阿木博主一句话概括：PL/I语言栈的实现与应用场景——表达式求值
阿木博主为你简单介绍：栈是一种先进后出（FILO）的数据结构，在程序设计中有着广泛的应用。本文将围绕PL/I语言栈的实现与应用场景——表达式求值展开，详细介绍栈在PL/I语言中的实现方法，并探讨其在表达式求值中的应用。
一、
表达式求值是计算机科学中一个基础且重要的课题，它广泛应用于编译原理、算法设计、程序设计等领域。在表达式求值过程中，栈作为一种重要的数据结构，发挥着至关重要的作用。本文将重点介绍PL/I语言中栈的实现与应用场景。
二、PL/I语言栈的实现
1. 栈的定义
在PL/I语言中，栈可以通过数组或指针实现。以下是一个使用数组实现的栈的定义：
DECLARE stack[1..100] CHAR(1) INITIALIZED;
DECLARE stack_top FIXED BINARY(31) DEFAULT 0;
其中，`stack` 是一个字符数组，用于存储栈中的元素；`stack_top` 是一个固定二进制数，用于指示栈顶元素的位置。
2. 栈的基本操作
栈的基本操作包括入栈（push）、出栈（pop）、判断栈空（is_empty）和判断栈满（is_full）。
（1）入栈（push）
入栈操作将一个元素添加到栈顶。以下是入栈操作的实现：
PROCEDURE push(x CHAR(1));
IF stack_top < 100 THEN
stack(stack_top + 1) := x;
stack_top := stack_top + 1;
ELSE
PUT SKIP LIST ('Stack is full');
END IF;
END push;
（2）出栈（pop）
出栈操作从栈顶移除一个元素。以下是出栈操作的实现：
PROCEDURE pop(OUT x CHAR(1));
IF stack_top > 0 THEN
x := stack(stack_top);
stack_top := stack_top - 1;
ELSE
PUT SKIP LIST ('Stack is empty');
END IF;
END pop;
（3）判断栈空（is_empty）
判断栈空操作用于检查栈是否为空。以下是判断栈空操作的实现：
FUNCTION is_empty RETURNS BOOLEAN;
is_empty := stack_top = 0;
END is_empty;
（4）判断栈满（is_full）
判断栈满操作用于检查栈是否已满。以下是判断栈满操作的实现：
FUNCTION is_full RETURNS BOOLEAN;
is_full := stack_top = 100;
END is_full;
三、栈在表达式求值中的应用
1. 中缀表达式求值
中缀表达式求值是表达式求值中的一个重要场景。以下是一个使用栈实现的中缀表达式求值的示例：
DECLARE operators CHAR(1) INITIALIZED;
DECLARE operands FIXED BINARY(31);
DECLARE operator_stack CHAR(1) INITIALIZED;
DECLARE operand_stack FIXED BINARY(31) INITIALIZED;
DECLARE operator_top FIXED BINARY(31) DEFAULT 0;
DECLARE operand_top FIXED BINARY(31) DEFAULT 0;
PROCEDURE evaluate_infix_expression(expression CHAR(1));
DECLARE i FIXED BINARY(31) DEFAULT 1;
DECLARE operator CHAR(1);
DECLARE operand FIXED BINARY(31);
DECLARE result FIXED BINARY(31);
WHILE expression(i) NOT = '' DO
IF expression(i) IN '+-/' THEN
WHILE NOT is_empty() AND operators(operand_stack(operand_top)) IN '+-/' THEN
pop(operand);
pop(operator);
result := CASE operator
WHEN '+' THEN operands(operand_stack(operand_top - 1)) + operands(operand_stack(operand_top))
WHEN '-' THEN operands(operand_stack(operand_top - 1)) - operands(operand_stack(operand_top))
WHEN '' THEN operands(operand_stack(operand_top - 1)) operands(operand_stack(operand_top))
WHEN '/' THEN operands(operand_stack(operand_top - 1)) / operands(operand_stack(operand_top))
END CASE;
operands(operand_stack(operand_top - 1)) := result;
operand_top := operand_top - 1;
END WHILE;
push(operators(expression(i)));
push(operands(expression(i)));
ELSE
push(operands(expression(i)));
END IF;
i := i + 1;
END WHILE;
WHILE NOT is_empty() DO
pop(operand);
pop(operator);
result := CASE operator
WHEN '+' THEN operands(operand_stack(operand_top - 1)) + operands(operand_stack(operand_top))
WHEN '-' THEN operands(operand_stack(operand_top - 1)) - operands(operand_stack(operand_top))
WHEN '' THEN operands(operand_stack(operand_top - 1)) operands(operand_stack(operand_top))
WHEN '/' THEN operands(operand_stack(operand_top - 1)) / operands(operand_stack(operand_top))
END CASE;
operands(operand_stack(operand_top - 1)) := result;
operand_top := operand_top - 1;
END WHILE;
PUT SKIP LIST ('Result:', result);
END evaluate_infix_expression;
evaluate_infix_expression('+-/123+456-7');
2. 后缀表达式求值
后缀表达式求值是另一种常见的表达式求值场景。以下是一个使用栈实现的后缀表达式求值的示例：
DECLARE operators CHAR(1) INITIALIZED;
DECLARE operands FIXED BINARY(31);
DECLARE operator_stack CHAR(1) INITIALIZED;
DECLARE operand_stack FIXED BINARY(31) INITIALIZED;
DECLARE operator_top FIXED BINARY(31) DEFAULT 0;
DECLARE operand_top FIXED BINARY(31) DEFAULT 0;
PROCEDURE evaluate_postfix_expression(expression CHAR(1));
DECLARE i FIXED BINARY(31) DEFAULT 1;
DECLARE operator CHAR(1);
DECLARE operand FIXED BINARY(31);
DECLARE result FIXED BINARY(31);
WHILE expression(i) NOT = '' DO
IF expression(i) IN '+-/' THEN
pop(operand);
pop(operator);
result := CASE operator
WHEN '+' THEN operands(operand_stack(operand_top - 1)) + operands(operand_stack(operand_top))
WHEN '-' THEN operands(operand_stack(operand_top - 1)) - operands(operand_stack(operand_top))
WHEN '' THEN operands(operand_stack(operand_top - 1)) operands(operand_stack(operand_top))
WHEN '/' THEN operands(operand_stack(operand_top - 1)) / operands(operand_stack(operand_top))
END CASE;
operands(operand_stack(operand_top - 1)) := result;
operand_top := operand_top - 1;
ELSE
push(operands(expression(i)));
END IF;
i := i + 1;
END WHILE;
WHILE NOT is_empty() DO
pop(operand);
pop(operator);
result := CASE operator
WHEN '+' THEN operands(operand_stack(operand_top - 1)) + operands(operand_stack(operand_top))
WHEN '-' THEN operands(operand_stack(operand_top - 1)) - operands(operand_stack(operand_top))
WHEN '' THEN operands(operand_stack(operand_top - 1)) operands(operand_stack(operand_top))
WHEN '/' THEN operands(operand_stack(operand_top - 1)) / operands(operand_stack(operand_top))
END CASE;
operands(operand_stack(operand_top - 1)) := result;
operand_top := operand_top - 1;
END WHILE;
PUT SKIP LIST ('Result:', result);
END evaluate_postfix_expression;
evaluate_postfix_expression('+-/123456789');
四、总结
本文介绍了PL/I语言中栈的实现方法，并探讨了其在表达式求值中的应用。通过栈，我们可以方便地实现中缀表达式和后缀表达式的求值。在实际应用中，栈作为一种重要的数据结构，在程序设计中具有广泛的应用前景。
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