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本文涉及知识点
状态压缩 广度优先搜索
LeetCode1494. 并行课程 II
给你一个整数 n 表示某所大学里课程的数目，编号为 1 到 n ，数组 relations 中， relations[i] = [xi, yi] 表示一个先修课的关系，也就是课程 xi 必须在课程 yi 之前上。同时你还有一个整数 k 。
在一个学期中，你 最多 可以同时上 k 门课，前提是这些课的先修课在之前的学期里已经上过了。
请你返回上完所有课最少需要多少个学期。题目保证一定存在一种上完所有课的方式。
示例 1：
输入：n = 4, relations = [[2,1],[3,1],[1,4]], k = 2
输出：3
解释：上图展示了题目输入的图。在第一个学期中，我们可以上课程 2 和课程 3 。然后第二个学期上课程 1 ，第三个学期上课程 4 。
示例 2：
输入：n = 5, relations = [[2,1],[3,1],[4,1],[1,5]], k = 2
输出：4
解释：上图展示了题目输入的图。一个最优方案是：第一学期上课程 2 和 3，第二学期上课程 4 ，第三学期上课程 1 ，第四学期上课程 5 。
示例 3：
输入：n = 11, relations = [], k = 2
输出：6
提示：
1 <= n <= 15
1 <= k <= n
0 <= relations.length <= n * (n-1) / 2
relations[i].length == 2
1 <= xi, yi <= n
xi != yi
所有先修关系都是不同的，也就是说 relations[i] != relations[j] 。
题目输入的图是个有向无环图。
状态压缩
15门课程。枚举最后一次选择（选择1到15门） 和之前的选择（0到15门）。共多少种可能。暴力做法是：230。
枚举第一门课 第二门课第三门课 的可能
不包括0，共7种可能。
const int iMaxMask = (1 << 3)-1;
for (int mask = iMaxMask; mask; mask = (mask - 1) & iMaxMask)
{
char sz1[100],sz2[100];
_itoa_s(mask, sz1, 2);
_itoa_s(iMaxMask - mask, sz2, 2);
std::cout << “最后一次选择:\t” << sz1 << " 之前的选择:\t" << sz2 << std::endl;
}
最后一次选择: 111 之前的选择: 0
最后一次选择: 110 之前的选择: 1
最后一次选择: 101 之前的选择: 10
最后一次选择: 100 之前的选择: 11
最后一次选择: 11 之前的选择: 100
最后一次选择: 10 之前的选择: 101
最后一次选择: 1 之前的选择: 110
枚举第一、三、四
不包括0，共7种可能，不需要枚举16种可能。自动忽略了不可能存在的状态2。
const int iMaxMask = 1+4+8;
最后一次选择: 111 之前的选择: 0
最后一次选择: 110 之前的选择: 1
最后一次选择: 101 之前的选择: 10
最后一次选择: 100 之前的选择: 11
最后一次选择: 11 之前的选择: 100
最后一次选择: 10 之前的选择: 101
最后一次选择: 1 之前的选择: 110
枚举iMaxMask [0,2n)
总时间复杂度是:O(3n) 315大约1.4e7。注意剪枝，否则容易超时。
动态规划
动态规划的状态表示
pre记录i学期能够完成的课程，dp记录i+1学期可以完成的课程。vHasDo记录已经完成的状态。状态没必要重复处理，i1<i2，如果某种状态i1学期能处理，那没必要i2学期处理。
空间复杂度:状态数 ,2n
时间复杂度: O(3n)
动态规划的转移方程
当前学期的课程，必须满足三个条件：
一，课程数小于等于k。
二，所有前置课程都已经完成。
三，这些课程没学习过。可以省略，会被淘汰。
预处理：
vPre[i] 表示第i门课需要的前面状态。
vNext[mask] 记录完成mask课程后，能够学习的课程。
动态规划的初始值
pre={0}
动态规划的填表顺序
i从0到大
动态规划的返回值
pre 包括(1<<n)-1时的i。
代码
核心代码
//通过 x &= (x-1)实现 int bitcount(unsigned x) { int countx = 0; while (x) { countx++; x &= (x - 1); } return countx; } class Solution { public: int minNumberOfSemesters(int n, vector<vector<int>>& relations, int k) { const int iMaskCount = 1 << n; vector<int> vPre(n); for (const auto& v : relations) { vPre[v[1] - 1] |= 1 << (v[0] - 1); } vector<int> vNext(iMaskCount); for (int i = 0; i < iMaskCount; i++) { for (int j = 0; j < n; j++) { if ((vPre[j] & i) == vPre[j]) { vNext[i] |= (1 << j); } } } vector<int> pre = { 0 }; vector<bool> vHasDo(iMaskCount); for (int i = 0; ; i++) { vector<int> dp; for (const int& iPre : pre) { if (iPre + 1 == iMaskCount) { return i; } const int iRemain = (iMaskCount - 1) - iPre; const int iCanSel = iRemain& vNext[iPre]; auto Add = [&](const int& cur) { const int iNew = cur | iPre; if (!vHasDo[iNew]) { dp.emplace_back(iNew); vHasDo[iNew] = true; } }; if (bitcount((unsigned int)iCanSel) <= k) { Add(iCanSel); continue; } for (int cur = iCanSel; cur; cur = (cur - 1) & iCanSel) { if (bitcount((unsigned int)cur) == k) { Add(cur); } } } pre.swap(dp); } return -1; } };
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; vector<vector<int>> relations; { Solution sln; n = 4, relations = { {2,1},{3,1},{1,4} }, k = 2; auto res = sln.minNumberOfSemesters(n, relations, k); Assert(3, res); } { Solution sln; n = 5, relations = { {2,1},{3,1},{4,1},{1,5} }, k = 2; auto res = sln.minNumberOfSemesters(n, relations, k); Assert(4, res); } { Solution sln; n = 11, relations = {}, k = 2; auto res = sln.minNumberOfSemesters(n, relations, k); Assert(6, res); } }
