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leetCode-241:Different Ways to Add Parentheses

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问题描述

给定一个表达式字符串，只包含数字和 +、-、* 符号，要求找出所有为表达式增加括号后的计算结果。题目链接：**点我**

样例输入输出

输入：”2-1-1”

输出：[0,2]

解释：

((2-1)-1) = 0
(2-(1-1)) = 2

输入：”2*3-4*5”

输出：[-34,-14,-10,-10,10]

解释：

(2*(3-(4*5))) = -34
((2*3)-(4*5)) = -14
((2*(3-4))*5) = -10
(2*((3-4)*5)) = -10
(((2*3)-4)*5) = 10

问题解法

直接根据题目要求，使用递归方式找出所有为表达式添加括号的式子，计算其结果，进行汇总。为了减少重复计算，可以使用一个 map 将计算过的表达式的值存起来，方便下次直接取用。代码如下

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class Solution
{
    public List<Integer> diffWaysToCompute(String expression)
    {
        Map<String, List<Integer>> map = new HashMap<>();
        return diffWaysToCompute(expression, map);
    }

    private List<Integer> diffWaysToCompute(String expression, Map<String, List<Integer>> map)
    {
        if (map.containsKey(expression))
        {
            return map.get(expression);
        }

        List<Integer> result = new ArrayList<>();
        if (getNextOpIndex(expression, 0) == -1)
        {
            result.add(Integer.parseInt(expression));
            map.put(expression, result);
            return result;
        }

        int len = expression.length();
        for (int i = 0; i < len; )
        {
            int index = getNextOpIndex(expression, i);
            if (index == -1)
            {
                break;
            }

            List<Integer> left = diffWaysToCompute(expression.substring(0, index), map);
            List<Integer> right = diffWaysToCompute(expression.substring(index + 1), map);
            result.addAll(calc(left, right, expression.charAt(index)));

            i = index + 1;
        }

        map.put(expression, result);
        return result;
    }

    private int getNextOpIndex(String expression, int start)
    {
        for (int i = start; i < expression.length(); i++)
        {
            if (!Character.isDigit(expression.charAt(i)))
            {
                return i;
            }
        }

        return -1;
    }

    private List<Integer> calc(List<Integer> left, List<Integer> right, char op)
    {
        List<Integer> result = new ArrayList<>();
        for (Integer leftValue : left)
        {
            for (Integer rightValue : right)
            {
                int value;
                if (op == '+')
                {
                    value = leftValue + rightValue;
                }
                else if (op == '-')
                {
                    value = leftValue - rightValue;
                }
                else
                {
                    value = leftValue * rightValue;
                }

                result.add(value);
            }
        }

        return result;
    }
}