【 线段树】P12347 [蓝桥杯 2025 省 A 第二场] 栈与乘积|普及+

P12347 [蓝桥杯 2025 省 A 第二场] 栈与乘积

题目背景

目前测试数据可能较水,我们之后会加强数据。

题目描述

给定一个栈,给出若干次如下类型的操作:

  1. 1 x 1 \ x 1 x: 将 x x x 加入栈顶。
  2. 2 2 2: 将栈顶的数弹出(如果栈是空的,则什么都不做)。
  3. 3 y 3 \ y 3 y: 查询栈内的最顶端 y y y 个数的乘积。如果大于等于 2 32 2^{32} 232,输出 OVERFLOW。如果栈内不足 y y y 个数,输出 ERROR

输入格式

输入的第一行包含一个正整数 Q Q Q,表示操作次数。

接下来 Q Q Q 行,每行包含一个或两个正整数表示一个操作,如果一行包含两个整数,两个整数之间用一个空格分隔。

输出格式

对于每个 3 y 3 \ y 3 y 形式的操作,输出一行包含一个整数,表示答案。

输入输出样例 #1

输入 #1

复制代码
9
1 65536
1 65536
3 2
3 3
2
1 1024
1 2
3 2
3 3

输出 #1

复制代码
OVERFLOW
ERROR
2048
134217728

说明/提示

评测用例规模与约定

  • 对于 30 % 30\% 30% 的评测用例, Q ≤ 5000 Q \leq 5000 Q≤5000;
  • 对于所有评测用例, 1 ≤ Q ≤ 10 5 1 \leq Q \leq 10^5 1≤Q≤105, 0 ≤ x < 2 30 0 \leq x < 2^{30} 0≤x<230, 1 ≤ y < 2 30 1 \leq y < 2^{30} 1≤y<230。

线段树

单点修改 区间查询

值类型,保存类型:long long

线段树[0,Q),初始全部为1。cnt记录栈中元素。

入栈 线段树[cnt++]=x 出栈[--cnt]=1

节点合并:一,两个节点包括0,结果0。二,有溢出(-1),结果溢出。三,转成unit64,相乘如果大于uint32,-1;否则,值就是成绩。

代码

核心代码

cpp 复制代码
#include <iostream>
#include <sstream>
#include <vector>
#include<map>
#include<unordered_map>
#include<set>
#include<unordered_set>
#include<string>
#include<algorithm>
#include<functional>
#include<queue>
#include <stack>
#include<iomanip>
#include<numeric>
#include <math.h>
#include <climits>
#include<assert.h>
#include<cstring>
#include<list>
#include<array>

#include <bitset>
using namespace std;

template<class T1, class T2>
std::istream& operator >> (std::istream& in, pair<T1, T2>& pr) {
	in >> pr.first >> pr.second;
	return in;
}

template<class T1, class T2, class T3 >
std::istream& operator >> (std::istream& in, tuple<T1, T2, T3>& t) {
	in >> get<0>(t) >> get<1>(t) >> get<2>(t);
	return in;
}

template<class T1, class T2, class T3, class T4 >
std::istream& operator >> (std::istream& in, tuple<T1, T2, T3, T4>& t) {
	in >> get<0>(t) >> get<1>(t) >> get<2>(t) >> get<3>(t);
	return in;
}

template<class T1, class T2, class T3, class T4, class T5, class T6, class T7 >
std::istream& operator >> (std::istream& in, tuple<T1, T2, T3, T4,T5,T6,T7>& t) {
	in >> get<0>(t) >> get<1>(t) >> get<2>(t) >> get<3>(t) >> get<4>(t) >> get<5>(t) >> get<6>(t);
	return in;
}

template<class T = int>
vector<T> Read() {
	int n;
	cin >> n;
	vector<T> ret(n);
	for (int i = 0; i < n; i++) {
		cin >> ret[i];
	}
	return ret;
}
template<class T = int>
vector<T> ReadNotNum() {
	vector<T> ret;
	T tmp;
	while (cin >> tmp) {
		ret.emplace_back(tmp);
		if ('\n' == cin.get()) { break; }
	}
	return ret;
}

