【动态规划】【滑动窗口】【C++算法】 629K 个逆序对数组

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【矩阵快速幂】封装类及测试用例及样例

本文涉及知识点

动态规划
C++算法：滑动窗口总结

LeetCode629: K 个逆序对数组

逆序对的定义如下：对于数组 nums 的第 i 个和第 j 个元素，如果满足 0 <= i < j < nums.length 且 nums[i] > nums[j]，则其为一个逆序对；否则不是。
给你两个整数 n 和 k，找出所有包含从 1 到 n 的数字，且恰好拥有 k 个 逆序对 的不同的数组的个数。由于答案可能很大，只需要返回对 109 + 7 取余的结果。
示例 1：
输入：n = 3, k = 0
输出：1
解释：
只有数组 [1,2,3] 包含了从1到3的整数并且正好拥有 0 个逆序对。
示例 2：
输入：n = 3, k = 1
输出：2
解释：
数组 [1,3,2] 和 [2,1,3] 都有 1 个逆序对。
提示：
1 <= n <= 1000
0 <= k <= 1000

动态规划

** 空间复杂度**: O(n)
时间复杂度?(n2)
动态规划的状态表示：pre[i]表示1到j-1的排列中，逆数对数量为i的数量。dp[i]表示1到j的排列中，逆数对的数量。 i 取值范围[0,1000]
动态规划的转移方程: 假定某个1到j-1 的排列，逆数对为x。插入j后，除j外的顺序不边，也就是除j外，不会产生新的逆数对。当然也不会减少逆数对。那如果将j插入到最后，逆序数不变。插入到倒数第一之前，逆数对+1。。。插入到最前面，逆序对+j-1。换过说法：
dp[i] = Sum ( i − j , i ] k ^{k}_{(i-j,i]} (i−j,i]k​pre[k]。 可以利用滑动窗口求和。
动态规划的初始状态: pre[0]=0
动态规划的填表顺序： j 从小到大，i从小到大。
动态规划的返回值:pre[k]

代码

使用到的类库

template<int MOD = 1000000007>
class C1097Int
{
public:
	C1097Int(long long llData = 0) :m_iData(llData% MOD)
	{

	}
	C1097Int  operator+(const C1097Int& o)const
	{
		return C1097Int(((long long)m_iData + o.m_iData) % MOD);
	}
	C1097Int& operator+=(const C1097Int& o)
	{
		m_iData = ((long long)m_iData + o.m_iData) % MOD;
		return *this;
	}
	C1097Int& operator-=(const C1097Int& o)
	{
		m_iData = (m_iData + MOD - o.m_iData) % MOD;
		return *this;
	}
	C1097Int  operator-(const C1097Int& o)
	{
		return C1097Int((m_iData + MOD - o.m_iData) % MOD);
	}
	C1097Int  operator*(const C1097Int& o)const
	{
		return((long long)m_iData * o.m_iData) % MOD;
	}
	C1097Int& operator*=(const C1097Int& o)
	{
		m_iData = ((long long)m_iData * o.m_iData) % MOD;
		return *this;
	}
	bool operator<(const C1097Int& o)const
	{
		return m_iData < o.m_iData;
	}
	C1097Int pow(long long n)const
	{
		C1097Int iRet = 1, iCur = *this;
		while (n)
		{
			if (n & 1)
			{
				iRet *= iCur;
			}
			iCur *= iCur;
			n >>= 1;
		}
		return iRet;
	}
	C1097Int PowNegative1()const
	{
		return pow(MOD - 2);
	}
	int ToInt()const
	{
		return m_iData;
	}
private:
	int m_iData = 0;;
};
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核心代码

class Solution {
public:
	int kInversePairs(int n, int k) {
		vector<C1097Int<>> pre(1001) ;
		pre[0] = 1;
		for (int j = 2; j <= n; j++)
		{
			vector<C1097Int<>> dp(1001);
			C1097Int<> iSum = 0;
			for (int i = 0; i < pre.size(); i++)
			{
				iSum += pre[i];
				if (i - j >= 0)
				{
					iSum -= pre[i - j];
				}
				dp[i] = iSum;
			}
			pre.swap(dp);
		}
		return pre[k].ToInt();
	}
};
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测试用例

template<class T>
void Assert(const T& t1, const T& t2)
{
	assert(t1 == t2);
}

template<class T>
void Assert(const vector<T>& v1, const vector<T>& v2)
{
	if (v1.size() != v2.size())
	{
		assert(false);
		return;
	}
	for (int i = 0; i < v1.size(); i++)
	{
		Assert(v1[i], v2[i]);
	}
}


int main()
{
	int n,k;
	{
		Solution sln;
		n = 3, k = 0;
		auto res = sln.kInversePairs(n, k);
		Assert(1, res);
	}
	{
		Solution sln;
		n = 3, k = 1;
		auto res = sln.kInversePairs(n, k);
		Assert(2, res);
	}

	{
		Solution sln;
		n = 1000, k = 1000;
		auto res = sln.kInversePairs(n, k);
		Assert(663677020, res);
	}
}
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2023年1月版

class CBigMath
{
public:
static void AddAssignment(int* dst, const int& iSrc)
{
*dst = (*dst + iSrc) % s_iMod;
}

 static void AddAssignment(int* dst, const int& iSrc, const int& iSrc1)
 {
	 *dst = (*dst + iSrc) % s_iMod;
	 *dst = (*dst + iSrc1) % s_iMod;
 }

 static void AddAssignment(int* dst, const int& iSrc, const int& iSrc1, const int& iSrc2)
 {
	 *dst = (*dst + iSrc) % s_iMod;
	 *dst = (*dst + iSrc1) % s_iMod;
	 *dst = (*dst + iSrc2) % s_iMod;
 }

 static void SubAssignment(int* dst, const int& iSrc)
 {
	 *dst = (s_iMod - iSrc + *dst) % s_iMod;
 }
 static int Add(const int& iAdd1, const int& iAdd2)
 {
	 return (iAdd1 + iAdd2) % s_iMod;
 }
 static int Mul(const int& i1, const int& i2)
 {
	 return((long long)i1 *i2) % s_iMod;
 }
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private:
static const int s_iMod = 1000000007;
};

class Solution {
public:
int kInversePairs(int n, int k) {
vector preDp(k + 1);
preDp[0] = 1;
for (int i = 2; i <= n; i++)
{
vector dp(k+1 );
for (int j = 0; j < dp.size(); j++)
{
if (j < preDp.size())
{
CBigMath::AddAssignment(&dp[j], preDp[j]);
}
if (j > 0)
{
CBigMath::AddAssignment(&dp[j], dp[j - 1]);
}
if ( j - i >= 0)
{
int iMod = 1000000007;
CBigMath::AddAssignment(&dp[j], iMod - preDp[j - i]);
}
}
preDp.swap(dp);
}
return k >= preDp.size() ? 0 : preDp[k];
}
};

