【BZOJ2762】[JLOI2011]不等式组(树状数组)

题目:

BZOJ2762

分析:

加入的不等式分三种情况
(a>0),可以变成(x>lfloor frac{c-b}{a} floor)
(a=0),若(b>c)则恒成立,否则恒不成立
(a<0),可以变成(x<lceil frac{c-b}{a} ceil)

对于(a=0),用一个变量(sum)记一下当前有多少不等式恒成立,删除的时候注意要维护(sum)

对于(a eq0),可以开两个权值树状数组(greater)(less)记录。当加入(a>0)时,令(x=lfloor frac{c-b}{a} floor),给(greater)(x)位置加(1),查询时查([0,k))区间的和。(a<0)时在(less)上类似。

对于删除操作,在树状数组上删除该不等式贡献的值即可。注意要记录已删除的不等式防止重复删除。

代码:

这题思路简单,但是代码细节比较多……

#include <cstdio>
#include <cmath>
#include <algorithm>
#include <cstring>
#include <iostream>
using namespace std;
namespace zyt
{
	const int DELETED = 1e9, P = 1e6 + 10, OPT = 1e5 + 10, N = P * 2;
	class Tree_Array
	{
	private:
		int data[N];
		inline int lowbit(const int x)
		{
			return x & -x;
		}
	public:
		Tree_Array()
		{
			memset(data, 0, sizeof(data));
		}
		inline void add(int a, const int x)
		{
			while (a < N)
				data[a] += x, a += lowbit(a);
		}
		inline int query(int a)
		{
			int ans = 0;
			while (a > 0)
				ans += data[a], a -= lowbit(a);
			return ans;
		}
	}less, greater;
	int n;
	pair<int, int> opt[OPT];
	int cnt, sum;
	int work()
	{
		ios::sync_with_stdio(false);
		cin.tie(NULL);
		cin >> n;
		for (int i = 0; i < n; i++)
		{
			string s;
			cin >> s;
			if (s == "Add")
			{
				int a, b, c, x;
				cin >> a >> b >> c;
				if (a == 0)
				{
					opt[++cnt] = make_pair(0, (bool)(b > c));
					if (b > c)
						sum++;
				}
				else if (a < 0)
				{
					x = (int)(ceil((c - b) / (double)a) + P);
					if (x < 1)
						x = 1;
					if (x >= N)
						x = N - 1;
					opt[++cnt] = make_pair(-1, x);
					less.add(x, 1);
				}
				else
				{
					x = (int)(floor((c - b) / (double)a) + P);
					if (x < 1)
						x = 1;
					if (x >= N)
						x = N - 1;
					opt[++cnt] = make_pair(1, x);
					greater.add(x, 1);
				}
			}
			else if (s == "Del")
			{
				int a;
				cin >> a;
				if (opt[a].first == 0)
					sum -= (opt[a].second == 1);
				else if (opt[a].second != DELETED)
				{
					if (opt[a].first == -1)
						less.add(opt[a].second, -1);
				   	else
						greater.add(opt[a].second, -1);
				}
				opt[a].second = DELETED;
			}
			else
			{
				int a;
				cin >> a;
				a += P;
				cout << sum + greater.query(a - 1) + less.query(N - 1) - less.query(a) << '
';
			}
		}
		return 0;
	}
}
int main()
{
	return zyt::work();
}
原文地址:https://www.cnblogs.com/zyt1253679098/p/9694972.html