动态规划
剪枝 忽略非法的前者状态。
//通过 x &= (x-1)实现 int bitcount(unsigned x) { int countx = 0; while (x) { countx++; x &= (x - 1); } return countx; } template<class ELE,class ELE2> void MinSelf(ELE* seft, const ELE2& other) { *seft = min(*seft,(ELE) other); } template<class ELE> void MaxSelf(ELE* seft, const ELE& other) { *seft = max(*seft, other); } class Solution { public: int minNumberOfSemesters(int n, vector<vector<int>>& relations, int k) { const int iMaskCount = 1 << n; vector<int> vPre(n); for (const auto& v : relations) { vPre[v[1] - 1] |= 1 << (v[0] - 1); } vector<int> vNext(iMaskCount), vLen(iMaskCount); for (int i = 0; i < iMaskCount; i++) { vLen[i] = bitcount((unsigned int)i); for (int j = 0; j < n; j++) { if ((vPre[j] & i) == vPre[j]) { vNext[i] |= (1 << j); } } } vector<int> vRet(iMaskCount,100); vRet[0] = 0; for (int i = 0; i < iMaskCount; i++) { if(vRet[i] >= 100 ) { continue; } const int iNeedStudy = (iMaskCount - 1) ^ i;//未学课程 const int iCanStudy = iNeedStudy & vNext[i]; //只能学前置课程已学的课程 if (vLen[iCanStudy] <= k) { MinSelf(&vRet[i| iCanStudy], vRet[i] + 1); } for (int j = iCanStudy; j; j= iCanStudy &(j-1)) {//i是已学课程，j是本学期将学的课程 if (bitcount((unsigned )j) != k ) { continue; } MinSelf(&vRet[i | j], vRet[i] + 1); } } return vRet.back(); } };
2023年2月第一版
class Solution {
public:
int minNumberOfSemesters(int n, vector<vector>& relations, int k) {
m_iN = n;
m_iK = k;
m_iMaskNum = 1 << n;
m_vPreCourse.resize(n);
for (const auto& v : relations)
{
m_vPreCourse[v[1] - 1] |= (1 << (v[0] - 1));
}
m_vMinSemesters.resize(m_iMaskNum, m_iNotMay);
vector pre(1);
m_vMinSemesters[0] = 0;
for (int iSem = 0;; iSem++)
{
vector dp;
for (const auto& pr : pre)
{
if (pr + 1 == m_iMaskNum)
{
return iSem;
}
int iCanStudy = GetCanStudy(pr);
dfs(dp, pr, iCanStudy, iCanStudy, k,-1);
}
pre.swap(dp);
}
return 0;
}
inline int GetCanStudy(int preMask)const
{
int iCanStudy = 0;
for (int n = 0; n < m_iN; n++)
{
if (preMask & (1 << n))
{//之前已经学习
continue;
}
if ((m_vPreCourse[n] & preMask) != m_vPreCourse[n])
{//先行课程没有学习
continue;
}
iCanStudy |= (1 << n);
}
return iCanStudy;
}
void dfs(vector& dp, const int& preMask, const int& iCanStudy, int iRemain, int iLeve,int iPreN)
{
if ((0 == iLeve) || (0 == iRemain))
{
const int iNewMask = preMask |(iCanStudy - iRemain );
if (m_iNotMay != m_vMinSemesters[iNewMask])
{
return;
}
dp.push_back(iNewMask);
m_vMinSemesters[iNewMask] = m_vMinSemesters[preMask] + 1;
return;
}
for (int n = iPreN+1; n < m_iN; n++)
{
if (iRemain & (1 << n))
{
dfs(dp, preMask, iCanStudy, iRemain -(1 << n ), iLeve - 1,n);
}
}
}
vector m_vPreCourse;
vector m_vMinSemesters;
int m_iMaskNum;
int m_iK;
int m_iN;
const int m_iNotMay = 1000 * 1000;
};
2023年2月第二版
class Solution {
public:
int minNumberOfSemesters(int n, vector<vector>& relations, int k) {
m_iN = n;
m_iK = k;
m_iMaskNum = 1 << n;
m_vPreCourse.resize(n);
for (const auto& v : relations)
{
m_vPreCourse[v[1] - 1] |= (1 << (v[0] - 1));
}
m_vMinSemesters.resize(m_iMaskNum, m_iNotMay);
vector pre(1);
m_vMinSemesters[0] = 0;
for (int iSem = 0;; iSem++)
{
vector dp;
for (const auto& pr : pre)
{
if (pr + 1 == m_iMaskNum)
{
return iSem;
}
int iCanStudy = GetCanStudy(pr);
dfs(dp, pr, iCanStudy, iCanStudy, k, iCanStudy);
}
pre.swap(dp);
}
return 0;
}
inline int GetCanStudy(int preMask)const
{
int iCanStudy = 0;
for (int n = 0; n < m_iN; n++)
{
if (preMask & (1 << n))
{//之前已经学习
continue;
}
if ((m_vPreCourse[n] & preMask) != m_vPreCourse[n])
{//先行课程没有学习
continue;