2023年6月

using namespace std;

template
void OutToConsoleInner(const vector& vec,const string& strSep = " ")
{
for (int i = 0; i < vec.size(); i++)
{
if (0 != i%25)
{
std::cout << strSep.c_str();
}
std::cout << setw(3) << setfill(’ ') << vec[i];
if (0 == (i+1) % 25)
{
std::cout << std::endl;
}
else if (0 == (i + 1) % 5)
{
std::cout << strSep.c_str();
}
}
}

class CConsole
{
public :

template
static void Out(const vector& vec, const string& strColSep = " ", const string& strRowSep = "\r\n")
{
	OutToConsoleInner(vec, strColSep);
	std::cout << strRowSep.c_str();
}

template
static void Out(const vector>& matrix, const string& strColSep = " ", const string& strRowSep = "\r\n")
{
	for (int i = 0; i < matrix.size(); i++)
	{
		OutToConsoleInner(matrix[i], strColSep);
		std::cout << strRowSep.c_str();
	}
}

template
static void Out(const std::map >& mTopPointToPoints, const string& strColSep = " ", const string& strRowSep = "\r\n")
{
	for (auto kv : mTopPointToPoints)
	{
		std::cout << kv.first << ":";
		OutToConsoleInner(kv.second, strColSep);
		std::cout << strRowSep.c_str();
	}
}


static void Out(const  std::string& t, const string& strColSep = " ", const string& strRowSep = "\r\n")
{
	std::cout << t.c_str() << strColSep.c_str();
}

template
static void Out(const T& t, const string& strColSep = " ", const string& strRowSep = "\r\n")
{
	std::cout << t << strColSep.c_str();
}
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};

void GenetateSum(vector& sums, const vector& nums)
{
sums.push_back(0);
for (int i = 0; i < nums.size(); i++)
{
sums.push_back(nums[i] + sums[i]);
}
}

//[iBegin，iEnd]之和
long long Total(int iBegin,int iEnd)
{
return (long long)(iBegin + iEnd)*(iEnd - iBegin + 1) / 2;
}

class CLadderhlp
{
public:
CLadderhlp( int ladders)
{
m_uLadderNum = ladders;
}
void AddNeedBick(int iNeedBick)
{
if (0 == m_uLadderNum)
{
return;
}
if (m_ladders.size() < m_uLadderNum)
{
m_ladders.push(iNeedBick);
m_iEaqualBicks += iNeedBick;
return;
}
int iTop = m_ladders.top();
if (iTop >= iNeedBick)
{
return;
}
m_iEaqualBicks -= iTop;
m_iEaqualBicks += iNeedBick;
m_ladders.pop();
m_ladders.push(iNeedBick);
}
std::priority_queue m_ladders;
unsigned int m_uLadderNum;
long long m_iEaqualBicks = 0;
};

struct CPeo
{
CPeo(string strName, CPeo* pParent=nullptr)
{
m_strName = strName;
m_pParent = pParent;
}
string m_strName;
vector m_childs;
CPeo* m_pParent = nullptr;
};

class CNeighborTable
{
public:
void Init(const vector& edges)
{

 }
 vector> m_vTable;
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};

//通过 x &= (x-1)实现
int bitcount(unsigned x) {
int countx = 0;
while (x) {
countx++;
x &= (x - 1);
}
return countx;
}

int bitcount(unsigned long long x) {
int countx = 0;
while (x) {
countx++;
x &= (x - 1);
}
return countx;
}

class CRange
{
public:
template
CRange(const T& v)
{
m_iBegin = 0;
m_iEnd = v.size();
}
bool In(int iIndex)
{
return (iIndex >= m_iBegin) && (iIndex < m_iEnd);
}
const int End()
{
return m_iEnd;
}
protected:
int m_iBegin;
int m_iEnd;
};

template
class CTrie
{
public:
CTrie() :m_vPChilds(iTypeNum)
{

 }
 template
 void Add(IT begin, IT end)
 {
	 CTrie * pNode = this;
	 for (; begin != end; ++begin)
	 {
		 pNode = pNode->AddChar(*begin).get();
	 }
 }
 template
 bool Search(IT begin, IT end)
 {
	 if (begin == end)
	 {
		 return true;
	 }

	 if ('.' == *begin)
	 {
		 for (auto& ptr : m_vPChilds)
		 {
			 if (!ptr)
			 {
				 continue;
			 }
			 if (ptr->Search(begin + 1, end))
			 {
				 return true;
			 }
		 }
	 }

	 auto ptr = GetChild(*begin);
	 if (nullptr == ptr)
	 {
		 return false;
	 }
	 return ptr->Search(begin + 1, end);
 }
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protected:
std::shared_ptr AddChar(char ch)
{
if ((ch < cBegin) || (ch >= cBegin + iTypeNum))
{
return nullptr;
}
const int index = ch - cBegin;
auto ptr = m_vPChilds[index];
if (!ptr)
{
m_vPChilds[index] = std::make_shared>();
}
return m_vPChilds[index];
}
std::shared_ptr GetChild(char ch)const
{
if ((ch < cBegin) || (ch >= cBegin + iTypeNum))
{
return nullptr;
}
return m_vPChilds[ch - cBegin];
}
std::vector m_vPChilds;
};

class CWords
{
public:
void Add(const string& word)
{
m_strStrs.insert(word);
}
bool Search(const string& word)
{
return Search(m_strStrs.begin(), m_strStrs.end(), 0, word.length(), word);
}
protected:
bool Search(std::set::const_iterator begin, std::set::const_iterator end, int iStrBegin, int iStrEnd, const string& str)
{
int i = iStrBegin;
for (; (i < iStrEnd) && (str[i] != ‘.’); i++);
auto it = std::equal_range(begin, end, str, [&iStrBegin, &i](const string& s, const string& sFind)
{
return s.substr(iStrBegin, i - iStrBegin) < sFind.substr(iStrBegin, i - iStrBegin);
});
if (i == iStrBegin)
{
it.first = begin;
it.second = end;
}
if (it.first == it.second)
{
return false;
}
if (i == iStrEnd)
{
return true;
}
if (i + 1 == iStrEnd)
{
return true;
}
string tmp = str;
for (char ch = ‘a’; ch <= ‘z’; ch++)
{
tmp[i] = ch;
auto ij = std::equal_range(it.first, it.second, tmp, [&ch, &i](const string& s, const string& sFind)
{
return s[i] < sFind[i];
});
if (ij.first == ij.second)
{
continue;
}

		 if (Search(ij.first, ij.second, i + 1, iStrEnd, str))
		 {
			 return true;
		 }
	 }
	 return false;
 }

 std::set m_strStrs;
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};
class WordDictionary {
public:
WordDictionary() {
for (int i = 0; i < 26; i++)
{
m_str[i] = std::make_unique();
}
}

 void addWord(string word) {
	 m_str[word.length()]->Add(word);
 }

 bool search(string word) {
	 return m_str[word.length()]->Search(word);
 }
 std::unique_ptr m_str[26];
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};

template
class C1097Int
{
public:
C1097Int(long long llData = 0) :m_iData(llData%MOD)
{

