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【线段树】P1438 无聊的数列|普及+

news 2025/7/29 16:56:46

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C++线段树

P1438 无聊的数列

题目背景

无聊的 YYB 总喜欢搞出一些正常人无法搞出的东西。有一天，无聊的 YYB 想出了一道无聊的题：无聊的数列。。。

题目描述

维护一个数列 $a_i$ ，支持两种操作：

1 l r K D：给出一个长度等于 $r - l + 1$ 的等差数列，首项为 $K$ ，公差为 $D$ ，并将它对应加到 $[l, r]$ 范围中的每一个数上。即：令 $a_l=a_l+K,a_{l+1}=a_{l+1}+K+D\ldots a_r=a_r+K+(r-l) \times D$ 。
2 p：询问序列的第 $p$ 个数的值 $a_p$ 。

输入格式

第一行两个整数数 $n, m$ 表示数列长度和操作个数。

第二行 $n$ 个整数，第 $i$ 个数表示 $a_i$ 。

接下来的 $m$ 行，每行先输入一个整数 $o pt$ 。

若 $o pt = 1$ 则再输入四个整数 $l\ r\ K\ D$ ；

若 $o pt = 2$ 则再输入一个整数 $p$ 。

输出格式

对于每个询问，一行一个整数表示答案。

输入输出样例 #1

输入 #1

输出 #1

说明/提示

数据规模与约定

对于 $100\%$ 数据， $0\le n,m \le 10^5,-200\le a_i,K,D\le 200, 1 \leq l \leq r \leq n, 1 \leq p \leq n$ 。

线段树

L，R 增加KD等差数列。 $\iff$ [L,R]之间的数，全部加上 k + iD - LD ，即Di+(k-LD)
线段树TSave long long：保存各区间的值。由于只会查询叶子节点，故非此叶子节点任意。
TRecord <long long,long long> 累加：D 和累加 (K - LD)