}
iCanStudy |= (1 << n);
}
return iCanStudy;
}
void dfs(vector& dp, const int& preMask, const int& iCanStudy, int iRemain, int iLeve,int iCanSel)
{
if ((0 == iLeve) || (0 == iCanSel))
{
const int iNewMask = preMask |(iCanStudy - iRemain );
if (m_iNotMay != m_vMinSemesters[iNewMask])
{
return;
}
dp.push_back(iNewMask);
m_vMinSemesters[iNewMask] = m_vMinSemesters[preMask] + 1;
return;
}
while (iCanSel)
{
const int iNextCanSel = (iCanSel - 1)& iCanSel;
const int n = iCanSel - iNextCanSel;
iCanSel = iNextCanSel;
dfs(dp, preMask, iCanStudy, iRemain-n, iLeve - 1, iCanSel);
}
}
vector m_vPreCourse;
vector m_vMinSemesters;
int m_iMaskNum;
int m_iK;
int m_iN;
const int m_iNotMay = 1000 * 1000;
};
2023年7月版
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<class T> static void Out(const vector<T>& vec, const string& strColSep = " ", const string& strRowSep = "\r\n") { OutToConsoleInner(vec, strColSep); std::cout << strRowSep.c_str(); } template<class T> static void Out(const vector<vector<T>>& 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<class T> static void Out(const std::map<T, std::vector<int> >& 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<class T > static void Out(const T& t, const string& strColSep = " ", const string& strRowSep = "\r\n") { std::cout << t << strColSep.c_str(); }
};
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<int, vector, std::greater > 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<CPeo*> m_childs;
CPeo* m_pParent = nullptr;
};
class CNeighborTable
{
public:
void Init(const vector<vector>& edges)
{
} vector<vector<int>> m_vTable;
};
//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<class IT> void Add(IT begin, IT end) { CTrie<iTypeNum, cBegin>* pNode = this; for (; begin != end; ++begin) { pNode = pNode->AddChar(*begin).get(); } } template<class IT> 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); }
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<CTrie<iTypeNum, cBegin>>();
}
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<std::shared_ptr> 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<string> m_strStrs;
};
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<CWords> m_str[26];
};
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; }
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); }
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); }
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<int, int> 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); }
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<T> m_vArr; vector<int> m_vChildAdd;
};
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); }
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;
}
}
//包括left right
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 GetHashExincludeRight(int left, int right)
{
return (m_vHash[right ] - m_vHash[left] * m_vP[right - left ]).ToInt();
}
inline int GetHashExincludeRight(int right)
{
return m_vHash[right].ToInt();
}
int m_c;
vector<C1097Int> m_vP;
vector<C1097Int> m_vHash;
};
template
class C2HashStr
{
public:
C2HashStr(string s) {
m_pHash1 = std::make_unique<CHashStr<>>(s, 26);
m_pHash2 = std::make_unique < CHashStr>(s, 27, 0);
}
//包括left right
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);
}
//包括Left，不包括Right
long long GetHashExincludeRight(int left, int right)
{
return (long long)m_pHash1->GetHashExincludeRight(left, right) * (MOD2 + 1) + m_pHash2->GetHashExincludeRight(left, right);