 }
 C1097Int  operator+(const C1097Int& o)const
 {
	 return C1097Int(((long long)m_iData + o.m_iData) % MOD);
 }
 C1097Int&  operator+=(const C1097Int& o)
 {
	 m_iData = ((long long)m_iData + o.m_iData) % MOD;
	 return *this;
 }
 C1097Int&  operator-=(const C1097Int& o)
 {
	 m_iData = (m_iData + MOD - o.m_iData) % MOD;
	 return *this;
 }
 C1097Int  operator-(const C1097Int& o)
 {
	 return C1097Int((m_iData + MOD - o.m_iData) % MOD);
 }
 C1097Int  operator*(const C1097Int& o)const
 {
	 return((long long)m_iData *o.m_iData) % MOD;
 }
 C1097Int&  operator*=(const C1097Int& o)
 {
	 m_iData = ((long long)m_iData *o.m_iData) % MOD;
	 return *this;
 }
 bool operator<(const C1097Int& o)const
 {
	 return m_iData < o.m_iData;
 }
 C1097Int pow( int n)const
 {
	 C1097Int iRet = 1, iCur = *this;
	while (n)
	{
		if (n & 1)
		{
			iRet *= iCur;
		}
		iCur *= iCur;
		n >>= 1;
	}
	return iRet;
 }
 C1097Int PowNegative1()const
 {
	 return pow(MOD - 2);
 }
 int ToInt()const
 {
	 return m_iData;
 }
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private:
int m_iData = 0;;
};

template
int operator+(int iData, const C1097Int& int1097)
{
int iRet = int1097.operator+(C1097Int(iData)).ToInt();
return iRet;
}

template
int& operator+=(int& iData, const C1097Int& int1097)
{
iData = int1097.operator+(C1097Int(iData)).ToInt();
return iData;
}

template
int operator*(int iData, const C1097Int& int1097)
{
int iRet = int1097.operator*(C1097Int(iData)).ToInt();
return iRet;
}

template
int& operator*=(int& iData, const C1097Int& int1097)
{
iData = int1097.operator*(C1097Int(iData)).ToInt();
return iData;
}

template
void MinSelf(T* seft, const T& other)
{
*seft = min(*seft, other);
}

template
void MaxSelf(T* seft, const T& other)
{
*seft = max(*seft, other);
}

int GetNotRepeateNum(int len, int iHasSel)
{
if (0 == len)
{
return 1;
}
if ((0 == iHasSel) && (1 == len))
{
return 10;
}
int iRet = 1;
if (iHasSel > 0)
{
for (int tmp = 10 - iHasSel; (tmp >= 2)&& len ; tmp–,len–)
{
iRet *= tmp;
}
}
else
{
iRet *= 9;
len–;
for (int tmp=9; (tmp>=2)&&len; len–,tmp–)
{
iRet *= tmp;
}
}
return iRet;
}

int GCD(int n1, int n2)
{
int t1 = min(n1, n2);
int t2 = max(n1, n2);
if (0 == t1)
{
return t2;
}
return GCD(t2%t1, t1);
}

void CreateMaskVector(vector& v,const int* const p,int n )
{
const int iMaxMaskNum = 1 << n;
v.resize(iMaxMaskNum);
for (int i = 0; i < n; i++)
{
v[1 << i] = p[i];
}
for (int mask = 1; mask < iMaxMaskNum ; mask++)
{
const int iSubMask = mask&(-mask);
v[mask] = v[iSubMask] + v[mask-iSubMask];
}
}

class CMaxLineTree
{
public:
CMaxLineTree(int iArrSize) :m_iArrSize(iArrSize), m_vData(iArrSize * 4)
{

 }
 //iIndex 从0开始
 void Modify( int iIndex, int iValue)
 {
	 Modify(1, 1, m_iArrSize, iIndex + 1, iValue);
 }
 //iNeedQueryLeft iNeedQueryRight 从0开始
 int Query(const int iNeedQueryLeft, const int iNeedQueryRight)
 {
	 return Query(1, 1, m_iArrSize, iNeedQueryLeft + 1, iNeedQueryRight + 1);
 }
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protected:
int Query(const int iTreeNodeIndex, const int iRecordLeft, const int iRecordRight, const int iNeedQueryLeft, const int iNeedQueryRight)
{
if ((iNeedQueryLeft <= iRecordLeft) && (iNeedQueryRight >= iRecordRight))
{
return m_vData[iTreeNodeIndex];
}
const int iMid = (iRecordLeft + iRecordRight) / 2;
int iRet = 0;
if (iNeedQueryLeft <= iMid)
{
iRet = Query(iTreeNodeIndex * 2, iRecordLeft, iMid, iNeedQueryLeft, iNeedQueryRight);
}
if (iNeedQueryRight > iMid)
{
iRet = max(iRet, Query(iTreeNodeIndex * 2 + 1, iMid + 1, iRecordRight, iNeedQueryLeft, iNeedQueryRight));
}
return iRet;
}
void Modify(int iTreeNodeIndex, int iLeft, int iRight, int iIndex, int iValue)
{
if (iLeft == iRight)
{
m_vData[iTreeNodeIndex] = max(m_vData[iTreeNodeIndex],iValue);
return;
}
const int iMid = (iLeft + iRight) / 2;
if (iIndex <= iMid)
{
Modify(iTreeNodeIndex * 2, iLeft, iMid, iIndex, iValue);
}
else
{
Modify(iTreeNodeIndex * 2 + 1, iMid + 1, iRight, iIndex, iValue);
}
m_vData[iTreeNodeIndex] = max(m_vData[iTreeNodeIndex * 2], m_vData[iTreeNodeIndex * 2 + 1]);
}
const int m_iArrSize;
std::vector m_vData;
};

class CMaxLineTreeMap
{
public:
CMaxLineTreeMap(int iArrSize) :m_iArrSize(iArrSize)
{

 }
 //iIndex 从0开始
 void Modify(int iIndex, int iValue)
 {
	 Modify(1, 1, m_iArrSize, iIndex + 1, iValue);
 }
 //iNeedQueryLeft iNeedQueryRight 从0开始
 int Query(const int iNeedQueryLeft, const int iNeedQueryRight)
 {
	 return Query(1, 1, m_iArrSize, iNeedQueryLeft + 1, iNeedQueryRight + 1);
 }
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protected:
int Query(const int iTreeNodeIndex, const int iRecordLeft, const int iRecordRight, const int iNeedQueryLeft, const int iNeedQueryRight)
{
if ((iNeedQueryLeft <= iRecordLeft) && (iNeedQueryRight >= iRecordRight))
{
return m_mData[iTreeNodeIndex];
}
const int iMid = (iRecordLeft + iRecordRight) / 2;
int iRet = 0;
if (iNeedQueryLeft <= iMid)
{
iRet = Query(iTreeNodeIndex * 2, iRecordLeft, iMid, iNeedQueryLeft, iNeedQueryRight);
}
if (iNeedQueryRight > iMid)
{
iRet = max(iRet, Query(iTreeNodeIndex * 2 + 1, iMid + 1, iRecordRight, iNeedQueryLeft, iNeedQueryRight));
}
return iRet;
}
void Modify(int iTreeNodeIndex, int iLeft, int iRight, int iIndex, int iValue)
{
if (iLeft == iRight)
{
m_mData[iTreeNodeIndex] = max(m_mData[iTreeNodeIndex], iValue);
return;
}
const int iMid = (iLeft + iRight) / 2;
if (iIndex <= iMid)
{
Modify(iTreeNodeIndex * 2, iLeft, iMid, iIndex, iValue);
}
else
{
Modify(iTreeNodeIndex * 2 + 1, iMid + 1, iRight, iIndex, iValue);
}
m_mData[iTreeNodeIndex] = max(m_mData[iTreeNodeIndex * 2], m_mData[iTreeNodeIndex * 2 + 1]);
}
const int m_iArrSize;
std::unordered_map m_mData;
};

template
class CSumLineTree
{
public:
CSumLineTree(int iEleSize) :m_iEleSize(iEleSize), m_vArr(m_iEleSize * 4), m_vChildAdd(m_iEleSize * 4)
{

