1057. Stack (30)-PAT

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本文探讨了在给定数据集上实现堆排序并优化中位数计算的方法，利用二叉索引树(Binary Indexed Tree)进行高效查找与更新操作，避免了传统排序方法在大规模数据集上的性能瓶颈。

1057. Stack (30)-中位数-BIT

时间限制

100 ms

内存限制

32000 kB

代码长度限制

16000 B

判题程序

Standard

Stack is one of the most fundamental data structures, which is based on the principle of Last In First Out (LIFO). The basic operations include Push (inserting an element onto the top position) and Pop (deleting the top element). Now you are supposed to implement a stack with an extra operation: PeekMedian -- return the median value of all the elements in the stack. With N elements, the median value is defined to be the (N/2)-th smallest element if N is even, or ((N+1)/2)-th if N is odd.

Input Specification:

Each input file contains one test case. For each case, the first line contains a positive integer N (<= 10⁵). Then N lines follow, each contains a command in one of the following 3 formats:

Push key
Pop
PeekMedian

where key is a positive integer no more than 10⁵.

Output Specification:

For each Push command, insert key into the stack and output nothing. For each Pop or PeekMedian command, print in a line the corresponding returned value. If the command is invalid, print "Invalid" instead.

Sample Input:

17
Pop
PeekMedian
Push 3
PeekMedian
Push 2
PeekMedian
Push 1
PeekMedian
Pop
Pop
Push 5
Push 4
PeekMedian
Pop
Pop
Pop
Pop

Sample Output:

Invalid
Invalid
3
2
2
1
2
4
4
5
3
Invalid

推荐指数※※

来源：http://pat.zju.edu.cn/contests/pat-a-practise/1057

这道题如果不考虑时间限制，那是比较简单的，一开始就直接使用一个数组计数，使用二分法搜索，但都是超时。

这样只能用上统计累计频次比较好的Bianry Indexed Tree(http://community.topcoder.com/tc?module=Static&d1=tutorials&d2=binaryIndexedTrees).

还有这里cin，cout还是不要用了，效率不如printf和scanf。

#include<iostream>
#include<string.h>
#include<stdio.h>
using namespace std;
#define Maxval 100009
int tree[Maxval+1];
int stack[Maxval+1];
void update(int idx,int val){
	while(idx<Maxval){
		tree[idx]+=val;
		idx+=(idx&-idx);
	}
}
int read(int idx){
	int sum=0;
	while(idx>0){
		sum+=tree[idx];
		idx-=(idx&-idx);
	}
	return sum;
}
int find_cumulate(int cumfre){
	int low=0,high=Maxval,mid;
	while(low<high-1){
		if((low+high)&1==1)
			mid=(low+high-1)/2;
		else
			mid=(low+high)/2;
		int sum=read(mid);
		if(sum>=cumfre)
			high=mid;
		else
		  	low=mid;
	}
	return high;
}
int main(){
	int n,i;
	char str[20];
	scanf("%d",&n);
	long tmp,top;
	memset(tree,0,Maxval*sizeof(int));
	memset(stack,0,Maxval*sizeof(int));
	top=0;
	for(i=0;i<n;i++){
		scanf("%str",str);
		if(str[1]=='o'){//POP
			if(top>0){
				tmp=stack[top--];
				printf("%d\n",tmp);
				update(tmp,-1);
			}
			else
				printf("Invalid\n");
		}
		else if(str[1]=='u'){//push
			cin>>tmp;
			stack[++top]=tmp;
			update(tmp,1);
		}
		else if(str[1]=='e'){//media
			if(top>0){
				if(top&1==1)
					tmp=(top+1)/2;
				else
					tmp=top/2;
				tmp=find_cumulate(tmp);
				printf("%d\n",tmp);
			}
			else
				printf("Invalid\n");
		}
		else{
			printf("Invalid\n");
		}
	}
	return 0;
}

这是我超时的代码，比较的朴素

#include<iostream>
#include<string.h>
#include<string>
#include<stack>
#include<vector>
#include<set>
#include<algorithm>
#define  N 100000
#define  Hash_N 10000
using namespace std;
long find_median(long *arr,long first,long last,long val){
	long mid;
	while(first<last&&first!=0&&last!=Hash_N-1){
		mid=(first+last)/2;
		if(arr[mid]==val){
			return mid;
		}else if(arr[mid]>val)
			last=mid;
		else
			first=mid;
	}
	return first;
}
int main()
{
	long n,i,j;
	char str[20];
	long totalnum,num[N],hash_num[Hash_N];
	stack<long> st;
	cin>>n;
	totalnum=0;
	long tmp;
	memset(num,0,N*sizeof(int));
	memset(hash_num,0,Hash_N*sizeof(int));
	long fhash=N/Hash_N;
	for(i=0;i<n;i++){
		cin>>str;
		if(strcmp(str,"Pop")==0){//POP
			if(!st.empty()){
				tmp=st.top();
				cout<<tmp<<endl;
				st.pop();
				totalnum--;
				num[tmp]--;
				for(j=tmp/fhash;j<Hash_N;j++)
					hash_num[j]--;
			}
			else
				cout<<"Invalid"<<endl;
		}
		else if(strcmp(str,"Push")==0){//push
			cin>>tmp;
			st.push(tmp);
			totalnum++;
			num[tmp]++;
			hash_num[tmp/fhash]++;
		}
		else{//media
			if(!st.empty()){
				if(totalnum&1==1)
					tmp=(totalnum+1)/2;
				else
					tmp=totalnum/2;
				long tmp_sum=0,k;
				k=find_median(hash_num,0,Hash_N,tmp);
				if(k>0)
					tmp_sum=hash_num[k-1];
				else
					tmp_sum=0;
				for(j=k*fhash;j<N;j++){
					tmp_sum+=num[j];
					if(tmp_sum>=tmp){
						cout<<j<<endl;
						break;
					}
				}
			}
			else
				cout<<"Invalid"<<endl;
		}
	}
	return 0;
}