如果公式格式不正确或缺少括号，则可能发生“索引越界”错误。要修复错误并确保代码正确处理边界，可以按如下方式修改代码：
python代码修复了边界问题：

def evaluate_formula(formula, variables, values):
    stack = []
    for char in formula:
        if char == '(':
            stack.append(char)
        elif char == ')':
            # Check for empty stack or missing opening parenthesis
            if not stack or stack[-1] != '(':
                return None

            while stack[-1] != '(':
                operator = stack.pop()
                operand2 = stack.pop()
                operand1 = stack.pop()
                if operator == '&':
                    stack.append(operand1 and operand2)
                elif operator == '|':
                    stack.append(operand1 or operand2)

            # Pop the opening parenthesis
            stack.pop()
        elif char in variables:
            if char in values:
                stack.append(values[char])
            else:
                return None
        elif char == '~':
            if stack and stack[-1] == '~':
                stack.pop()
                if stack and stack[-1] == '(':
                    return None
            else:
                stack.append('~')
        elif char in ['&', '|']:
            stack.append(char)

    # Ensure that there is only one element in the stack and it's a boolean
    if len(stack) == 1 and type(stack[0]) == bool:
        return stack[0]
    else:
        return None

java代码：
保存为：FormulaEvaluator.java

import java.util.Stack;

public class FormulaEvaluator {
    public static Boolean evaluateFormula(String formula, String[] variables, Boolean[] values) {
        Stack<Object> stack = new Stack<>();
        for (char c : formula.toCharArray()) {
            if (c == '(') {
                stack.push(c);
            } else if (c == ')') {
                if (stack.isEmpty() || !stack.peek().equals('(')) {
                    return null;
                }
                stack.pop(); // Remove the opening parenthesis

                while (!stack.isEmpty() && stack.peek() instanceof Boolean) {
                    Boolean operand2 = (Boolean) stack.pop();
                    char operator = (char) stack.pop();
                    Boolean operand1 = (Boolean) stack.pop();

                    if (operator == '&') {
                        stack.push(operand1 && operand2);
                    } else if (operator == '|') {
                        stack.push(operand1 || operand2);
                    }
                }
            } else if (contains(variables, c)) {
                int index = getIndex(variables, c);
                if (index != -1) {
                    stack.push(values[index]);
                } else {
                    return null;
                }
            } else if (c == '~') {
                if (!stack.isEmpty() && stack.peek().equals('~')) {
                    stack.pop();
                    if (!stack.isEmpty() && stack.peek().equals('(')) {
                        return null;
                    }
                } else {
                    stack.push('~');
                }
            } else if (c == '&' || c == '|') {
                stack.push(c);
            }
        }

        if (stack.size() == 1 && stack.peek() instanceof Boolean) {
            return (Boolean) stack.peek();
        } else {
            return null;
        }
    }

    private static boolean contains(String[] array, char c) {
        for (String s : array) {
            if (s.equals(String.valueOf(c))) {
                return true;
            }
        }
        return false;
    }

    private static int getIndex(String[] array, char c) {
        for (int i = 0; i < array.length; i++) {
            if (array[i].equals(String.valueOf(c))) {
                return i;
            }
        }
        return -1;
    }
}

使用 char 值 0 和 1 来表示 bool 值。

Character evaluateFormula(String formula, String variables, String values) {
    Deque<Character> stack = new ArrayDeque<>();
    for (char c : formula.toCharArray())
        if (c == '(')
            stack.add(c);
        else if (c == ')')
            while (stack.getLast() != '(') {
                char operator = stack.pop();
                boolean operand2 = stack.pop() == 1;
                boolean operand1 = stack.pop() == 1;
                if (operator == '&') 
                    stack.add((char) (operand1 && operand2 ? 1 : 0));
                else if (operator == '|') 
                    stack.add((char) (operand1 || operand2 ? 1 : 0));
            }
        else if (variables.contains(String.valueOf(c)))
            if (values.contains(String.valueOf(c)))
                stack.add(values.charAt(c))
            else
                return null;
        else if (c == '~')
            if (!stack.isEmpty() && stack.getLast() == '~') {
                stack.pop();
                if (!stack.isEmpty() && stack.getLast() == '(')
                    return null;
            } else
                stack.add('~');
        else if (c == '&' || c == '|')
            stack.add(c);

    if (stack.size() == 1 && stack.getFirst() <= 1)
        return stack.getFirst();
    else
        return null;
}

这里是一个优化的版本，用于重用变量。

import static java.lang.String.valueOf;

Character evaluateFormula(String formula, String variables, String values) {
    Deque<Character> s = new ArrayDeque<>();
    char op;
    boolean op1, op2;
    for (char c : formula.toCharArray())
        switch (c) {
            case '(', '&', '|' -> s.add(c);
            case ')' -> {
                while (s.getLast() != '(') {
                    op = s.pop();
                    op1 = s.pop() == 1;
                    op2 = s.pop() == 1;
                    if (op == '&') s.add((char) (op1 && op2 ? 1 : 0));
                    else if (op == '|') s.add((char) (op1 || op2 ? 1 : 0));
                }
            }
            case '~' -> {
                if (!s.isEmpty() && s.getLast() == '~') {
                    s.pop();
                    if (!s.isEmpty() && s.getLast() == '(') return null;
                } else s.add('~');
            }
            default -> {
                if (variables.contains(valueOf(c)))
                    if (values.contains(valueOf(c))) s.add(values.charAt(c));
                    else return null;
            }
        }
    if (s.size() == 1 && s.getFirst() <= 1) return s.getFirst();
    else return null;
}