 }
 void Add(int iLeftIndex, int iRightIndex, int iValue)
 {
	 Add(1, 1, m_iEleSize, iLeftIndex+1, iRightIndex+1, iValue);
 }
 T Query(int iLeftIndex, int iRightIndex)
 {
	 return Query(1, 1, m_iEleSize, iLeftIndex + 1, iRightIndex + 1);
 }
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private:
T Query(int iNode, int iDataLeft, int iDataRight, int iOpeLeft, int iOpeRight)
{
if ((iOpeLeft <= iDataLeft) && (iOpeRight >= iDataRight))
{
return m_vArr[iNode];
}
Fresh(iNode, iDataLeft, iDataRight);
const int iMid = iDataLeft + (iDataRight - iDataLeft) / 2;
T ret(0);
if (iMid >= iOpeLeft)
{
ret += Query(iNode * 2, iDataLeft, iMid, iOpeLeft, iOpeRight);
}
if (iMid + 1 <= iOpeRight)
{
ret += Query(iNode * 2 + 1, iMid + 1, iDataRight, iOpeLeft, iOpeRight);
}
return ret;
}
/* 暴力解法
void Add(int iNode, int iDataLeft, int iDataRight, int iOpeLeft, int iOpeRight, int iValue)
{
m_vArr[iNode] += T(iValue)*(min(iDataRight, iOpeRight) - max(iDataLeft, iOpeLeft)+1);
if (iDataLeft == iDataRight)
{
return;
}
const int iMid = iDataLeft + (iDataRight - iDataLeft) / 2;
if (iMid >= iOpeLeft)
{
Add(iNode * 2, iDataLeft, iMid, iOpeLeft, iOpeRight, iValue);
}
if (iMid + 1 <= iOpeRight)
{
Add(iNode * 2 + 1, iMid + 1, iDataRight, iOpeLeft, iOpeRight, iValue);
}
}
/
void Fresh(int iNode, int iDataLeft, int iDataRight)
{
const int iMid = iDataLeft + (iDataRight - iDataLeft) / 2;
if (m_vChildAdd[iNode] != 0)
{
Add(iNode * 2, iDataLeft, iMid, iDataLeft, iMid, m_vChildAdd[iNode]);
Add(iNode * 2 + 1, iMid + 1, iDataRight, iMid + 1, iDataRight, m_vChildAdd[iNode]);
m_vChildAdd[iNode] = 0;
}
}
//懒惰法
void Add(int iNode, int iDataLeft, int iDataRight, int iOpeLeft, int iOpeRight, int iValue)
{
m_vArr[iNode] += T(iValue)(min(iDataRight, iOpeRight) - max(iDataLeft, iOpeLeft) + 1);
if ((iOpeLeft <= iDataLeft) && (iOpeRight >= iDataRight))
{
m_vChildAdd[iNode] += T(iValue);
return;
}

	 Fresh(iNode,iDataLeft,iDataRight);
	 const int iMid = iDataLeft + (iDataRight - iDataLeft) / 2;
	 if (iMid >= iOpeLeft)
	 {
		 Add(iNode * 2, iDataLeft, iMid, iOpeLeft, iOpeRight, iValue);
	 }
	 if (iMid + 1 <= iOpeRight)
	 {
		 Add(iNode * 2 + 1, iMid + 1, iDataRight, iOpeLeft, iOpeRight, iValue);
	 }
 }

 const int m_iEleSize;
 vector m_vArr;
 vector m_vChildAdd;
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};

template
class CTreeArr
{
public:
CTreeArr(int iSize) :m_vData(iSize+1)
{

 }
 void Add(int index, T value)
 {
	 index++;
	 while (index < m_vData.size())
	 {
		 m_vData[index] += value;
		 index += index&(-index);
	 }
 }
 T Sum(int index)
 {
	 index++;
	 T ret = 0;
	 while (index )
	 {
		 ret += m_vData[index];
		 index -= index&(-index);
	 }
	 return ret;
 }
 T Get(int index)
 {
	 return Sum(index) - Sum(index - 1);
 }
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private:
vector m_vData;
};

//iCodeNum 必须大于等于可能的字符数
template
class CHashStr {
public:
CHashStr(string s, int iCodeNum, int iCodeBegin = 1, char chBegin = ‘a’) {
m_c = s.length();
m_vP.resize(m_c + 1);
m_vP[0] = 1;
m_vHash.resize(m_c + 1);
for (int i = 0; i < m_c; i++)
{
const int P = iCodeBegin + iCodeNum;
m_vHash[i + 1] = m_vHash[i] * P + s[i] - chBegin + iCodeBegin;
m_vP[i + 1] = m_vP[i] * P;
}
}
int GetHash(int left, int right)
{
return ( m_vHash[right + 1] - m_vHash[left] * m_vP[right - left + 1]).ToInt();
}
inline int GetHash(int right)
{
return m_vHash[right + 1].ToInt();
}
int m_c;
vector m_vP;
vector m_vHash;
};

template
class C2HashStr
{
public:
C2HashStr(string s) {
m_pHash1 = std::make_unique>(s, 26);
m_pHash2 = std::make_unique < CHashStr>(s, 27, 0);
}

 long long GetHash(int left, int right)
 {
	 return (long long)m_pHash1->GetHash(left, right)*(MOD2 + 1) + m_pHash2->GetHash(left, right);
 }
 long long GetHash( int right)
 {
	 return (long long)m_pHash1->GetHash( right)*(MOD2 + 1) + m_pHash2->GetHash( right);
 }
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private:
std::unique_ptr> m_pHash1;
std::unique_ptr m_pHash2;
};

template
class CDynaHashStr {
public:
CDynaHashStr(int iCodeNum, int iCodeBegin = 1, char chBegin = ‘a’) :m_iUnit(iCodeNum + iCodeBegin), m_iP(1), m_iBegin(iCodeBegin - chBegin)
{

 }
 inline void push_back(const char& ch)
 {
	const int iNum = ch + m_iBegin;
	m_iHash *= m_iUnit;
	m_iHash += iNum;
	m_iP *= m_iUnit;
 }
 inline void push_front(const char& ch)
 {
	 const int iNum = ch + m_iBegin;
	 m_iHash +=  m_iP*iNum;
	 m_iP *= m_iUnit;
 }
 inline int GetHash() const
 {
	 return m_iHash;
 }
 const int m_iUnit;
 const int m_iBegin;
 C1097Int m_iHash;
 C1097Int m_iP;
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};

template
class C2DynaHashStr {
public:
C2DynaHashStr(int iCodeNum, int iCodeBegin = 1, char chBegin = ‘a’)
{
m_pHash1 = new CDynaHashStr<>(iCodeNum, iCodeBegin, chBegin);
m_pHash2 = new CDynaHashStr(iCodeNum, iCodeBegin, chBegin);
}
~C2DynaHashStr()
{
delete m_pHash1;
delete m_pHash2;
}
inline void push_back(const char& ch)
{
m_pHash1->push_back(ch);
m_pHash2->push_back(ch);
}
inline void push_front(const char& ch)
{
m_pHash1->push_front(ch);
m_pHash2->push_front(ch);
}
long long Hash()const
{
return (long long)MOD2m_pHash1->m_iHash.ToInt() + m_pHash2->m_iHash.ToInt();
}
bool operator==(const C2DynaHashStr& other) const
{
return (m_pHash1->m_iHash.ToInt() == other.m_pHash1->m_iHash.ToInt()) && (m_pHash2->m_iHash.ToInt() == other.m_pHash2->m_iHash.ToInt());
}
CDynaHashStr<> m_pHash1;
CDynaHashStr* m_pHash2 ;
};
namespace NSort
{
template
bool SortVecVec(const vector& v1, const vector& v2)
{
return v1[ArrIndex] < v2[ArrIndex];
};
}