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 <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 T = int>
vector<T> Read() {int n;scanf("%d", &n);vector<T> ret(n);for (int i = 0; i < n; i++) {cin >> ret[i];}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 = 12 * 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;}inline void write(char ch){*m_p++ = ch;}inline void ToFile() {fwrite(puffer, 1, m_p - puffer, stdout);}
private:char  puffer[N], * m_p;
};template<int N = 12 * 1'000'000>
class CInBuff
{
public:inline CInBuff() {fread(buffer, 1, N, stdin);}inline int Read() {int x(0), f(0);while (!isdigit(*S))f |= (*S++ == '-');while (isdigit(*S))x = (x << 1) + (x << 3) + (*S++ ^ 48);return f ? -x : x;}
private:char buffer[N], * S = buffer;
};template<class TSave, class TRecord >
class CRangUpdateLineTree
{
protected:virtual void OnQuery(TSave& ans, const TSave& save, const int& iSaveLeft, const int& iSaveRight) = 0;virtual void OnUpdate(TSave& save, const int& iSaveLeft, const int& iSaveRight, const TRecord& update) = 0;virtual void OnUpdateParent(TSave& par, const TSave& left, const TSave& r, const int& iSaveLeft, const int& iSaveRight) = 0;virtual void OnUpdateRecord(TRecord& old, const TRecord& newRecord) = 0;
};template<class TSave, class TRecord >
class CVectorRangeUpdateLineTree : public CRangUpdateLineTree<TSave, TRecord>
{
public:CVectorRangeUpdateLineTree(int iEleSize, TSave tDefault, TRecord tRecordNull) :m_iEleSize(iEleSize), m_tDefault(tDefault), m_save(iEleSize * 4, tDefault), m_record(iEleSize * 4, tRecordNull) {m_recordNull = tRecordNull;}void Update(int iLeftIndex, int iRightIndex, TRecord value){Update(1, 0, m_iEleSize - 1, iLeftIndex, iRightIndex, value);}TSave Query(int leftIndex, int rightIndex) {return Query(leftIndex, rightIndex, m_tDefault);}TSave Query(int leftIndex, int rightIndex, const TSave& tDefault) {TSave ans = tDefault;Query(ans, 1, 0, m_iEleSize - 1, leftIndex, rightIndex);return ans;}//void Init() {//	Init(1, 0, m_iEleSize - 1);//}TSave QueryAll() {return m_save[1];}void swap(CVectorRangeUpdateLineTree<TSave, TRecord>& other) {m_save.swap(other.m_save);m_record.swap(other.m_record);std::swap(m_recordNull, other.m_recordNull);assert(m_iEleSize == other.m_iEleSize);}
protected://void Init(int iNodeNO, int iSaveLeft, int iSaveRight)//{//	if (iSaveLeft == iSaveRight) {//		this->OnInit(m_save[iNodeNO], iSaveLeft);//		return;//	}//	const int mid = iSaveLeft + (iSaveRight - iSaveLeft) / 2;//	Init(iNodeNO * 2, iSaveLeft, mid);//	Init(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], iSaveLeft, iSaveRight);return;}if (iSaveLeft == iSaveRight) {//没有子节点return;}Fresh(iNodeNO, iSaveLeft, iSaveRight);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 iNode, int iSaveLeft, int iSaveRight, int iOpeLeft, int iOpeRight, TRecord value){if ((iOpeLeft <= iSaveLeft) && (iOpeRight >= iSaveRight)){this->OnUpdate(m_save[iNode], iSaveLeft, iSaveRight, value);this->OnUpdateRecord(m_record[iNode], value);return;}if (iSaveLeft == iSaveRight) {return;//没有子节点}Fresh(iNode, iSaveLeft, iSaveRight);const int iMid = iSaveLeft + (iSaveRight - iSaveLeft) / 2;if (iMid >= iOpeLeft){Update(iNode * 2, iSaveLeft, iMid, iOpeLeft, iOpeRight, value);}if (iMid + 1 <= iOpeRight){Update(iNode * 2 + 1, iMid + 1, iSaveRight, iOpeLeft, iOpeRight, value);}// 如果有后代，至少两个后代this->OnUpdateParent(m_save[iNode], m_save[iNode * 2], m_save[iNode * 2 + 1], iSaveLeft, iSaveRight);}void Fresh(int iNode, int iDataLeft, int iDataRight){if (m_recordNull == m_record[iNode]){return;}const int iMid = iDataLeft + (iDataRight - iDataLeft) / 2;Update(iNode * 2, iDataLeft, iMid, iDataLeft, iMid, m_record[iNode]);Update(iNode * 2 + 1, iMid + 1, iDataRight, iMid + 1, iDataRight, m_record[iNode]);m_record[iNode] = m_recordNull;}vector<TSave> m_save;vector<TRecord> m_record;TRecord m_recordNull;TSave m_tDefault;const int m_iEleSize;
};typedef long long TSave;
typedef pair<long long, long long>  TRecord;
class  CMyLineTree : public  CVectorRangeUpdateLineTree<TSave, TRecord>
{
public:using CVectorRangeUpdateLineTree::CVectorRangeUpdateLineTree;
protected:virtual void OnQuery(TSave& ans, const TSave& save, const int& iSaveLeft, const int& iSaveRight) {ans = save;}virtual void OnUpdate(TSave& save, const int& iSaveLeft, const int& iSaveRight, const TRecord& update) override{save += iSaveLeft * update.first + update.second;}virtual void OnUpdateParent(TSave& par, const TSave& left, const TSave& r, const int& iSaveLeft, const int& iSaveRight)  override{}virtual void OnUpdateRecord(TRecord& old, const TRecord& newRecord) override{old.first += newRecord.first;old.second += newRecord.second;}
};
class Solution {
public:vector<long long> Ans(const vector<int>& a, vector<tuple<int, int, int, int>>& que) {const int N = a.size();CMyLineTree lineTree(N + 1, 0, { 0,0 });for (int i = 1; i <= N; i++) {lineTree.Update(i, i, { 0,a[i - 1] });}vector<long long> ans;for (const auto& [left, r, K, D] : que) {if (0 == r) {ans.emplace_back(lineTree.Query(left, left));}else{lineTree.Update(left, r, { D,K - left * D });}}return ans;}
};int main() {	
#ifdef _DEBUGfreopen("a.in", "r", stdin);
#endif // DEBUG		int n, m;cin >> n >> m;auto a = Read<int>(n);vector<tuple<int, int, int, int>> que(m);int kind;for (int i = 0; i < m; i++) {cin >> kind >> get<0>(que[i]);if (1 == kind) {cin >> get<1>(que[i]) >> get<2>(que[i]) >> get<3>(que[i]);}}
#ifdef _DEBUG		/*printf("T=%d,", T);*//*Out(a, "a=");Out(que, "que=");*/
#endif // DEBUG	auto res = Solution().Ans(a,que);for (const auto& i : res){cout << i << endl;}return 0;
}

单元测试

vector<int> a;vector<tuple<int, int, int, int>> que;TEST_METHOD(TestMethod11){a = { 1,2,3,4,5 },que = { {2,4,1,2},{3,0,0,0} };auto res = Solution().Ans(a,que);AssertEx({ 6LL }, res);}

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