机试练习Day6-有深度的题目--真题

矩阵快速幂

快速幂算法

这个道理和转二进制很像：

例如：现在要求3的9次方，最关键的是如何表示9，我们可以选择让3乘9次，也就是3 * 3 * 3 * 3 * 3 * 3 * 3 * 3* 3；
但是如果是10000000000次方就会让效率很低，现在可以考虑用二进制表示9，也就是1001，刚开始K=9是奇数，那么转成二进制后，最后一位一定是1，只要在大于0的范围内出现1，就有意义。

K	B	A
9	1	3
9	3	3 * 3
4	不变：3	（3 * 3） *（ 3 * 3）
2	不变：3	（3 * 3 * 3 * 3 ）*（ 3 * 3 * 3 * 3）
1	3 * （3 * 3 * 3 * 3 * 3 * 3 * 3 * 3）	（3 * 3 * 3 * 3 * 3 * 3 * 3 * 3）*（3 * 3 * 3 * 3 * 3 * 3 * 3 * 3）
0	END	END

代码部分

#include 
void Calculation(int a[10][10], int b[10][10], int n)
{
    int c[10][10] = {0};
    //矩阵乘法
    for (int i = 0; i < n; i ++) 
	{
        for (int j = 0; j < n; j ++) 
		{
            for (int k = 0; k < n; k ++) 
			{
                c[i][j] += a[i][k] * b[k][j];
            }
        }
    }
    
    for (int i = 0; i < n; i ++) 
	{
        for (int j = 0; j < n; j ++) 
		{
            a[i][j] = c[i][j];
        }
    }
}

int main() {
    int n, k;
    int a[10][10];
    int b[10][10];
    while (scanf("%d %d", &n, &k) != EOF) 
	{

        //读入矩阵到a
        for (int i = 0; i < n; i ++) 
            for (int j = 0; j < n; j ++) 
                scanf("%d", &a[i][j]);

        //构造单位矩阵
        for (int i = 0; i < n; i ++) 
		{
            for (int j = 0; j < n; j ++) 
			{
                if(i == j) 
                    b[i][j] = 1;
				else 
                    b[i][j] = 0;
            }
        }

        //核心
        while (k > 0)
		{
            if (k % 2 == 1) 
                Calculation(b, a, n);
            
            Calculation(a, a, n);
            k /= 2;
        }

        //输出计算结果
        for (int i = 0; i < n; i ++) 
		{
            for (int j = 0; j < n; j ++) 
                printf("%d ", b[i][j]);         
            printf("\n");
        }
    }
}

复数的集合

优先队列

• priority_queue
• 一个带优先级的队列【队头的优先级最高】
• empty 队列是否为空
• push 插入元素到队尾
• top 访问队头元素
• pop 弹出队头元素
• size 返回队列内元素个数

运算符重载

• 运算符重载实质上是函数的重载。
• 一般格式：函数类型 operator 运算符名称（形参表）{对运算符的重载处理}
• 当运算符重载为类的成员函数时，函数的参数个数比原来的操作数个数要少一个（后置“++”，“–”除外），原因：类的this指针所指的对象默认穿进去。
• 用const对成员函数进行声明，表示这个函数不会修改类中的任何数据成员。下面这个函数承载如果去掉const会报错：“this”参数的类型为“const comp”，但方法未标记为const。

