libvieter/src/heap

This min-heap implementation is a pretty standard binomial heap.

Representation in memory

A heap consists of one or more binomial trees, each with a different order k and 2^k total nodes. This heap can contain 2^64 - 1 elements at most, which is far more than your memory can contain, but it's still fun to mention.

A tree does not have its own memory structure; a node that's the root of a binomial tree is simply called the tree.

Each node has the following layout:

typedef struct vieter_heap_node {
    uint64_t key;
    void *data;
    struct vieter_heap_node *largest_order;
    union {
      struct vieter_heap_node *next_tree;
      struct vieter_heap_node *next_largest_order;
    } ptr;
    uint8_t order;
} vieter_heap_node;

Each node has a pointer to its child with the largest order (if the node's order is 0, this pointer will be NULL). Each non-root node has a pointer to its sibling with the next-highest order. These pointers allow the children of a binomial tree to be recombined into a new tree, once their root has been pop'ed.

Roots point to the binomial tree in the heap with the next largest order.