#ifndef VIETER_HEAP_TREE
#define VIETER_HEAP_TREE

#include <stdint.h>
#include <stdlib.h>

typedef struct vieter_heap_node {
  uint64_t key;
  void *data;
  struct vieter_heap_node *largest_order;
  union {
    // Roots point to next tree in the heap, other nodes point to their first
    // neighbour.
    struct vieter_heap_node *next_tree;
    struct vieter_heap_node *next_largest_order;
  } ptr;
  uint8_t order;
} vieter_heap_node;

/*
 * Allocate and initialize a heap node object.
 */
vieter_heap_node *vieter_heap_node_init();

/*
 * Deallocate a node object.
 */
void vieter_heap_node_free(vieter_heap_node *node);

/*
 * Deallocate a node's entire structure.
 */
void vieter_heap_tree_free(vieter_heap_node *root);

/*
 * Given the roots of the smallest trees in two heaps, merge them into a single
 * large heap.
 */
vieter_heap_node *vieter_heap_tree_merge(vieter_heap_node *root_a,
                                         vieter_heap_node *root_b);

/*
 * Given the roots of two trees of the same order, merge them into a heap of one
 * order larger.
 */
vieter_heap_node *vieter_heap_tree_merge_same_order(vieter_heap_node *root_a,
                                                    vieter_heap_node *root_b);

/*
 * Remove the smallest element from the given heap.
 */
vieter_heap_node *vieter_heap_tree_pop(void **out, vieter_heap_node *root);

#endif