template<class T = int>
vector<T> Read(int n) {
	vector<T> ret(n);
	for (int i = 0; i < n; i++) {
		cin >> ret[i];
	}
	return ret;
}

template<int N = 1'000'000>
class COutBuff
{
public:
	COutBuff() {
		m_p = puffer;
	}
	template<class T>
	void write(T x) {
		int num[28], sp = 0;
		if (x < 0)
			*m_p++ = '-', x = -x;

		if (!x)
			*m_p++ = 48;

		while (x)
			num[++sp] = x % 10, x /= 10;

		while (sp)
			*m_p++ = num[sp--] + 48;
		AuotToFile();
	}
	void writestr(const char* sz) {
		strcpy(m_p, sz);
		m_p += strlen(sz);
		AuotToFile();
	}
	inline void write(char ch)
	{
		*m_p++ = ch;
		AuotToFile();
	}
	inline void ToFile() {
		fwrite(puffer, 1, m_p - puffer, stdout);
		m_p = puffer;
	}
	~COutBuff() {
		ToFile();
	}
private:
	inline void AuotToFile() {
		if (m_p - puffer > N - 100) {
			ToFile();
		}
	}
	char  puffer[N], * m_p;
};

template<int N = 1'000'000>
class CInBuff
{
public:
	inline CInBuff() {}
	inline CInBuff<N>& operator>>(char& ch) {
		FileToBuf();
		while (('\r' == *S) || ('\n' == *S) || (' ' == *S)) { S++; }//忽略空格和回车
		ch = *S++;
		return *this;
	}
	inline CInBuff<N>& operator>>(int& val) {
		FileToBuf();
		int x(0), f(0);
		while (!isdigit(*S))
			f |= (*S++ == '-');
		while (isdigit(*S))
			x = (x << 1) + (x << 3) + (*S++ ^ 48);
		val = f ? -x : x; S++;//忽略空格换行		
		return *this;
	}
	inline CInBuff& operator>>(long long& val) {
		FileToBuf();
		long long x(0); int f(0);
		while (!isdigit(*S))
			f |= (*S++ == '-');
		while (isdigit(*S))
			x = (x << 1) + (x << 3) + (*S++ ^ 48);
		val = f ? -x : x; S++;//忽略空格换行
		return *this;
	}
	template<class T1, class T2>
	inline CInBuff& operator>>(pair<T1, T2>& val) {
		*this >> val.first >> val.second;
		return *this;
	}
	template<class T1, class T2, class T3>
	inline CInBuff& operator>>(tuple<T1, T2, T3>& val) {
		*this >> get<0>(val) >> get<1>(val) >> get<2>(val);
		return *this;
	}
	template<class T1, class T2, class T3, class T4>
	inline CInBuff& operator>>(tuple<T1, T2, T3, T4>& val) {
		*this >> get<0>(val) >> get<1>(val) >> get<2>(val) >> get<3>(val);
		return *this;
	}
	template<class T = int>
	inline CInBuff& operator>>(vector<T>& val) {
		int n;
		*this >> n;
		val.resize(n);
		for (int i = 0; i < n; i++) {
			*this >> val[i];
		}
		return *this;
	}
	template<class T = int>
	vector<T> Read(int n) {
		vector<T> ret(n);
		for (int i = 0; i < n; i++) {
			*this >> ret[i];
		}
		return ret;
	}
	template<class T = int>
	vector<T> Read() {
		vector<T> ret;
		*this >> ret;
		return ret;
	}
private:
	inline void FileToBuf() {
		const int canRead = m_iWritePos - (S - buffer);
		if (canRead >= 100) { return; }
		if (m_bFinish) { return; }
		for (int i = 0; i < canRead; i++)
		{
			buffer[i] = S[i];//memcpy出错			
		}
		m_iWritePos = canRead;
		buffer[m_iWritePos] = 0;
		S = buffer;
		int readCnt = fread(buffer + m_iWritePos, 1, N - m_iWritePos, stdin);
		if (readCnt <= 0) { m_bFinish = true; return; }
		m_iWritePos += readCnt;
		buffer[m_iWritePos] = 0;
		S = buffer;
	}
	int m_iWritePos = 0; bool m_bFinish = false;
	char buffer[N + 10], * S = buffer;
};

