1057. Stack

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本文介绍了一种特殊的数据结构——栈，该栈除了基本的压栈和弹栈操作外，还支持查询栈内元素的中位数。通过使用树状数组和二分查找算法，文章详细阐述了如何高效地实现这一功能，并提供了一个完整的C++代码示例。

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1057. Stack (30)

时间限制

100 ms

内存限制

65536 kB

代码长度限制

16000 B

判题程序

Standard

作者

CHEN, Yue

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

考查：树状数组，二分查找。如果运用stack库，会超时！

#include<stdio.h>
#include<string.h>
#include<string>
#include<iostream>
using namespace std;

const int n = 100002;

int c[n];

int lowbit(int i)
{
	return i & (-i);
}

void add(int pos, int value)
{
	while(pos < n)
	{
		c[pos] += value;
		pos += lowbit(pos); 
	}
}

int sum(int pos)
{
	int res = 0;
	while(pos > 0)
	{
		res += c[pos];
		pos -= lowbit(pos);
	}
	return res;
}


int find(int value)
{
	int l = 0, r = n - 1;
	int median, res;
	
	while(l < r - 1)
	{
		if((l + r) % 2 == 0)
			median = (l+r) / 2;
		else
			median = (l+r-1) / 2;
		
		res = sum(median);
		if(res < value)
			l = median;
		else
			r = median;
	}
	return l + 1;
}

int main()
{
	freopen("F://Temp/input.txt", "r", stdin);
	char ss[15];
	int stack[n], top = 0, k, pos;
	memset(c, 0, sizeof(c));
	scanf("%d", &k);
	
	while(k --)
	{
		scanf("%s", ss);
		if(strcmp(ss, "Push") == 0)
		{
			scanf("%d", &pos);
			stack[++ top] = pos;
			add(pos , 1);
		}
		else if(strcmp(ss, "Pop") == 0)
		{
			if(top == 0)
			{
				printf("Invalid\n");
				continue;
			}
			
			int out = stack[top];
			add(out, -1);
			printf("%d\n", stack[top --]);
		}
		else if(strcmp(ss, "PeekMedian") == 0)
		{
			if(top == 0)
			{
				printf("Invalid\n");
				continue;
			}
			int res;
			if(top % 2 == 0)
				res = find(top / 2);
			else
				res = find((top+1) / 2);
			printf("%d\n", res);
		}
		else
			printf("Invalid\n");
	}
	return 0;
}