}
long long GetHashExincludeRight(int right)
{
return (long long)m_pHash1->GetHashExincludeRight(right) * (MOD2 + 1) + m_pHash2->GetHashExincludeRight(right);
}
private:
std::unique_ptr<CHashStr<>> m_pHash1;
std::unique_ptr<CHashStr> 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<MOD> m_iHash; C1097Int<MOD> m_iP;
};
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)MOD2 * m_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<Class1, int>& p, Class1 iData)
{
return p.first < iData;
}
template<class Class1> bool Greater(const std::pair<Class1, int>& p, Class1 iData) { return p.first > iData; } template<class _Ty1, class _Ty2> 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 _Ty1, class _Ty2> class CGreatePair { public: bool operator()(const std::pair<_Ty1, _Ty2>& p1, const std::pair<_Ty1, _Ty2>& p2)const { return p1.first > p2.first; } };
}
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<class T> void PopIsTopIsDel(T& que, std::unordered_multiset<int>& 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<int> m_queTopMax; std::priority_queue<int, vector<int>, greater<int>> m_queTopMin; std::unordered_multiset<int> m_setTopMaxDel, m_setTopMinDel;
};
template
class CDistanceGrid
{
public:
CDistanceGrid(const vector<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<vector<int>> vDis(iMaxRow, vector<int>(iMaxCol, INT_MAX)); auto Add = [&vDis, this](std::priority_queue<pair<int, int>, vector<std::pair<int, int>>, greater<pair<int, int>>>& 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<pair<int, int>, vector<std::pair<int, int>>, greater<pair<int, int>>>& 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<pair<int, int>, vector<std::pair<int, int>>, greater<pair<int, int>>> 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; }
private:
virtual bool IsCanMoveStatue(int r, int c)
{
return m_grid[r][c] >= 1;
}
const int m_r;
const int m_c;
const vector<vector>& m_grid;
};
class CBFSGridDist
{
public:
CBFSGridDist(const vector<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<vector>& Dis()const
{
return m_vDis;
}
const vector<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<vector> vHasDo(m_r, vector(m_c));
std::queue<std::pair<int, int>> 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<vector<int>> m_vDis; const int m_r; const int m_c;
};
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<std::string> 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(); }
};
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<std::string> ToStrings()const { vector<std::string> vRet; for (const auto& item : m_items) { if (0 == item.m_iCoefficient) { continue; } vRet.emplace_back(item.ToString()); } return vRet; } std::set<SValueItem> m_items;
};
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; }
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<bool> m_bDels; vector<int> m_vNext;
};
class CUnionFind
{
public:
CUnionFind(int iSize) :m_vNodeToRegion(iSize)
{
for (int i = 0; i < iSize; i++)
{
m_vNodeToRegion[i] = i;
}
m_iConnetRegionCount = iSize;
}
int GetConnectRegionIndex(int iNode)
{
int& iConnectNO = m_vNodeToRegion[iNode];
if (iNode == iConnectNO)
{
return iNode;
}
return iConnectNO = GetConnectRegionIndex(iConnectNO);
}
void Union(int iNode1, int iNode2)
{
const int iConnectNO1 = GetConnectRegionIndex(iNode1);
const int iConnectNO2 = GetConnectRegionIndex(iNode2);
if (iConnectNO1 == iConnectNO2)
{
return;
}
m_iConnetRegionCount–;
if (iConnectNO1 > iConnectNO2)
