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【离散化线段树】P3740 [HAOI2014] 贴海报|普及+

news 2025/7/2 21:09:13

本文涉及知识点

C++线段树

[HAOI2014] 贴海报

题目描述

Bytetown 城市要进行市长竞选，所有的选民可以畅所欲言地对竞选市长的候选人发表言论。为了统一管理，城市委员会为选民准备了一个张贴海报的 electoral 墙。

张贴规则如下：

electoral 墙是一个长度为 $N$ 个单位的长方形，每个单位记为一个格子；
所有张贴的海报的高度必须与 electoral 墙的高度一致的；
每张海报以 A B 表示，即从第 $A$ 个格子到第 $B$ 个格子张贴海报；
后贴的海报可以覆盖前面已贴的海报或部分海报。

现在请你判断，张贴完所有海报后，在 electoral 墙上还可以看见多少张海报。

输入格式

第一行，两个正整数 $N, M$ ，分别表示 electoral 墙的长度和海报个数。

接下来 $M$ 行，每行两个正整数 $A_i,B_i$ ，表示每张海报张贴的位置。

输出格式

输出贴完所有海报后，在 electoral 墙上还可以看见的海报数。

样例 #1

样例输入 #1

样例输出 #1

提示

约束条件

$10\le N \le 10000000,1\le M\le 1000,1\le A_i \le B_i \le 10000000$

所有的数据都是正整数，数据之间有一个空格。

离散化+线段树

第i块海报，如果被第i+1到M块海报覆盖，则看不到。
由于M只有1000，故可以离散。
i = T to 1
线段树：
保存类型，int：被覆盖的点数
设置类型,int: 覆盖次数。
注意：
离散化的时候，不但要离散L,R，还要离散L-1,R+1。否则[1,6] [1,3] [5,6]会变成[1,4][1,2][3,4]。前者可以看到3个海报，后者只能看到2个。

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(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_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);}void Query(int leftIndex, int rightIndex) {Query(1, 0, m_iEleSize - 1, leftIndex, rightIndex);}//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(int iNodeNO, int iSaveLeft, int iSaveRight, int iQueryLeft, int iQueryRight) {if ((iSaveLeft >= iQueryLeft) && (iSaveRight <= iQueryRight)) {this->OnQuery(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(iNodeNO * 2, iSaveLeft, mid, iQueryLeft, iQueryRight);}if (mid + 1 <= iQueryRight) {Query(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;const int m_iEleSize;
};template<class T = int>
class CDiscretize //离散化
{
public:CDiscretize(vector<T> nums){sort(nums.begin(), nums.end());nums.erase(std::unique(nums.begin(), nums.end()), nums.end());m_nums = nums;for (int i = 0; i < nums.size(); i++){m_mValueToIndex[nums[i]] = i;}}int operator[](const T value)const{auto it = m_mValueToIndex.find(value);if (m_mValueToIndex.end() == it){return -1;}return it->second;}int size()const{return m_mValueToIndex.size();}vector<T> m_nums;
protected:unordered_map<T, int> m_mValueToIndex;
};
//P3740 [HAOI2014] 贴海报typedef int TSave;
typedef int  TRecord;
class  CMyLineTree : public  CVectorRangeUpdateLineTree<TSave, TRecord>
{
public:TSave m_ans = 0;using CVectorRangeUpdateLineTree::CVectorRangeUpdateLineTree;
protected:virtual void OnQuery(const TSave& save, const int& iSaveLeft, const int& iSaveRight) {m_ans += save;}virtual void OnUpdate(TSave& save, const int& iSaveLeft, const int& iSaveRight, const TRecord& update) override{if (0 == update) { return; }save = iSaveRight - iSaveLeft + 1;}virtual void OnUpdateParent(TSave& par, const TSave& left, const TSave& r, const int& iSaveLeft, const int& iSaveRight)  override{par = left + r;}virtual void OnUpdateRecord(TRecord& old, const TRecord& newRecord) override{old += newRecord;}
};class Solution {public:int Ans(vector<pair< int, int>>& LR) {vector<int> tmp;for (const auto& [L, R] : LR) {tmp.emplace_back(L - 1);tmp.emplace_back(L);tmp.emplace_back(R);tmp.emplace_back(R+1);}CDiscretize dis(tmp);const int N = dis.size();CMyLineTree lineTree(N, 0, 0);int ans = 0;for (int i = LR.size() - 1; i >= 0; i--) {const int left = dis[LR[i].first];const int r = dis[LR[i].second];lineTree.m_ans = 0;lineTree.Query(left, r);ans += lineTree.m_ans < (r - left + 1);lineTree.Update(left, r, 1);}return ans;}};int main() {
#ifdef _DEBUGfreopen("a.in", "r", stdin);
#endif // DEBUG	int n,T;cin >> T >> n ;auto a = Read<pair<int,int>>(n);	auto res = Solution().Ans(a);cout << res;
#ifdef _DEBUG		/*printf("T=%d,", T);*///Out(a, "a=");//Out(edge, "edge=");
#endif // DEBUG	return 0;
}

单元测试

	vector<pair< int, int>> a;TEST_METHOD(TestMethod11){a = { {1,4},{2,6},{8,10},{3,4},{7,10}};auto res = Solution().Ans(a);AssertEx(4, res);}

扩展阅读

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如果程序是一条龙，那算法就是他的是睛
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