This file contains (part of) the code from "Algorithms in C, Third Edition,
Parts 1-4," by Robert Sedgewick, and is covered under the copyright
and warranty notices in that book. Permission is granted for this
code to be used for educational purposes in association with the text,
and for other uses not covered by copyright laws, provided that
the following notice is included with the code:

 	"This code is from "Algorithms in C, Third Edition,"
	by Robert Sedgewick, Addison Wesley Longman, 1998."

Commercial uses of this code require the explicit written
permission of the publisher. Send your request for permission,
stating clearly what code you would like to use, and in what
specific way, to: aw.cse@aw.com

CHAPTER 16. External Searching
-----
typedef struct STnode* link;
typedef struct
  { Key key; union { link next; Item item; } ref; } 
entry;
struct STnode { entry b[M]; int m; };
static link head;
static int H, N; 
link NEW()
  { link x = malloc(sizeof *x); 
    x->m = 0;
    return x; 
  }
void STinit(int maxN) 
  { head = NEW(); H = 0; N = 0; }
-----
Item searchR(link h, Key v, int H)
  { int j;
    if (H == 0)
      for (j = 0; j < h->m; j++)
        if (eq(v, h->b[j].key)) 
          return h->b[j].ref.item;
    if (H != 0)
      for (j = 0; j < h->m; j++)
        if ((j+1 == h->m) || less(v, h->b[j+1].key))
          return searchR(h->b[j].ref.next, v, H-1);
    return NULLitem;
  }
Item STsearch(Key v)
  { return searchR(head, v, H); }
-----
link insertR(link h, Item item, int H)
  { int i, j; Key v = key(item); entry x; link u;
    x.key = v; x.ref.item = item;
    if (H == 0)
      for (j = 0; j < h->m; j++)
        if (less(v, h->b[j].key)) break;
    if (H != 0)
      for (j = 0; j < h->m; j++)
        if ((j+1 == h->m) || less(v, h->b[j+1].key))
          {
            u = insertR(h->b[j++].ref.next, v, H-1);
            if (u == NULL) return NULL;
            x.key = u->b[0].key; x.ref.next = u;
            break;
          }
    for (i = ++(h->m); (i > j) && (i != M); i--) 
      h->b[i] = h->b[i-1];
    h->b[j] = x;
    if (h->m < M) return NULL; else return split(h);
  }
void STinsert(Item item)
  { link t, u = insertR(head, item, H); 
    if (u == NULL) return;
    t = NEW(); t->m = 2; 
    t->b[0].key = head->b[0].key; 
    t->b[0].ref.next = head;
    t->b[1].key =  u->b[0].key;
    t->b[1].ref.next = u;
    head = t; H++;
  }
-----
link split(link h)
  { int j; link t = NEW();
    for (j = 0; j < M/2; j++)
      t->b[j] = h->b[M/2+j]; 
    h->m = M/2; t->m = M/2; 
    return t;    
  }
-----
typedef struct STnode* link;
struct STnode { Item b[M]; int m; int k; };
static link *dir;
static int d, D, N; 
link NEW()
  { link x = malloc(sizeof *x); 
    x->m = 0;  x->k = 0;
    return x; 
  }
void STinit(int maxN) 
  { 
    d = 0; N = 0; D = 1;
    dir = malloc(D*(sizeof *dir));
    dir[0] = NEW(); 
  }
-----
Item search(link h, Key v)
  { int j;
    for (j = 0; j < h->m; j++)
      if (eq(v, key(h->b[j])))
        return h->b[j];
    return NULLitem;
  }
Item STsearch(Key v)
  { return search(dir[bits(v, 0, d)], v); }
-----
link split(link h)
  { int j; link t = NEW();
    while (h->m == M)
      {
        h->m = 0; t->m = 0; 
        for (j = 0; j < M; j++)
          if (bits(h->b[j], h->k, 1) == 0)
               h->b[(h->m)++] = h->b[j]; 
          else t->b[(t->m)++] = h->b[j]; 
        t->k = ++(h->k);
        if (t->m == M) h = t;
      }
    insertDIR(t, t->k);
  }
void insert(link h, Item item)
  { int i, j; Key v = key(item); 
    for (j = 0; j < h->m; j++)
      if (less(v, key(h->b[j]))) break;
    for (i = (h->m)++; i > j; i--) 
      h->b[i] = h->b[i-1];
    h->b[j] = item;
    if (h->m == M) split(h);
  }
void STinsert(Item item)
  { insert(dir[bits(key(item), 0, d)], item); }
-----
void insertDIR(link t, int k)
  { int i, m, x = bits(t->b[0], 0, k);
    while (d < k) 
      { link *old = dir;
        d += 1; D += D;
        dir = malloc(D*(sizeof *dir));
        for (i = 0; i < D; i++) dir[i] = old[i/2];        
        if (d < k) dir(bits(x, 0, d) ^ 1) = NEW();
      }
    for (m = 1; k < d; k++) m *= 2; 
    for (i = 0; i < m; i++) dir[x*m+i] = t;        
  }