Different Ways to Add Parentheses
问题描述
Given a string of numbers and operators, return all possible results from computing all the different possible ways to group numbers and operators. The valid operators are+
, -
and *
.
Example 1
Input: "2-1-1"
.
((2-1)-1) = 0 (2-(1-1)) = 2
Output: [0, 2]
Example 2
Input: "2*3-4*5"
(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
Output: [-34, -14, -10, -10, 10]
解决思路
其实挺巧妙的,主要参考https://leetcode.com/discuss/48488/c-4ms-recursive-method
理解这句话很重要:The key idea for this solution is: each operator in this string could be the last operator to be operated.
核心思想是递归,然后边界条件是输入的字符串仅为数字。
程序
public class DifferentWaysToCompute { public List<Integer> diffWaysToCompute(String input) { List<Integer> list = new ArrayList<Integer>(); for (int i = 0; i < input.length(); i++) { char c = input.charAt(i); if (c == '+' || c == '-' || c == '*') { // Split input string into two parts and solve them recursively List<Integer> left = diffWaysToCompute(input.substring(0, i)); List<Integer> right = diffWaysToCompute(input.substring(i+1)); // calculate each part for (int j = 0; j < left.size(); j++) { for (int k = 0; k < right.size(); k++) { if (c == '+') { list.add(left.get(j) + right.get(k)); } else if (c == '-') { list.add(left.get(j) - right.get(k)); }else { list.add(left.get(j) * right.get(k)); } } } } } if (list.isEmpty()) { // input string contains only number list.add(Integer.valueOf(input)); } return list; } }