luogu1168 中位数

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;elsereturn 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\n", g.GetKeyByRank(i / 2 + 1));g.Insert(A[i + 1]);}return 0;
}