/* * UCW Library -- Universal Heap Macros * * (c) 2001--2012 Martin Mares * (c) 2005--2012 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. * * 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)