【 线段树】P12347 [蓝桥杯 2025 省 A 第二场] 栈与乘积|普及+ - 指南
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 x 1 \ x 1x: 将 x x x 加入栈顶。
- 2 2 2: 将栈顶的数弹出（如果栈是空的，则什么都不做）。
-
3
y
3 \ y
3y: 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 3y 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 ≤ 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
#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
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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