREASE(heap,num,type,less,swap,pos) \
do { \
uint _j, _l; \
type x; \
_j = pos; \
HEAP_BUBBLE_DOWN_J(heap,num,less,swap); \
} while(0)
/**
* If you need to decrease the value of `heap[pos]`, just do it and then call this macro to rebuild the heap.
* Only `heap[pos]` can be changed, the rest of the array must form a valid heap.
* The time complexity is `O(log(n))`.
**/
#define HEAP_DECREASE(heap,num,type,less,swap,pos) \
do { \
uint _j, _u; \
type x; \
_j = pos; \
HEAP_BUBBLE_UP_J(heap,num,less,swap); \
} while(0)
/**
* Delete `heap[pos]` in `O(log(n))` time.
**/
#define HEAP_DELETE(heap,num,type,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)