template<class TSave, class TRecord >
class CSingeUpdateLineTree
{
protected:
	virtual void OnQuery(TSave& ans, const TSave& cur) = 0;
	virtual void OnUpdate(TSave& save, int iSave, const TRecord& update) = 0;
	virtual void OnUpdateParent(TSave& par, const TSave& left, const TSave& r, int iSaveLeft, int iSaveRight) = 0;
};

template<class TSave, class TRecord >
class CVectorSingUpdateLineTree : public CSingeUpdateLineTree<TSave, TRecord>
{
public:
	CVectorSingUpdateLineTree(int iEleSize, TSave tDefault) :m_iEleSize(iEleSize), m_save(iEleSize * 4, tDefault), m_tDefault(tDefault) {

	}
	void Update(int index, TRecord update) {
		Update(1, 0, m_iEleSize - 1, index, update);
	}
	TSave Query(int leftIndex, int leftRight, TSave tDefault) {
		TSave ans = tDefault;
		Query(ans, 1, 0, m_iEleSize - 1, leftIndex, leftRight);
		return ans;
	}
	TSave Query(int leftIndex, int leftRight) {
		return Query(leftIndex, leftRight, m_tDefault);
	}
	void Init(std::function<void(TSave&, const int&)> fun) {
		Init(fun, 1, 0, m_iEleSize - 1);
	}
	TSave QueryAll() {
		return m_save[1];
	}
protected:
	int m_iEleSize;
	void Init(std::function<void(TSave&, const int&)> fun, int iNodeNO, int iSaveLeft, int iSaveRight)
	{
		if (iSaveLeft == iSaveRight) {
			fun(m_save[iNodeNO], iSaveLeft);
			return;
		}
		const int mid = iSaveLeft + (iSaveRight - iSaveLeft) / 2;
		Init(fun, iNodeNO * 2, iSaveLeft, mid);
		Init(fun, iNodeNO * 2 + 1, mid + 1, iSaveRight);
		this->OnUpdateParent(m_save[iNodeNO], m_save[iNodeNO * 2], m_save[iNodeNO * 2 + 1], iSaveLeft, iSaveRight);
	}
	void Query(TSave& ans, int iNodeNO, int iSaveLeft, int iSaveRight, int iQueryLeft, int iQueryRight) {
		if ((iSaveLeft >= iQueryLeft) && (iSaveRight <= iQueryRight)) {
			this->OnQuery(ans, m_save[iNodeNO]);
			return;
		}
		if (iSaveLeft == iSaveRight) {//没有子节点
			return;
		}
		const int mid = iSaveLeft + (iSaveRight - iSaveLeft) / 2;
		if (mid >= iQueryLeft) {
			Query(ans, iNodeNO * 2, iSaveLeft, mid, iQueryLeft, iQueryRight);
		}
		if (mid + 1 <= iQueryRight) {
			Query(ans, iNodeNO * 2 + 1, mid + 1, iSaveRight, iQueryLeft, iQueryRight);
		}
	}
	void Update(int iNodeNO, int iSaveLeft, int iSaveRight, int iUpdateNO, TRecord update) {
		if (iSaveLeft == iSaveRight)
		{
			this->OnUpdate(m_save[iNodeNO], iSaveLeft, update);
			return;
		}
		const int mid = iSaveLeft + (iSaveRight - iSaveLeft) / 2;
		if (iUpdateNO <= mid) {
			Update(iNodeNO * 2, iSaveLeft, mid, iUpdateNO, update);
		}
		else {
			Update(iNodeNO * 2 + 1, mid + 1, iSaveRight, iUpdateNO, update);
		}
		this->OnUpdateParent(m_save[iNodeNO], m_save[iNodeNO * 2], m_save[iNodeNO * 2 + 1], iSaveLeft, iSaveRight);
	}
	vector<TSave> m_save;
	const TSave m_tDefault;
};