{
UnionConnect(iConnectNO1, iConnectNO2);
}
else
{
UnionConnect(iConnectNO2, iConnectNO1);
}
}
bool IsConnect(int iNode1, int iNode2) { return GetConnectRegionIndex(iNode1) == GetConnectRegionIndex(iNode2); } int GetConnetRegionCount()const { return m_iConnetRegionCount; } vector<int> GetNodeCountOfRegion()//各联通区域的节点数量 { const int iNodeSize = m_vNodeToRegion.size(); vector<int> vRet(iNodeSize); for (int i = 0; i < iNodeSize; i++) { vRet[GetConnectRegionIndex(i)]++; } return vRet; }
private:
void UnionConnect(int iFrom, int iTo)
{
m_vNodeToRegion[iFrom] = iTo;
}
vector m_vNodeToRegion;//各点所在联通区域的索引,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
int m_iConnetRegionCount;
};
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<int>& v) { AddEdge(v[0], v[1], v[2]); } int MST() { if (m_uf.GetConnetRegionCount() > 1) { return -1; } return m_iMST; }
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<vector<int>>& edges) { for (const auto& v : edges) { Add(v); } } void Add(const vector<int>& 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; }
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<bool> m_bDo; vector<long long> m_vDis; vector < vector<std::pair<int, int>>> m_vNeiTable; long long m_iMST = 0;
};
typedef pair<long long, int> PAIRLLI;
class CDis
{
public:
static void Dis(vector& vDis, int start, const vector<vector<pair<int, int>>>& vNeiB)
{
std::priority_queue<PAIRLLI, vector, greater> 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);
}
}
}
};
class CNearestDis
{
public:
CNearestDis(int iSize) :m_iSize(iSize), DIS(m_vDis), PRE(m_vPre)
{
} void Cal(int start, const vector<vector<pair<int, int>>>& vNeiB) { m_vDis.assign(m_iSize, -1); m_vPre.assign(m_iSize, -1); vector<bool> 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<vector<int>>& edges) { vector<vector<pair<int, int>>> 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<long long>& DIS; const vector<int>& PRE;
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<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<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_iNum * o.m_iNum, m_iDeno * o.m_iDeno);
}
SDecimal operator/(const SDecimal& o)const
{
return SDecimal(m_iNum * o.m_iDeno, m_iDeno * o.m_iNum);
}
SDecimal operator+(const SDecimal& o)const
{
const int iGCD = GCD(m_iDeno, o.m_iDeno);
const int iDeno = m_iDeno * o.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_iDeno * o.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(r * r - d * d);
//计算垂线
point ba(b.x - a.x, b.y - a.y);
point hd(-ba.y, ba.x);
double len = sqrt(hd.x * hd.x + hd.y * hd.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;
};
/*
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<TreeNode*> 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 minNumberOfSemesters(int n, vector<vector>& relations, int k) {
m_iMaskNum = 1 << n;
vector dp(m_iMaskNum,1000*1000),vPre(m_iMaskNum);
for (const auto& v : relations)
{
vPre[1 << (v[1] - 1)] |= (1 << (v[0] - 1));
}
dp[0] = 0;
for (int i = 0; i < m_iMaskNum; i++)
{
vPre[i] = vPre[i & (-i)] | vPre[i & (i - 1)];
if ((i | vPre[i]) != i)
{
continue;//非发课程：前置课程没学
}
unsigned int uCanStudy = vPre[i] ^ i;
if (bitcount(uCanStudy) <= k)
{
dp[i ] = min(dp[i ], dp[i- uCanStudy] + 1);
continue;
}
for (unsigned int uStudy = uCanStudy; uStudy; uStudy = uCanStudy & (uStudy - 1))
{
if (bitcount(uStudy) <= k)
{
dp[i] = min(dp[i ], dp[i - uStudy] + 1);
}
}
}
return dp.back();
}
int m_iMaskNum;
};
.