---

报错信息如下：

编译错误
您提交的代码无法完成编译
a.cpp:43:32: warning: format specifies type 'int' but the argument has type 'std::priority_queue>, std::less>::size_type' (aka 'unsigned long') [-Wformat]
printf("SIZE = %d\n",myqueue.size());
~~ ^~~~~~~~~~~~~~
%lu
a.cpp:51:30: warning: format specifies type 'int' but the argument has type 'std::priority_queue>, std::less>::size_type' (aka 'unsigned long') [-Wformat]
printf("SIZE = %d\n",myqueue.size());
~~ ^~~~~~~~~~~~~~
%lu
In file included from a.cpp:1:
In file included from /usr/bin/../lib/gcc/x86_64-linux-gnu/7.5.0/../../../../include/c++/7.5.0/iostream:39:
In file included from /usr/bin/../lib/gcc/x86_64-linux-gnu/7.5.0/../../../../include/c++/7.5.0/ostream:38:
In file included from /usr/bin/../lib/gcc/x86_64-linux-gnu/7.5.0/../../../../include/c++/7.5.0/ios:42:
In file included from /usr/bin/../lib/gcc/x86_64-linux-gnu/7.5.0/../../../../include/c++/7.5.0/bits/ios_base.h:41:
In file included from /usr/bin/../lib/gcc/x86_64-linux-gnu/7.5.0/../../../../include/c++/7.5.0/bits/locale_classes.h:40:
In file included from /usr/bin/../lib/gcc/x86_64-linux-gnu/7.5.0/../../../../include/c++/7.5.0/string:48:
/usr/bin/../lib/gcc/x86_64-linux-gnu/7.5.0/../../../../include/c++/7.5.0/bits/stl_function.h:386:20: error: invalid operands to binary expression ('const comp' and 'const comp')
{ return __x < __y; }
~~~ ^ ~~~
/usr/bin/../lib/gcc/x86_64-linux-gnu/7.5.0/../../../../include/c++/7.5.0/bits/predefined_ops.h:143:23: note: in instantiation of member function 'std::less::operator()' requested here
{ return bool(_M_comp(*__it1, *__it2)); }
^
/usr/bin/../lib/gcc/x86_64-linux-gnu/7.5.0/../../../../include/c++/7.5.0/bits/stl_heap.h:222:8: note: in instantiation of function template specialization '__gnu_cxx::__ops::_Iter_comp_iter>::operator()<__gnu_cxx::__normal_iterator>>, __gnu_cxx::__normal_iterator>>>' requested here
if (__comp(__first + __secondChild,
^
/usr/bin/../lib/gcc/x86_64-linux-gnu/7.5.0/../../../../include/c++/7.5.0/bits/stl_heap.h:253:12: note: in instantiation of function template specialization 'std::__adjust_heap<__gnu_cxx::__normal_iterator>>, long, comp, __gnu_cxx::__ops::_Iter_comp_iter>>' requested here
std::__adjust_heap(__first, _DistanceType(0),
^
/usr/bin/../lib/gcc/x86_64-linux-gnu/7.5.0/../../../../include/c++/7.5.0/bits/stl_heap.h:320:9: note: in instantiation of function template specialization 'std::__pop_heap<__gnu_cxx::__normal_iterator>>, __gnu_cxx::__ops::_Iter_comp_iter>>' requested here
std::__pop_heap(__first, __last, __last, __cmp);
^
/usr/bin/../lib/gcc/x86_64-linux-gnu/7.5.0/../../../../include/c++/7.5.0/bits/stl_queue.h:633:7: note: in instantiation of function template specialization 'std::pop_heap<__gnu_cxx::__normal_iterator>>, std::less>' requested here
std::pop_heap(c.begin(), c.end(), comp);
^
a.cpp:42:19: note: in instantiation of member function 'std::priority_queue>, std::less>::pop' requested here
myqueue.pop();
^
/usr/bin/../lib/gcc/x86_64-linux-gnu/7.5.0/../../../../include/c++/7.5.0/bits/stl_pair.h:454:5: note: candidate template ignored: could not match 'pair' against 'const comp'
operator<(const pair<_T1, _T2>& __x, const pair<_T1, _T2>& __y)
^
/usr/bin/../lib/gcc/x86_64-linux-gnu/7.5.0/../../../../include/c++/7.5.0/bits/stl_iterator.h:308:5: note: candidate template ignored: could not match 'reverse_iterator' against 'const comp'
operator<(const reverse_iterator<_Iterator>& __x,
^
/usr/bin/../lib/gcc/x86_64-linux-gnu/7.5.0/../../../../include/c++/7.5.0/bits/stl_iterator.h:346:5: note: candidate template ignored: could not match 'reverse_iterator' against 'const comp'
operator<(const reverse_iterator<_IteratorL>& __x,
^
/usr/bin/../lib/gcc/x86_64-linux-gnu/7.5.0/../../../../include/c++/7.5.0/bits/stl_iterator.h:1145:5: note: candidate template ignored: could not match 'move_iterator' against 'const comp'
operator<(const move_iterator<_IteratorL>& __x,
^
/usr/bin/../lib/gcc/x86_64-linux-gnu/7.5.0/../../../../include/c++/7.5.0/bits/stl_iterator.h:1151:5: note: candidate template ignored: could not match 'move_iterator' against 'const comp'
operator<(const move_iterator<_Iterator>& __x,
^
a.cpp:15:8: note: candidate function not viable: 'this' argument has type 'const comp', but method is not marked const
bool operator < (comp c) //运算符重载
^
2 warnings and 1 error generated.

结构体构造函数

【此处使用的是有参数版本】

• 首先注意结尾处没有分号
• 是初始化函数的简版：为了验证这个说法正确，我在源代码的基础上做了修改，如下所示：

struct comp{
  int real;
  int imag;
  //comp(int a,int b):real(a),imag(b){}
  comp(int a,int b)
  {
    this->real=a;
    this->imag=b;
  }
  bool operator < (comp c) const //运算符重载
  {
    if(real*real+imag*imag==c.real*c.real+c.imag*c.imag)
    	return imag > c.imag;//题目中并没有指出两个复数模一样大该如何计算，所以改为小于号也通过了
    else 
    	return real*real+imag*imag < c.real*c.real+c.imag*c.imag;//模小才为小
  }
};

代码部分

#include
#include
#include
using namespace std;

struct comp{
  int real;
  int imag;
  comp(int a,int b):real(a),imag(b){} //有参数结构体构造函数
  bool operator < (comp c) const //运算符重载
  {
    if(real*real+imag*imag == c.real*c.real+c.imag*c.imag)
    	return imag > c.imag;//题目中并没有指出两个复数模一样大该如何计算，所以改为小于号也通过了
    else 
    	return real*real+imag*imag < c.real*c.real+c.imag*c.imag;//模小才为小
  }
};

int main()
{
  int n;
  while(scanf("%d",&n)!=EOF)
  {
    priority_queue<comp> myqueue;
    while(n--)
    {
      string str;
      cin>>str;
      
      if(str=="Pop")
      {
        if(myqueue.empty())
        	printf("empty\n");
        else
        {
          printf("%d+i%d\n",myqueue.top().real,myqueue.top().imag);
          myqueue.pop();
          printf("SIZE = %d\n",myqueue.size());
        }
      }
      else
      {
        int a,b;
        scanf("%d+i%d",&a,&b);
        myqueue.push(comp(a,b));
        printf("SIZE = %d\n",myqueue.size());
      }
    }
  }
}