namespace NCmp
{
template
bool Less(const std::pair& p, Class1 iData)
{
return p.first < iData;
}

 template
 bool  Greater(const std::pair& p, Class1 iData)
 {
	 return p.first > iData;
 }

template
class CLessPair
{
public:
	bool operator()(const std::pair<_Ty1, _Ty2>& p1, const std::pair<_Ty1, _Ty2>& p2)const
	{
		return p1.first < p2.first;
	}
};

template
class CGreatePair
{
public:
	bool operator()(const std::pair<_Ty1, _Ty2>& p1, const std::pair<_Ty1, _Ty2>& p2)const
	{
		return p1.first > p2.first;
	}
};
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}

class CIndexVector
{
public:
template
CIndexVector(vector& data)
{
for (int i = 0; i < data.size(); i++)
{
m_indexs.emplace_back(i);
}
std::sort(m_indexs.begin(), m_indexs.end(), [data](const int& i1, const int& i2)
{
return data[i1] < data[i2];
});
}
int GetIndex(int index)
{
return m_indexs[index];
}
private:
vector m_indexs;
};

class CMedian
{
public:
void AddNum(int iNum)
{
m_queTopMin.emplace(iNum);
MakeNumValid();
MakeSmallBig();
}
void Remove(int iNum)
{
if (m_queTopMax.size() && (iNum <= m_queTopMax.top()))
{
m_setTopMaxDel.insert(iNum);
}
else
{
m_setTopMinDel.insert(iNum);
}

	PopIsTopIsDel(m_queTopMin, m_setTopMinDel);
	PopIsTopIsDel(m_queTopMax, m_setTopMaxDel);
	MakeNumValid();
	MakeSmallBig();
}
double Median()
{
	const int iMaxNum = m_queTopMin.size() - m_setTopMinDel.size();
	const int iMinNum = m_queTopMax.size() - m_setTopMaxDel.size();
	if (iMaxNum > iMinNum)
	{
		return m_queTopMin.top();
	}
	return ((double)m_queTopMin.top() + m_queTopMax.top())/2.0;
}
template
void PopIsTopIsDel(T& que, std::unordered_multiset& setTopMaxDel)
{
	while (que.size() && (setTopMaxDel.count(que.top())))
	{
		setTopMaxDel.erase(setTopMaxDel.find(que.top()));
		que.pop();
	}
}
void MakeNumValid()
{
	const int iMaxNum = m_queTopMin.size() - m_setTopMinDel.size();
	const int iMinNum = m_queTopMax.size() - m_setTopMaxDel.size();
	//确保两个队的数量
	if (iMaxNum > iMinNum + 1)
	{
		int tmp = m_queTopMin.top();
		m_queTopMin.pop();
		m_queTopMax.emplace(tmp);
		PopIsTopIsDel(m_queTopMin, m_setTopMinDel);
	}
	if (iMinNum > iMaxNum)
	{
		int tmp = m_queTopMax.top();
		m_queTopMax.pop();
		m_queTopMin.push(tmp);
		PopIsTopIsDel(m_queTopMax, m_setTopMaxDel);
	}
}
void MakeSmallBig()
{
	if (m_queTopMin.empty() || m_queTopMax.empty())
	{
		return;
	}
	while (m_queTopMin.top() < m_queTopMax.top())
	{
		const int iOldTopMin = m_queTopMin.top();
		const int iOldTopMax = m_queTopMax.top();
		m_queTopMin.pop();
		m_queTopMax.pop();
		m_queTopMin.emplace(iOldTopMax);
		m_queTopMax.emplace(iOldTopMin);
		PopIsTopIsDel(m_queTopMin, m_setTopMinDel);
		PopIsTopIsDel(m_queTopMax, m_setTopMaxDel);
	}
}
std::priority_queue m_queTopMax;
std::priority_queue, greater> m_queTopMin;
std::unordered_multiset m_setTopMaxDel, m_setTopMinDel;
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};

template
class CDistanceGrid
{
public:
CDistanceGrid(const vector& grid) :m_grid(grid), m_r(grid.size()), m_c(grid[0].size())
{

}
//单源路径 D 算法 ,时间复杂度:r*c*log(r*c)
inline int Dis(int r1, int c1, int r2, int c2)
{	
	vector> vDis(iMaxRow, vector(iMaxCol, INT_MAX));

	auto Add = [&vDis, this](std::priority_queue, vector>, greater>>& queCur, int iDis, int r, int c)
	{
		const int iRowColMask = iMaxCol * r + c;
		if (iDis >= vDis[r][c])
		{
			return;
		}
		queCur.emplace(iDis,iRowColMask);
		vDis[r][c] = iDis;
	};
	auto Move = [&](std::priority_queue, vector>, greater>>& queCur, int iDis, int r, int c)
	{
		if ((r < 0) || (r >= m_r))
		{
			return;
		}
		if ((c < 0) || (c >= m_c))
		{
			return;
		}
		if (m_grid[r][c] < 1)
		{
			return;
		}
		Add(queCur,iDis, r, c);
	};

	std::priority_queue, vector>, greater>> que;		
	Add(que,0,r1, c1);
	while (que.size())
	{
		const int iDis = que.top().first;
		const int iStart = que.top().second;
		que.pop();
		const int r = iStart / iMaxCol;
		const int c = iStart % iMaxCol;
		if ((r == r2) && (c == c2))
		{
			return iDis;
		}
		if (iDis > vDis[r][c])
		{
			continue;
		}
		
		Move(que, iDis + 1, r + 1, c);
		Move(que, iDis + 1, r - 1, c);
		Move(que, iDis + 1, r, c + 1);
		Move(que, iDis + 1, r, c - 1);
	}

	return -1;
}
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private:
virtual bool IsCanMoveStatue(int r, int c)
{
return m_grid[r][c] >= 1;
}
const int m_r;
const int m_c;
const vector& m_grid;

};

class CBFSGridDist
{
public:
CBFSGridDist(const vector& bCanVisit, int r, int c) :m_bCanVisit(bCanVisit), m_r(m_bCanVisit.size()), m_c(m_bCanVisit[0].size())
{
m_vDis.assign(m_r, vector(m_c,INT_MAX/2));
Dist(r, c);
}
bool Vilid(const int r,const int c )
{
if ((r < 0) || (r >= m_r))
{
return false;
}
if ((c < 0) || (c >= m_c))
{
return false;
}
return true;
}
const vector& Dis()const
{
return m_vDis;
}
const vector& m_bCanVisit;
private:
//INT_MAX/2 表示无法到达
void Dist(int r, int c)
{
m_vDis.assign(m_r, vector(m_c, INT_MAX / 2));
vector vHasDo(m_r, vector(m_c));
std::queue> que;
auto Add = [&](const int& r, const int& c, const int& iDis)
{
if (!Vilid(r, c))
{
return;
}
if (vHasDo[r][c])
{
return;
}
if (!m_bCanVisit[r][c])
{
vHasDo[r][c] = true;
return;
}
if (iDis >= m_vDis[r][c])
{
return;
}

		que.emplace(r, c);
		m_vDis[r][c] = iDis;
		vHasDo[r][c] = true;
	};
	Add(r, c, 0);
	while (que.size())
	{
		const int r = que.front().first;
		const int c = que.front().second;
		que.pop();
		const int iDis = m_vDis[r][c];
		Add(r + 1, c, iDis + 1);
		Add(r - 1, c, iDis + 1);
		Add(r, c + 1, iDis + 1);
		Add(r, c - 1, iDis + 1);
	}

