利用栈解决括号匹配和逆波兰表达式

当我们学习了栈这种数据结构滞后，我们就可以利用栈来解决一些实际问题。

这里是我们给出的动态顺序栈的实现

template< class T>class Stack{public:Stack():_array(new T[3]), _size(0), _capacity(3){}void Push(const T& data){_Checkcapacity();_array[_size++] = data;}void Pop(){_size--;}bool Empty(){if (_size == 0)return true;return false;}T& Top(){return _array[_size-1];}T& Top()const{return _array[_size - 1];}size_t  Size(){return _size;}size_t Capacity(){return _capacity;}void  _Checkcapacity(){if (_size >= _capacity){T* newarray = new T[_size * 2 + 3];for (int i = 0; i < _size; i++){newarray[i] = _array[i];}_capacity = _size * 2 + 3;delete _array;_array = newarray;} }~Stack(){if (_array)delete _array;_array = NULL;_size = 0;_capacity = 0;}private:T * _array;int _size;int _capacity;};

1.括号匹配问题

char a[] = "(())abc{[(])}";//左右括号次序不对
char b[] = "(()))abc{[]}";//右括号多于左括号
char c[] = "(()()abc{[]}";//左括号多于右括号
char d[] = "(())abc{[]()}";///左右括号正确

bool MatchBrackets(char* c,int size)
{
 Stack<char> ch;
 for (int i = 0; i < size; i++)
 {
  if (c[i] == '(' || c[i] == '{' || c[i] == '[')
  {
   ch.Push(c[i]);
   continue;
  }
  else if (c[i] == ')' || c[i] == ']' || c[i] == '}')
  {
   if (ch.Empty())
   {
    cout << "右括号多于左括号" << endl;
    return true;
   }
   else
   {
    if ((c[i]==')'&&ch.Top()=='(')||(c[i] == ']'&&ch.Top() == '[')|| (c[i] == '}'&&ch.Top() == '{'))
    {
     ch.Pop();
     continue;
    }
    else {
     cout << "左右括号匹配次序不正确" << endl;
     return false;
    }
   }

  }
  else {
   continue;
  }
 }
 if (ch.Empty())
 {
  cout << "匹配正确" << endl;
  return true;
 }
 else {
  cout << "左括号多于右括号" << endl;
  return false;
 }

}

2.逆波兰表达式问题

实现代码：

enum op { OPERAND,OPERATOR, ADD, SUB, MUL, DIV };typedef struct Cell{op _op;int data; }Cell;int RPN(Cell*s, int size){Stack<int> c;for (int i = 0; i < size; i++){if (s[i]._op == OPERAND){c.Push(s[i].data);continue;}else if (s[i]._op == OPERATOR){int right = c.Top();c.Pop();int left = c.Top();c.Pop();switch (s[i].data){case ADD:c.Push(left + right);break;case SUB:c.Push(left - right);break;case MUL:c.Push(left*right);break;case DIV:assert(right != 0);c.Push(left / right);break;default:assert(0);break;}}}return c.Top();}

下面我们给出 表达式：

Cell A[] = { {OPERAND,12},{OPERAND,3},{OPERAND,4},{OPERATOR,ADD},{OPERATOR,MUL},{OPERAND,6},{OPERATOR,SUB},{OPERAND,8},{OPERAND,2},{OPERATOR,DIV},{OPERATOR,ADD} };

即 表达式 12*（3+4）-6+8/2  =82；

来看程序运行结果：

结果正确。