左偏树

左偏树

/*
*  合并复杂度 O(log N)
*  INIT: init()读入数据并进行初始化;
*  CALL: merge() 合并两棵左偏树;
*        ins() 插入一个新节点;
*        top() 取得最小结点;
*        pop() 取得并删除最小结点;
*        del() 删除某结点;
*        add() 增/减一个结点的键值;
*        iroot() 获取结点i的根;
*/
#define typec int       //  type of key val
const int na = -1;
const int N = 1010;

struct node
{
typec key;
int l, r, f, dist;
} tr
;

int iroot(int i)
{   //  find i's root
if (i == na)
{
return i;
}
while (tr[i].f != na)
{
i = tr[i].f;
}
return i;
}

int merge(int rx, int ry)
{
//  two root:   rx, ry
if (rx == na)
{
return ry;
}
if (ry == na)
{
return rx;
}
if (tr[rx].key > tr[ry].key)
{
swap(rx, ry);
}
int r = merge(tr[rx].r, ry);
tr[rx].r = r;
tr[r].f = rx;
if (tr[r].dist > tr[tr[rx].l].dist)
{
swap(tr[rx].l, tr[rx].r);
}
if (tr[rx].r == na)
{
tr[rx].dist = 0;
}
else
{
tr[rx].dist = tr[tr[rx].r].dist + 1;
}
return rx;  //  return new root
}

int ins(int i, typec key, int root)
{   //  add a new node(i, key)
tr[i].key = key;
tr[i].l = tr[i].r = tr[i].f = na;
tr[i].dist = 0;
return root = merge(root, i);   //  return new root
}

int del(int i)
{   //  delete node i
if (i == na)
{
return i;
}
int x, y, l, r;
l = tr[i].l;
r = tr[i].r;
y = tr[i].f;
tr[i].l = tr[i].r = tr[i].f = na;
tr[x = merge(l, r)].f = y;
if (y != na && tr[y].l == i)
{
tr[y].l = x;
}
if (y != na && tr[y].r == i)
{
tr[y].r = x;
}
for (; y != na; x = y, y = tr[y].f)
{
if (tr[tr[y].l].dist < tr[tr[y].r].dist)
{
swap(tr[y].l, tr[y].r);
}
if (tr[tr[y].r].dist + 1 == tr[y].dist)
{
break;
}
tr[y].dist = tr[tr[y].r].dist + 1;
}
if (x != na)    //  return new root
{
return iroot(x);
}
else return iroot(y);
}

node top(int root)
{
return tr[root];
}

node pop(int &root)
{
node out = tr[root];
int l = tr[root].l, r = tr[root].r;
tr[root].l = tr[root].r = tr[root].f = na;
tr[l].f = tr[r].f = na;
root = merge(l, r);
return out;
}

int add(int i, typec val)   //  tr[i].key += val
{
if (i == na)
{
return i;
}
if (tr[i].l == na && tr[i].r == na && tr[i].f == na)
{
tr[i].key += val;
return i;
}
typec key = tr[i].key + val;
int rt = del(i);
return ins(i, key, rt);
}

void init(int n)
{
for (int i = 1; i <= n; i++)
{
scanf("%d", &tr[i].key);    //  %d: type of key
tr[i].l = tr[i].r = tr[i].f = na;
tr[i].dist = 0;
}
return ;
}