一些常見函數的寫法

LL 被宏定義爲 long long

1.GCD（非遞歸）

```c

inline int gcd(register int x,register int y)
{
	if(x == 0 || y == 0) return x | y;
    
	register int t;

	while(t = x % y) {x = y;y = t;}

	return y;
}

```

2.GCD（遞歸）

```c

inline LL Gcd(const LL a,const LL b){return b ? Gcd(b,a % b) : a;}

```

3.龜速乘

```c
inline LL Multiply(LL x,LL y,const LL& mod)
{
	LL res = 0;
	
	for(; x ; x >>= 1,y = (y << 1) % mod) 
		if(x & 1) res = (res + y) % mod;

	return res;
}
```

4.快速冪（防溢出）

```c
inline LL Fast_Pow(LL x,LL p,const LL& mod)
{
	LL res = 1;
	
	for(; p ; p >>= 1,x = Multiply(x,x,mod)) 
		if(p & 1) res = Multiply(res,x,mod);

	return res;
}
    ```

5.擴展歐幾里德

```c
inline LL Exgcd(const LL a,const LL b,LL& x,LL& y)
{
	if(b == 0) x = 1;

	else {
		Exgcd(b,a % b,y,x);
	
		y -= a / b * x;
	}
}
    ```

--2020/5/4

6.二分(lower_bound)

```c
  template<class T>
  inline int find(const T a[],const int n,const T key)
  {
        register int l = 0,r = n;
    
        while(l < r)
        {
        register int mid = (l + r)>>1;
        
        if(a[mid] <= key) r = mid;      
        else l = mid + 1;
       }
  } 
  ```

6.二分(upper_bound)

```c
  template<class T>
  inline int find(const T a[],const int n,const T key)
  {
        register int l = 0,r = n;
    
        while(l < r)
        {
              register int mid = (l + r)>>1;
        
              if(a[mid] < key) r = mid;
              else l = mid + 1;
        }
  } 
  ```

2020/7/1

方形矩陣

```c
  struct matrix
  {
        int len;
        int Matrix[105][105];

        matrix(){memset(Matrix,0,sizeof(Matrix));len = 0;}

        inline void clear(){memset(Matrix,0,sizeof(Matrix));len = 0;}

        inline void init()
        {
              memset(Matrix,0,sizeof(Matrix));
              for(reg int i = 1; i <= len; ++i) Matrix[i][i] = 1;
        }

        inline matrix operator * (const matrix &rhs) const
        {
              matrix res;res.len = len;
              for (reg int i = 1; i <= len; ++i)
                    for (reg int j = 1; j <= len; ++j){
                          for (reg int k = 1; k <= len; ++k) res.Matrix[i][j] += Matrix[i][k] * rhs.Matrix[k][j]; 
                
                          res.Matrix[i][j] %= 2009; 
                          }
              return res; 
        }

      inline matrix operator ^ (int p) const
      {
            matrix res,x = *this; res.len = len;res.init();
            for (; p; p >>= 1, x = x * x)
                  if (p & 1) res = res * x; 
            return res; 
      }
  } ma;
  ```

快讀（非負整數）

```c
  inline void in(int& x)
  {
      x = 0; char ch = getchar();

      while(ch < '0' || ch > '9') ch = getchar();

      while(ch >= '0' && ch <= '9'){x = (x << 3) + (x << 1) + (ch ^ 48);ch = getchar();}
  }

  inline int Read()
  {
      reg int x = 0;reg char ch = getchar();

      while(ch < '0' || ch > '9') ch = getchar();

      while(ch >= '0' && ch <= '9'){x = (x << 3) + (x << 1) + (ch ^ 48);ch = getchar();}

      return x;
  }
  ```

2020/7/7

矩陣

```
  struct Matrix
  {
      int width,length;
      int matrix[42][42];

      Matrix(const int w=0,const int l=0):width(w),length(l){}
  };

  Matrix operator * (const Matrix& a,const Matrix& b)
  {
      Matrix res = Matrix(a.width,b.length);

      for(reg int i = 1; i <= a.width; ++i)
	      for(reg int j = 1; j <= b.length; ++j)
		      for(reg int k = 1; k <= a.length; ++k)
			      res.matrix[i][j] += a.matrix[i][k] * b.matrix[k][j];
			
      return res;
  }
  ```

2020/7/10