}
vector> m_vDis;
const int m_r;
const int m_c;
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};

class C2BNumTrieNode
{
public:
C2BNumTrieNode()
{
m_childs[0] = m_childs[1] = nullptr;
}
bool GetNot0Child(bool bFirstRight)
{
auto ptr = m_childs[bFirstRight];
if (ptr && (ptr->m_iNum >0))
{
return bFirstRight;
}
return !bFirstRight;
}
int m_iNum = 0;
C2BNumTrieNode* m_childs[2];
};

template
class C2BNumTrie
{
public:
C2BNumTrie()
{
m_pRoot = new C2BNumTrieNode();
}
void Add(int iNum)
{
m_setHas.emplace(iNum);
C2BNumTrieNode* p = m_pRoot;
for (int i = iLeveNum - 1; i >= 0; i–)
{
p->m_iNum++;
bool bRight = iNum & (1 << i);
if (nullptr == p->m_childs[bRight])
{
p->m_childs[bRight] = new C2BNumTrieNode();
}
p = p->m_childs[bRight];
}
p->m_iNum++;
}
void Del(int iNum)
{
auto it = m_setHas.find(iNum);
if (m_setHas.end() == it)
{
return;
}
m_setHas.erase(it);
C2BNumTrieNode* p = m_pRoot;
for (int i = iLeveNum - 1; i >= 0; i–)
{
p->m_iNum–;
bool bRight = iNum & (1 << i);
p = p->m_childs[bRight];
}
p->m_iNum–;
}
int MaxXor(int iNum)
{
C2BNumTrieNode* p = m_pRoot;
int iRet = 0;
for (int i = iLeveNum - 1; i >= 0; i–)
{
bool bRight = !(iNum & (1 << i));
bool bSel = p->GetNot0Child(bRight);
p = p->m_childs[bSel];
if (bSel == bRight)
{
iRet |= (1 << i);
}
}
return iRet;
}
C2BNumTrieNode* m_pRoot;
std::unordered_multiset m_setHas;
};

struct SValueItem
{
SValueItem()
{

}
SValueItem(int iValue)
{
	m_iCoefficient = iValue;
}
SValueItem operator*(const SValueItem& o)const
{
	SValueItem ret(m_iCoefficient*o.m_iCoefficient);
	int i = 0, j = 0;
	while ((i < m_vVars.size()) && (j < o.m_vVars.size()))
	{
		if (m_vVars[i] < o.m_vVars[j])
		{
			ret.m_vVars.emplace_back(m_vVars[i]);
			i++;
		}
		else
		{
			ret.m_vVars.emplace_back(o.m_vVars[j]);
			j++;
		}
	}
	ret.m_vVars.insert(ret.m_vVars.end(), m_vVars.begin()+i, m_vVars.end());
	ret.m_vVars.insert(ret.m_vVars.end(), o.m_vVars.begin()+j, o.m_vVars.end());
	return ret;
}
bool operator<(const SValueItem& o)const
{
	if (m_vVars.size() == o.m_vVars.size())
	{
		return m_vVars < o.m_vVars;
	}
	return m_vVars.size() > o.m_vVars.size();
}
vector m_vVars;
int m_iCoefficient=1;//系数、倍率
std::string ToString()const
{
	std::ostringstream os;
	os << m_iCoefficient ;
	for (const auto&s : m_vVars)
	{
		os << "*" << s;
	}
	return os.str();
}
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};

struct SValue
{
SValue()
{

}
SValue(int iValue)
{
	SValueItem item;
	item.m_iCoefficient = iValue;
	m_items.emplace(item);
}
SValue(std::string strName)
{
	SValueItem item;
	item.m_vVars.emplace_back(strName);
	m_items.emplace(item);
}
SValue operator-(const SValue& o)const
{
	SValue ret;
	ret.m_items = m_items;
	for (auto it : o.m_items)
	{
		ret -= it;
	}
	return ret;
}
SValue operator+(const SValue& o)const
{
	SValue ret;
	ret.m_items = m_items;
	for (auto it : o.m_items)
	{
		ret += it;
	}			
	return ret;
}
SValue operator*(const SValue& o)const
{
	SValue ret;
	for (const auto it : m_items)
	{
		for (const auto ij : o.m_items)
		{
			ret += it*ij;
		}
	}
	return ret;
}
SValue& operator+=(const SValueItem& item)
{
	auto it = m_items.find(item);
	if (m_items.end() == it)
	{
		m_items.emplace(item);
	}
	else
	{
		auto tmp = *it;
		tmp.m_iCoefficient += item.m_iCoefficient;
		m_items.erase(it);
		m_items.emplace(tmp);
	}
	return *this;
}
SValue& operator-=(const SValueItem& item)
{
	auto it = m_items.find(item);
	if (m_items.end() == it)
	{
		auto tmp = item;
		tmp.m_iCoefficient *= -1;
		m_items.emplace(tmp);
	}
	else
	{
		auto tmp = *it;
		tmp.m_iCoefficient -= item.m_iCoefficient;
		m_items.erase(it);
		m_items.emplace(tmp);
	}
	return *this;
}
vector ToStrings()const
{
	vector vRet;
	for (const auto& item : m_items)
	{
		if (0 == item.m_iCoefficient)
		{
			continue;
		}
		vRet.emplace_back(item.ToString());
	}
	return vRet;
}
std::set m_items;
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};

class CDelIndexs
{
public:
CDelIndexs()
{

}
CDelIndexs(int iSize)
{
	Init(iSize);
}
void Init(int iSize)
{
	m_bDels.assign(iSize, false);
	m_vNext.resize(iSize);
	for (int i = 0; i < iSize; i++)
	{
		m_vNext[i] = i + 1;
	}
}
void Del(int index)
{
	if ((index < 0) || (index >= m_vNext.size()))
	{
		return;
	}
	if (m_bDels[index])
	{
		return;
	}
	m_bDels[index] = true;

}
void SetCur(int index)
{
	if (index < 0)
	{
		m_iCur = m_vNext.size();
	}
	else
	{
		m_iCur = FreshCur(index);
	}
}
int NextIndex()
{
	if (m_iCur >= m_vNext.size())
	{
		return -1;
	}
	auto ret = m_iCur;
	SetCur(m_vNext[m_iCur]);
	return ret;
}
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private:
int FreshCur(int index)
{
if (index >= m_vNext.size())
{
return m_vNext.size();
}
if (!m_bDels[index])
{
return index;
}

	return m_vNext[index] = FreshCur(m_vNext[index]);
}
int m_iCur = 0;
vector m_bDels;
vector m_vNext;
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};

