【树 图论 阶乘 组合 深度优先搜索】1916. 统计为蚁群构筑房间的不同顺序

template<class T = long long>
class CFactorial
{
public:
  CFactorial(int n):m_res(n+1){
    m_res[0] = 1;
    for (int i = 1; i <= n; i++) {
      m_res[i] = m_res[i - 1] * i;
    }
  }
  vector<T> m_res;
};
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;
  }
  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;;
};
class Solution {
public:
  int waysToBuildRooms(vector<int>& prevRoom) {
    const int n = prevRoom.size();
    m_fact = new CFactorial<C1097Int<>>(n);
    m_vSubTreeNodeCnt.resize(n);
    vector<vector<int>> neiBo(n);
    for (int i = 1; i < n; i++) {     
      neiBo[prevRoom[i]].emplace_back(i);
    }   
    DFSSubTreeNodeCount(neiBo, 0);
    return DFS(neiBo, 0).ToInt();
  }
  void DFSSubTreeNodeCount(vector<vector<int>>& neiBo, int cur)
  {
    m_vSubTreeNodeCnt[cur] = 1;
    for (const auto& next : neiBo[cur])
    {   
      DFSSubTreeNodeCount(neiBo, next);
      m_vSubTreeNodeCnt[cur] += m_vSubTreeNodeCnt[next];
    }
  }
  C1097Int<> DFS(vector<vector<int>>& neiBo, int cur)
  {
    C1097Int<> biRet = 1;
    int iCanSel = m_vSubTreeNodeCnt[cur] - 1;
    for (const auto& next : neiBo[cur])
    {
      biRet *= m_fact->m_res[iCanSel];
      const int iChildCnt = m_vSubTreeNodeCnt[next];
      biRet *= m_fact->m_res[iChildCnt].PowNegative1();
      biRet *= m_fact->m_res[iCanSel-iChildCnt].PowNegative1();
      iCanSel -= iChildCnt;
      biRet *= DFS(neiBo, next);
    }
    return biRet;
  }
  vector<int> m_vSubTreeNodeCnt;//子
  CFactorial<C1097Int<>> * m_fact;
};

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()
{
  vector<int> prevRoom;
  {
    Solution sln;
    prevRoom = { -1,0,0,1,2 };
    auto res = sln.waysToBuildRooms(prevRoom);
    Assert(6, res);
  }
  {
    Solution sln;
    prevRoom = {-1, 0, 1};
    auto res = sln.waysToBuildRooms(prevRoom);
    Assert(1, res);
  }
  
}