题目大意
给出一个长度为N的非负整数序列A[i],对于所有1 ≤ k ≤ (N + 1) / 2,输出A[1], A[3], …, A[2k - 1]的中位数。即前1,3,5,……个数的中位数。
题解
要找到中位数我们需要的序列是单调不减的,故可以用二叉平衡树解决。
#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
const int MAX_NODE = 100010;
struct SplayTree
{
private:
struct Node
{
Node *LeftSon, *RightSon, *Father;
int Key, Size, Count;
Node(Node *fa, int key) : Father(fa), LeftSon(NULL), RightSon(NULL), Key(key), Size(1), Count(1){}
bool IsLeftSon()
{
return Father->LeftSon == this;
}
void Refresh()
{
Size = (LeftSon ? LeftSon->Size : 0) + (RightSon ? RightSon->Size : 0) + Count;
}
bool IsRoot()
{
return Father == NULL || (Father->LeftSon != this && Father->RightSon != this);
}
}*Root;
void Rotate(Node *cur)
{
Node *gfa = cur->Father->Father;
Node **gfaSon = gfa ? (cur->Father->IsLeftSon() ? &gfa->LeftSon : &gfa->RightSon) : &Root;
Node **faSon = cur->IsLeftSon() ? &cur->Father->LeftSon : &cur->Father->RightSon;
Node **curSon = cur->IsLeftSon() ? &cur->RightSon : &cur->LeftSon;
*faSon = *curSon;
if (*faSon)
(*faSon)->Father = cur->Father;
*curSon = cur->Father;
(*curSon)->Father = cur;
*gfaSon = cur;
(*gfaSon)->Father = gfa;
(*curSon)->Refresh();
cur->Refresh();
}
void PushDown() {}
void Splay(Node *cur)
{
PushDown();
while (cur->Father)
{
if (!cur->Father->IsRoot())
Rotate(cur->Father->IsLeftSon() == cur->IsLeftSon() ? cur->Father : cur);
Rotate(cur);
}
}
int GetKeyByRank(Node *cur, int rank)
{
int rootSize, leftSize = (cur->LeftSon ? cur->LeftSon->Size : 0);
if (rank <= leftSize)
return GetKeyByRank(cur->LeftSon, rank);
else if (rank <= (rootSize = leftSize + cur->Count))
return cur->Key;
else
return GetKeyByRank(cur->RightSon, rank - rootSize);
}
public:
void Insert(int key)
{
Node **cur = &Root, *fa = NULL;
while (*cur)
{
fa = *cur;
if (key == (*cur)->Key)
{
(*cur)->Count++;
Splay(*cur);
return;
}
else if (key < (*cur)->Key)
cur = &(*cur)->LeftSon;
else if (key > (*cur)->Key)
cur = &(*cur)->RightSon;
}
*cur = new Node(fa, key);
Splay(*cur);
}
int GetKeyByRank(int rank)
{
return GetKeyByRank(Root, rank);
}
}g;
int main()
{
static int A[MAX_NODE];
int n;
scanf("%d", &n);
for (int i = 1; i <= n; i++)
scanf("%d", A + i);
for (int i = 1; i <= n; i += 2)
{
g.Insert(A[i]);
printf("%d
", g.GetKeyByRank(i / 2 + 1));
g.Insert(A[i + 1]);
}
return 0;
}