class CUnionFind
{
public:
CUnionFind(int iSize) :m_vConnetNO(iSize), m_vConnectSize(iSize, 1)
{
for (int i = 0; i < iSize; i++)
{
m_vConnetNO[i] = i;
}
m_iConnetSize = iSize;
}
int GetConnectNO(int iNode)
{
int& iConnectNO = m_vConnetNO[iNode];
if (iNode == iConnectNO)
{
return iNode;
}
return iConnectNO = GetConnectNO(iConnectNO);
}
void Union(int iNode1, int iNode2)
{
const int iConnectNO1 = GetConnectNO(iNode1);
const int iConnectNO2 = GetConnectNO(iNode2);
if (iConnectNO1 == iConnectNO2)
{
return ;
}
m_iConnetSize–;
if (iConnectNO1 > iConnectNO2)
{
UnionConnect(iConnectNO1, iConnectNO2);
}
else
{
UnionConnect(iConnectNO2, iConnectNO1);
}
}
int GetAConnectSizeByNode(int iNode)
{
return m_vConnectSize[GetConnectNO(iNode)];
}
bool IsConnect(int iNode1, int iNode2)
{
return GetConnectNO(iNode1) == GetConnectNO(iNode2);
}
int ConnetSize()const
{
return m_iConnetSize;
}
private:
void UnionConnect(int iFrom, int iTo)
{
m_vConnectSize[iTo] += m_vConnectSize[iFrom];
m_vConnetNO[iFrom] = iTo;
}
vector m_vConnetNO;//各点所在联通区域的编号,本联通区域任意一点的索引，为了增加可理解性，用最小索引
vector m_vConnectSize;//各联通区域点数量
int m_iConnetSize;
};

class CUnionFindMST
{
public:
CUnionFindMST(const int iNodeSize) :m_uf(iNodeSize)
{

}
void AddEdge(const int iNode1, const int iNode2, int iWeight)
{
	if (m_uf.IsConnect(iNode1, iNode2))
	{
		return;
	}
	m_iMST += iWeight;
	m_uf.Union(iNode1, iNode2);
}
void AddEdge(const vector& v )
{
	AddEdge(v[0], v[1], v[2]);
}
int MST()
{
	if (m_uf.ConnetSize() > 1)
	{
		return -1;
	}
	return m_iMST;
}
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private:
int m_iMST = 0;
CUnionFind m_uf;
};

class CNearestMST
{
public:
CNearestMST(const int iNodeSize) :m_bDo(iNodeSize), m_vDis(iNodeSize, INT_MAX), m_vNeiTable(iNodeSize)
{

}
void Init(const vector>& edges)
{
	for (const auto& v : edges)
	{
		Add(v);
	}
}
void Add(const vector& v )
{
	m_vNeiTable[v[0]].emplace_back(v[1], v[2]);
	m_vNeiTable[v[1]].emplace_back(v[0], v[2]);
}
int MST(int start)
{
	int next = start;
	while ((next = AddNode(next)) >= 0);
	return m_iMST;
}
int MST(int iNode1, int iNode2,int iWeight)
{
	m_bDo[iNode1] = true;
	for (const auto& it : m_vNeiTable[iNode1])
	{
		if (m_bDo[it.first])
		{
			continue;
		}
		m_vDis[it.first] = min(m_vDis[it.first],(long long) it.second);
	}
	m_iMST = iWeight;

	int next = iNode2;
	while ((next = AddNode(next)) >= 0);
	return m_iMST;
}
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private:
int AddNode(int iCur)
{
m_bDo[iCur] = true;
for (const auto& it : m_vNeiTable[iCur])
{
if (m_bDo[it.first])
{
continue;
}
m_vDis[it.first] = min(m_vDis[it.first], (long long)it.second);
}

	int iMinIndex = -1;
	for (int i = 0; i < m_vDis.size(); i++)
	{
		if (m_bDo[i])
		{
			continue;
		}
		if ((-1 == iMinIndex) || (m_vDis[i] < m_vDis[iMinIndex]))
		{
			iMinIndex =i;		
		}
	}
	if ( -1 != iMinIndex)
	{
		if (INT_MAX == m_vDis[iMinIndex])
		{
			m_iMST = -1;
			return -1;
		}
		m_iMST += m_vDis[iMinIndex];
	}
	
	return iMinIndex;
}
vector m_bDo;
vector m_vDis;
vector < vector>> m_vNeiTable;
long long m_iMST = 0;
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};

typedef pair PAIRLLI;
class CDis
{
public:
static void Dis(vector& vDis, int start, const vector>>& vNeiB)
{
std::priority_queue minHeap;
minHeap.emplace(0, start);
while (minHeap.size())
{
const long long llDist = minHeap.top().first;
const int iCur = minHeap.top().second;
minHeap.pop();
if (-1 != vDis[iCur])
{
continue;
}
vDis[iCur] = llDist;
for (const auto& it : vNeiB[iCur])
{
minHeap.emplace(llDist + it.second, it.first);
}
}

}
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};

class CNearestDis
{
public:
CNearestDis(int iSize) :m_iSize(iSize), DIS(m_vDis), PRE(m_vPre)
{

}
void Cal(int start, const vector>>& vNeiB)
{
	m_vDis.assign(m_iSize, -1);
	m_vPre.assign(m_iSize, -1);
	vector vDo(m_iSize);//点是否已处理
	auto AddNode = [&](int iNode)
	{
		//const int iPreNode = m_vPre[iNode];
		long long llPreDis = m_vDis[iNode];

		vDo[iNode] = true;
		for (const auto& it : vNeiB[iNode])
		{
			if (vDo[it.first])
			{
				continue;
			}

			if ((-1 == m_vDis[it.first]) || (it.second + llPreDis < m_vDis[it.first]))
			{
				m_vDis[it.first] = it.second + llPreDis;
				m_vPre[it.first] = iNode;
			}				
		}

		long long llMinDis = LLONG_MAX;
		int iMinIndex = -1;
		for (int i = 0; i < m_vDis.size(); i++)
		{
			if (vDo[i])
			{
				continue;
			}
			if (-1 == m_vDis[i])
			{
				continue;
			}
			if (m_vDis[i] < llMinDis)
			{
				iMinIndex = i;
				llMinDis = m_vDis[i];
			}
		}
		return (LLONG_MAX == llMinDis) ? -1 : iMinIndex;
	};

	int next = start;
	m_vDis[start] = 0;
	while (-1 != (next= AddNode(next)));
}
void Cal(const int start, vector>& edges)
{
	vector>> vNeiB(m_iSize);
	for (int i = 0; i < edges.size(); i++)
	{
		const auto& v = edges[i];
		vNeiB[v[0]].emplace_back(v[1], v[2]);
		vNeiB[v[1]].emplace_back(v[0], v[2]);
	}
	Cal(start, vNeiB);
}
const vector& DIS;
const vector& PRE;
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private:
const int m_iSize;
vector m_vDis;//各点到起点的最短距离
vector m_vPre;//最短路径的前一点
};

class CNeiBo2
{
public:
CNeiBo2(int n, vector& edges, bool bDirect)
{
m_vNeiB.resize(n);
for (const auto& v : edges)
{
m_vNeiB[v[0]].emplace_back(v[1]);
if (!bDirect)
{
m_vNeiB[v[1]].emplace_back(v[0]);
}
}
}
vector m_vNeiB;
};