template<class TSave, class TRecord >
class CTreeSingeLineTree : public CSingeUpdateLineTree<TSave, TRecord>
{
protected:
	struct CTreeNode
	{
		int Cnt()const { return m_iMaxIndex - m_iMinIndex + 1; }
		int m_iMinIndex;
		int m_iMaxIndex;
		TSave data;
		CTreeNode* m_lChild = nullptr, * m_rChild = nullptr;
		~CTreeNode() {
			delete m_lChild; m_lChild = nullptr;
			delete m_rChild; m_rChild = nullptr;
		}
	};
	CTreeNode* m_root;
	TSave m_tDefault;
public:
	CTreeSingeLineTree(int iMinIndex, int iMaxIndex, TSave tDefault) {
		m_tDefault = tDefault;
		m_root = CreateNode(iMinIndex, iMaxIndex);
	}
	void Update(int index, TRecord update) {
		Update(m_root, index, update);
	}
	TSave QueryAll() {
		return m_root->data;
	}
	TSave Query(int leftIndex, int leftRight) {
		TSave ans = m_tDefault;
		Query(ans, m_root, leftIndex, leftRight);
		return ans;
	}
	~CTreeSingeLineTree() {
		delete m_root;
	}
protected:
	void Query(TSave& ans, CTreeNode* node, int iQueryLeft, int iQueryRight) {
		if ((node->m_iMinIndex >= iQueryLeft) && (node->m_iMaxIndex <= iQueryRight)) {
			this->OnQuery(ans, node->data);
			return;
		}
		if (1 == node->Cnt()) {//没有子节点
			return;
		}
		CreateChilds(node);
		const int mid = node->m_iMinIndex + (node->m_iMaxIndex - node->m_iMinIndex) / 2;
		if (mid >= iQueryLeft) {
			Query(ans, node->m_lChild, iQueryLeft, iQueryRight);
		}
		if (mid + 1 <= iQueryRight) {
			Query(ans, node->m_rChild, iQueryLeft, iQueryRight);
		}
	}
	void Update(CTreeNode* node, int iUpdateNO, TRecord update) {
		if ((iUpdateNO < node->m_iMinIndex) || (iUpdateNO > node->m_iMaxIndex)) {
			return;
		}
		if (1 == node->Cnt()) {
			this->OnUpdate(node->data, node->m_iMinIndex, update);
			return;
		}
		CreateChilds(node);
		Update(node->m_lChild, iUpdateNO, update);
		Update(node->m_rChild, iUpdateNO, update);
		this->OnUpdateParent(node->data, node->m_lChild->data, node->m_rChild->data, node->m_iMinIndex, node->m_iMaxIndex);
	}
	void CreateChilds(CTreeNode* node) {
		if (nullptr != node->m_lChild) { return; }
		const int iSaveLeft = node->m_iMinIndex;
		const int iSaveRight = node->m_iMaxIndex;
		const int mid = iSaveLeft + (iSaveRight - iSaveLeft) / 2;
		node->m_lChild = CreateNode(iSaveLeft, mid);
		node->m_rChild = CreateNode(mid + 1, iSaveRight);
	}
	CTreeNode* CreateNode(int iMinIndex, int iMaxIndex) {
		CTreeNode* node = new CTreeNode;
		node->m_iMinIndex = iMinIndex;
		node->m_iMaxIndex = iMaxIndex;
		node->data = m_tDefault;
		return node;
	}
};
typedef long long TSave;
typedef long long TRecord;
class  CMyLineTree : public CTreeSingeLineTree<TSave, TRecord>
{
public:
	CMyLineTree() :CTreeSingeLineTree<TSave, TRecord>(0, 100'000, 1)
	{
	}
protected:
	virtual void OnInit(TSave& save, int iSave) {};
	virtual void OnQuery(TSave& ans, const TSave& cur) {
		if ((0 == ans) || (0 == cur)) { ans = 0; return; }
		if ((-1 == ans) || (-1 == cur)) { ans = -1; return; }
		unsigned long long tmp = ans * cur;
		if (tmp >= (1LL << 32)) {
			ans = -1;
		}
		else {
			ans = tmp;
		}
	}
	virtual void OnUpdate(TSave& save, int iSave, const TRecord& update)
	{
		save = update;
	}
	virtual void OnUpdateParent(TSave& par, const TSave& left, const TSave& r, int iSaveLeft, int iSaveRight)
	{
		par = left;
		OnQuery(par, r);
	}
};
class Solution {
		public:
			vector<long long> Ans(vector<pair<int,unsigned int>>& ope) {
				CMyLineTree sg;
				int cnt = 0;
				vector<long long> ans;
				for (const auto& [kind, x] : ope) {
					if (1 == kind) {
						sg.Update(cnt++, x);
					}
					else if (2 == kind) {
						if (cnt > 0) { sg.Update(--cnt, 1); };
					}
					else if (3 == kind) {
						if (x > cnt) {
							ans.emplace_back(-2);
						}
						else
						{
							ans.emplace_back(sg.Query(cnt - x, cnt - 1));
						}
					}
				}
				return ans;
			}
		};

