【线段树】P9349 [JOI 2023 Final] Stone Arranging 2|普及+

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C++线段树

P9349 [JOI 2023 Final] Stone Arranging 2

题目描述

JOI-kun has $N$ go stones. The stones are numbered from $1$ to $N$ . The color of each stone is an integer between $1$ and $10^9$ , inclusive. In the beginning, the color of Stone $i$ ( $\le i \le N$ ) is $A_i$ .

From now, JOI-kun will perform $N$ operations. He will put the stones on the table in a line. The operation $i$ ( $\le i \le N$ ) will be performed as follows:

JOI-kun will put Stone $i$ on the immediate right of Stone $i - 1$ . However, when $i = 1$ , JOI-kun will put Stone 1 on the table.
If there is a stone among Stones $1,2,\cdots,i-1$ whose current color is the same as Stone $i$ , let $j$ be the maximum index of such stones, and JOI-kun will paint all of Stones $j+1,j+2,\cdots,i-1$ with the color $A_i$ .

In order to confirm whether the operations are correctly performed, JOI-kun wants to know in advance the colors of the stones after all the operations are performed.

Given information of the go stones, write a program which determines the colors of the stones after the $N$ operations are performed.

输入格式

Read the following data from the standard input.

$N$
$A_1$
$A_2$
$\vdots$
$A_N$

输出格式

Write $N$ lines to the standard output. The $i$ -th line ( $\le i \le N$ ) should contain the color of Stone $i$ after the $N$ operations are performed.

输入输出样例 #1

输入 #1

输出 #1

输入输出样例 #2

输入 #2

输出 #2

说明/提示

Samples

Sample 1

The operations are performed as in the following table.

Finally, the colors of Stones 1, 2, 3, 4, 5, 6 will be 1, 1, 1, 2, 2, 2, respectively.

This sample input satisfies the constraints of Subtasks 1, 3.

Sample 2

This sample input satisfies the constraints of all the subtasks.

Constraints

$\le N \le 2\times 10^5$ .
$\le A_i \le 10^9$ ( $\le i \le N$ ).
Given values are all integers.

Subtasks

(25 points) $\le 2 000$ .
(35 points) $A_i \le 2$ ( $\le i \le N$ ).
(40 points) No additional constraints.

线段树

以下两个变量记录所有已经排列，且不属于任意a[j…i-1]的棋子。
unordered_map<int, vector> mColorIndexs; 键是颜色，值是下标，升序。
set inxs;下标。
线段树记录修改状态。

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;
};

template<class TSave, class TRecord >
class  CSetMaxLineTree : public CVectorRangeUpdateLineTree<TSave, TRecord>
{
public:
	using CVectorRangeUpdateLineTree<TSave, TRecord>::CVectorRangeUpdateLineTree;
protected:
	virtual void OnQuery(TSave& ans, const TSave& save, const int& iSaveLeft, const int& iSaveRight) {
		ans = max(ans, save);
	}
	virtual void OnUpdate(TSave& save, const int& iSaveLeft, const int& iSaveRight, const TRecord& update) {
		save = update;
	}
	virtual void OnUpdateParent(TSave& par, const TSave& left, const TSave& r, const int& iSaveLeft, const int& iSaveRight) {
		par = max(left, r);
	}
	virtual void OnUpdateRecord(TRecord& old, const TRecord& newRecord)
	{
		old = newRecord;
	}
};

class Solution {
public:
	vector<int> Ans(const vector<int>& a) {
		const int N = a.size();
		CSetMaxLineTree<int, int> lineTree(N, 0, 0);
		set<int> inxs;
		unordered_map<int, vector<int>> mColorIndexs;
		for (int i = 0; i < N; i++) {
			int j = i;
			if (mColorIndexs.count(a[i]) && mColorIndexs[a[i]].size()) {
				j = mColorIndexs[a[i]].back();
			};

			for (auto it = inxs.lower_bound(i);;) {
				if (inxs.begin() == it) { break; }
				--it;
				if (*it < j) { break; }
				mColorIndexs[a[*it]].pop_back();
			}
			inxs.erase(inxs.lower_bound(j), inxs.lower_bound(i));
			inxs.emplace(i);
			mColorIndexs[a[i]].emplace_back(i);
			lineTree.Update(j, i, a[i]);
		}
		vector<int> ans;
		for (int i = 0; i < N; i++) {
			ans.emplace_back(lineTree.Query(i, i));
		}
		return ans;
	}
};

int main() {	
#ifdef _DEBUG
	freopen("a.in", "r", stdin);
#endif // DEBUG	
	auto a = Read<int>();
	auto res = Solution().Ans(a);
	for (const auto& i : res) {
		cout << i << endl;
	}
	cout << endl;
#ifdef _DEBUG		
	/*printf("T=%d,", T);*/
	Out(a, "a=");
#endif // DEBUG	
	return 0;
}

单元测试

vector<int> a;
		TEST_METHOD(TestMethod11)
		{
			a = {1,2};
			auto res = Solution().Ans(a);
			AssertV({1,2}, res);
		}
		TEST_METHOD(TestMethod12)
		{
			a = { 1,2 ,1};
			auto res = Solution().Ans(a);
			AssertV({ 1,1,1 }, res);
		}
		TEST_METHOD(TestMethod13)
		{
			a = { 4,1,2,3,2,1 };
			auto res = Solution().Ans(a);
			AssertV({4,1,1, 1,1,1 }, res);
		}
		TEST_METHOD(TestMethod14)
		{
			a = { 1,2,1,2,3,2 };
			auto res = Solution().Ans(a);
			AssertV({ 1,1,1,2,2,2 }, res);
		}
		TEST_METHOD(TestMethod15)
		{
			a = { 1,1,2,2,1,2,2,1,1,2 };
			auto res = Solution().Ans(a);
			AssertV({ 1,1,1,1,1,1,1,1,1,2 }, res);
		}

不用线段树

在inxs中存在的下标，颜色是原色，不存在的颜色就是inxs存在的后一个下标的颜色。
即：a[i] = *inxs.lower(i);

class Solution {
		public:
			vector<int> Ans(const vector<int>& a) {
				const int N = a.size();
				set<int> inxs;
				unordered_map<int, vector<int>> mColorIndexs;
				for (int i = 0; i < N; i++) {
					int j = i;
					if (mColorIndexs.count(a[i]) && mColorIndexs[a[i]].size()) {
						j = mColorIndexs[a[i]].back();
					};
					
					for (auto it = inxs.lower_bound(i);;) {
						if (inxs.begin() == it) { break; }
						--it;
						if (*it < j) { break; }
						mColorIndexs[a[*it]].pop_back();
					}
					inxs.erase(inxs.lower_bound(j), inxs.lower_bound(i));
					inxs.emplace(i);
					mColorIndexs[a[i]].emplace_back(i);					;
				}
				vector<int> ans;
				for (int i = 0; i < N; i++) {
					ans.emplace_back(a[*inxs.lower_bound(i)]);
				}
				return ans;
			}
		};

扩展阅读

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失败+反思=成功成功+反思=成功