struct SDecimal
{
SDecimal(int iNum=0, int iDeno = 1)
{
m_iNum = iNum;
m_iDeno = iDeno;
int iGCD = GCD(abs(m_iNum), abs(m_iDeno));
m_iNum /= iGCD;
m_iDeno /= iGCD;
if (m_iDeno < 0)
{
m_iDeno = -m_iDeno;
m_iNum = -m_iNum;
}
}
SDecimal operator*(const SDecimal& o)const
{
return SDecimal(m_iNumo.m_iNum, m_iDenoo.m_iDeno);
}
SDecimal operator/(const SDecimal& o)const
{
return SDecimal(m_iNumo.m_iDeno, m_iDenoo.m_iNum);
}
SDecimal operator+(const SDecimal& o)const
{
const int iGCD = GCD(m_iDeno, o.m_iDeno);
const int iDeno = m_iDenoo.m_iDeno / iGCD;
return SDecimal(m_iNum(iDeno / m_iDeno) + o.m_iNum*(iDeno / o.m_iDeno), iDeno);
}
SDecimal operator-(const SDecimal& o)const
{
const int iGCD = GCD(m_iDeno, o.m_iDeno);
const int iDeno = m_iDenoo.m_iDeno / iGCD;
return SDecimal(m_iNum(iDeno / m_iDeno) - o.m_iNum*(iDeno / o.m_iDeno), iDeno);
}
bool operator==(const SDecimal& o)const
{
return (m_iNum == o.m_iNum) && (m_iDeno == o.m_iDeno);
}
bool operator<(const SDecimal& o)const
{
auto tmp = *this - o;
return tmp.m_iNum < 0;
}
int m_iNum=0;//分子
int m_iDeno=1;//分母
};

struct point{
double x, y;
point(double i, double j) :x(i), y(j){}
};

//算两点距离
double dist(double x1, double y1, double x2, double y2){
return sqrt((x1 - x2)(x1 - x2) + (y1 - y2)(y1 - y2));
}

//计算圆心
point CircleCenter(point& a, point& b, int r){
//算中点
point mid((a.x + b.x) / 2.0, (a.y + b.y) / 2.0);
//AB距离的一半
double d = dist(a.x, a.y, mid.x, mid.y);
//计算h
double h = sqrt(rr - dd);
//计算垂线
point ba(b.x - a.x, b.y - a.y);
point hd(-ba.y, ba.x);
double len = sqrt(hd.xhd.x + hd.yhd.y);
hd.x /= len, hd.y /= len;
hd.x *= h, hd.y *= h;
return point(hd.x + mid.x, hd.y + mid.y);
}

class C01LineTree
{
public:
C01LineTree(const vector& nums) :m_iEleSize(nums.size())
{
m_arr.resize(m_iEleSize * 4);
Init(nums,1, 1, m_iEleSize);
m_vNeedFreshChilds.assign(m_iEleSize * 4, false);
}
void Rotato(int iLeftZeroIndex,int iRightZeroIndex )
{
int iRotatoLeft = iLeftZeroIndex + 1;
int iRotatoRight = iRightZeroIndex + 1;
Rotato(1, 1, m_iEleSize, iRotatoLeft, iRotatoRight);
}
int Query()
{
return m_arr[1];
}
private:
void Rotato(int iSaveIndex, int iDataBegin, int iDataEnd, int iRotatoLeft, int iRotatoRight)
{
if ((iRotatoLeft <= iDataBegin) && (iRotatoRight >= iDataEnd))
{//整个范围需要更新
RotatoSelf(iSaveIndex, iDataBegin, iDataEnd);
return;
}

	int iMid = iDataBegin + (iDataEnd - iDataBegin) / 2;
	if (m_vNeedFreshChilds[iSaveIndex])
	{
		RotatoSelf(iSaveIndex * 2, iDataBegin, iMid);
		RotatoSelf(iSaveIndex * 2 + 1, iMid + 1, iDataEnd);
		m_vNeedFreshChilds[iSaveIndex] = false;
	}	
	if (iMid >= iRotatoLeft)
	{
		Rotato(iSaveIndex * 2, iDataBegin, iMid, iRotatoLeft, iRotatoRight);
	}
	if (iMid + 1 <= iRotatoRight)
	{
		Rotato(iSaveIndex * 2 + 1, iMid + 1, iDataEnd, iRotatoLeft, iRotatoRight);
	}
	m_arr[iSaveIndex] = m_arr[iSaveIndex * 2] + m_arr[iSaveIndex * 2 + 1];
}
void RotatoSelf(int iSaveIndex, int iDataBegin, int iDataEnd)
{
	//总数量 - 翻转后0(翻转前1）的数量
	m_arr[iSaveIndex] = (iDataEnd - iDataBegin + 1) - m_arr[iSaveIndex];
	//懒惰法，标记本节点的子孙节点没更新
	m_vNeedFreshChilds[iSaveIndex] = !m_vNeedFreshChilds[iSaveIndex];
}
void Init(const vector& nums, int iSaveIndex,int iDataBegin, int iDataEnd)
{
	if (iDataBegin == iDataEnd)
	{
		m_arr[iSaveIndex] = nums[iDataBegin - 1];
		return;
	}
	int iMid = iDataBegin + (iDataEnd - iDataBegin) / 2;
	Init(nums, iSaveIndex * 2  , iDataBegin, iMid);
	Init(nums, iSaveIndex * 2 + 1, iMid + 1, iDataEnd);
	m_arr[iSaveIndex] = m_arr[iSaveIndex * 2] + m_arr[iSaveIndex * 2 + 1];
}
const int m_iEleSize;
vector m_arr;
vector m_vNeedFreshChilds;
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};

/*
struct TreeNode {
int val;
TreeNode *left;
TreeNode *right;
TreeNode(int x) : val(x), left(NULL), right(NULL) {}
TreeNode(int x, int iLeft) : val(x), left(new TreeNode(iLeft)), right(nullptr) {}
TreeNode(int x, int iLeft, int iRghit) : val(x), left(new TreeNode(iLeft)), right(new TreeNode(iRghit)) {}
};

namespace NTree
{
TreeNode* Init(const vector& nums, int iNull = 10000)
{
if (0 == nums.size())
{
return nullptr;
}
vector ptrs(nums.size() + 1), ptrParent(1);
for (int i = 0; i < nums.size(); i++)
{
if (iNull == nums[i])
{
continue;
}
const int iNO = i + 1;
ptrs[iNO] = new TreeNode(nums[i]);
ptrParent.emplace_back(ptrs[iNO]);
if (1 == iNO)
{
continue;
}
if (iNO & 1)
{//奇数是右支
ptrParent[iNO / 2]->right = ptrs[iNO];
}
else
{
ptrParent[iNO / 2]->left = ptrs[iNO];
}
}
return ptrs[1];
}
}
*/

class Solution {
public:
int kInversePairs(int n, int k) {
//n为1时，只有一种情况：逆序0
vector> pre = { C1097Int<>(1) };
for (int i = 2; i <= n; i++)
{
const int iNewLen = min(k + 1, (int)pre.size() + i);
vector> dp(iNewLen);
C1097Int<> iSum = 0;
for (int j = 0; j < iNewLen; j++)
{
if (j < pre.size())
{
iSum += pre[j];
}
const int iDelIndex = j - i;
if (iDelIndex >= 0)
{
iSum -= pre[iDelIndex];
}
dp[j] = iSum;
}
pre.swap(dp);
}
return (k < pre.size()) ? pre[k].ToInt() : 0;
}
};

扩展阅读

视频课程

有效学习：明确的目标 及时的反馈 拉伸区（难度合适），可以先学简单的课程，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

相关

下载

想高屋建瓴的学习算法，请下载《喜缺全书算法册》doc版
https://download.csdn.net/download/he_zhidan/88348653

我想对大家说的话
闻缺陷则喜是一个美好的愿望，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

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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