左偏树（转）

1左偏树(Leftist Tree)是一种可并堆(Mergeable Heap) ，它除了支持优先队列的三个基本操作（插入，删除，取最小节点），还支持一个很特殊的操作——合并操作。

 

2左偏树是一棵堆有序(Heap Ordered)二叉树。

 

3左偏树满足左偏性质(Leftist Property)。

[性质1] 节点的键值小于或等于它的左右子节点的键值。

[性质2] 节点的左子节点的距离不小于右子节点的距离。

[性质3] 节点的左子节点右子节点也是一颗左偏树。

 

合并操作的代码如下：

Function Merge(A, B)

    If A = NULL Then return B

    If B = NULL Then return A

    If key(B) < key(A) Then swap(A, B)

    right(A) ← Merge(right(A), B)

    If dist(right(A)) > dist(left(A)) Then

        swap(left(A), right(A))

    If right(A) = NULL Then dist(A) ← 0

    Else dist(A) ← dist(right(A)) + 1

    return A

End Function

hdoj 1512 Monkey King

#include <iostream>

#include <vector>

using namespace std;

 

const int maxn = 100005;

 

 

struct tree {

    int l, r, v, dis, f;

}heap[maxn];

 

 

int merge( int a, int b ) {

    if( a == 0 ) return b;

    if( b == 0 ) return a;

    if( heap[a].v < heap[b].v ) swap( a, b );

    heap[a].r = merge( heap[a].r, b );

    heap[heap[a].r].f = a;

    if( heap[heap[a].l].dis < heap[heap[a].r].dis ) swap( heap[a].l, heap[a].r );

    if( heap[a].r == 0 ) heap[a].dis = 0;

    else heap[a].dis = heap[heap[a].r].dis + 1;

    return a;

}

 

 

int pop( int a ) {

    int l = heap[a].l;

    int r = heap[a].r;

    heap[l].f = l;

    heap[r].f = r;

    heap[a].l = heap[a].r = heap[a].dis = 0;

    return merge(l, r);

}

 

 

int find( int a ) { return heap[a].f == a ? a : find( heap[a].f ) ; }

 

void Read( int &x ) {

    char ch;

    x = 0;

    ch = getchar();

    while( !(ch >= '0' && ch <= '9') ) ch = getchar();

    while( ch >= '0' && ch <= '9' ) {

        x = x * 10 + ch - '0' ;

        ch = getchar();

    }

}

 

     

int main() {

//  freopen( "c:/aaa.txt", "r", stdin );

    int i, a, b, finda, findb, n, m;

    while( scanf( "%d", &n ) == 1 ) {

        for( i=1; i<=n; ++i ) {

            Read(heap[i].v);

            //scanf( "%d", &st[i].v );

            heap[i].l = heap[i].r = heap[i].dis = 0;

            heap[i].f = i;

        }

         

        //scanf( "%d", &m );

        Read( m );

        while( m-- ) {

            //scanf( "%d %d", &a, &b );

            Read( a ); Read( b );

            finda = find( a );

            findb = find( b );

            if( finda == findb ) {

                printf("-1 ");

            } else {

                heap[finda].v /= 2;

                int u = pop( finda );

                u = merge( u, finda );

 

                heap[findb].v /= 2;

                int v = pop( findb );

                v = merge( v, findb );

 

                printf( "%d ", heap[merge( u, v )].v );

            }

        }  

    }

    return 0;

}