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

news 2025/9/4 13:04:52

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. 1x1 \ x1 x: 将 xxx 加入栈顶。
  2. 222: 将栈顶的数弹出（如果栈是空的，则什么都不做）。
  3. 3y3 \ y3 y: 查询栈内的最顶端 yyy 个数的乘积。如果大于等于 2322^{32}232，输出 OVERFLOW。如果栈内不足 yyy 个数，输出 ERROR。

输入格式

输入的第一行包含一个正整数 QQQ，表示操作次数。

接下来 QQQ 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 3y3 \ y3 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

9
1 65536
1 65536
3 2
3 3
2
1 1024
1 2
3 2
3 3

输出 #1

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≤5000Q \leq 5000Q≤5000；
  • 对于所有评测用例，1≤Q≤1051 \leq Q \leq 10^51≤Q≤105，0≤x<2300 \leq x < 2^{30}0≤x<230，1≤y<2301 \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

#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 _DEBUGfreopen("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

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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