int main() {
#ifdef _DEBUG
	freopen("a.in", "r", stdin);
#endif // DEBUG	
	ios::sync_with_stdio(0); cin.tie(nullptr);
	//CInBuff<> in; COutBuff<10'000'000> ob;	
	int Q;
	cin >> Q;
	vector<pair<int, unsigned int>> ope(Q);
	for (int i = 0; i < Q; i++) {
		cin >> ope[i].first;
		if (2 != ope[i].first) {
			cin >> ope[i].second;
		}
	}
#ifdef _DEBUG	
	//	printf("K=%d", K);
		Out(ope, ",ope=");
		//Out(P, ",P=");
		/*Out(edge, ",edge=");		
		Out(que, ",que=");*/
	   //Out(ab, ",ab=");
	   //Out(par, "par=");
	   //Out(que, "que=");
	   //Out(B, "B=");
#endif // DEBUG	
	auto res = Solution().Ans(ope);
	for (const auto& ll : res)
	{
		if (-1 == ll) {
			cout << "OVERFLOW";
		}
		else if (-2 == ll) {
			cout << "ERROR";
		}
		else {
			cout << ll;
		}
		cout << "\n";
	}
	return 0;
};

单元测试

cpp 复制代码
TEST_METHOD(TestMethod11)
		{
			ope = { {1,65536},{1,65536},{3,2},{3,3},{2,0},{1,1024},{1,2},{3,2},{3,3} };
			auto res = Solution().Ans(ope);
			AssertV({-1,-2,2048,134217728 }, res);
		}
		TEST_METHOD(TestMethod12)
		{
			ope = { {2,0},{2,0},{2,0},{1,65536},{3,2},{3,1} };
			auto res = Solution().Ans(ope);
			AssertV({-2,65536 }, res);
		}

# 扩展阅读

我想对大家说的话
工作中遇到的问题,可以按类别查阅鄙人的算法文章,请点击《算法与数据汇总》。
学习算法:按章节学习《喜缺全书算法册》,大量的题目和测试用例,打包下载。重视操作
有效学习:明确的目标 及时的反馈 拉伸区(难度合适) 专注
闻缺陷则喜(喜缺)是一个美好的愿望,早发现问题,早修改问题,给老板节约钱。
子墨子言之:事无终始,无务多业。也就是我们常说的专业的人做专业的事。
如果程序是一条龙,那算法就是他的是睛
失败+反思=成功 成功+反思=成功

视频课程

先学简单的课程,请移步CSDN学院,听白银讲师(也就是鄙人)的讲解。
https://edu.csdn.net/course/detail/38771

如何你想快速形成战斗了,为老板分忧,请学习C#入职培训、C++入职培训等课程
https://edu.csdn.net/lecturer/6176

测试环境

操作系统:win7 开发环境: VS2019 C++17

或者 操作系统:win10 开发环境: VS2022 C++17

如无特殊说明,本算法 用**C++**实现。

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