Given an array of integers that is already sorted in ascending order, find two numbers such that they add up to a specific target number.
The function twoSum should return indices of the two numbers such that they add up to the target, where index1 must be less than index2.
Note:
- Your returned answers (both index1 and index2) are not zero-based.
- You may assume that each input would have exactly one solution and you may not use the same element twice.
Example:
Input: numbers = [2,7,11,15], target = 9
Output: [1,2]
Explanation: The sum of 2 and 7 is 9. Therefore index1 = 1, index2 = 2.
来自 <https://leetcode.com/problems/two-sum-ii-input-array-is-sorted/description/>
思路1：最简单直接的做法
1 class Solution(object): 2 def twoSum(self, numbers, target): 3 """ 4 :type numbers: List[int] 5 :type target: int 6 :rtype: List[int] 7 """ 8 length = len(numbers) 9 for i in range(length): 10 for j in range(1,length-i): 11 if numbers[i] + numbers[i + j] == target: 12 return i + 1, i + j + 1
思路2: 发现上面的做法将会超时，问题出现在最后一个测试样例，最后一个测试样例有许多重复样本，考虑先去除重复样本，减小计算花费
1 class Solution(object): 2 def twoSum(self, numbers, target): 3 """ 4 :type numbers: List[int] 5 :type target: int 6 :rtype: List[int] 7 """ 8 new_numbers = [] 9 counts = [] 10 for i in numbers: 11 if new_numbers in new_numbers: 12 counts[-1] += 1 13 else: 14 new_numbers.append(i) 15 counts.append(1) 16 17 length = len(new_numbers) 18 for i in range(length): 19 for j in range(1, length - i): 20 if new_numbers[i] + new_numbers[i + j] == target: 21 pos_1 = pos_2 = 1 22 for k in range(i): 23 pos_1 += counts[k] 24 for q in range(i + j): 25 pos_2 += counts[q] 26 return pos_1, pos_2
思路3：以上做法还是会超时，对于每个选中的元素，改用二分查找的做法查找另一个相加数
1 class Solution(object): 2 def twoSum(self, numbers, target): 3 """ 4 :type numbers: List[int] 5 :type target: int 6 :rtype: List[int] 7 """ 8 length = len(numbers) 9 for i in range(length): 10 p = i 11 q = length 12 while q - p > 1: 13 mid = (p + q) // 2 14 if numbers[i] + numbers[mid] == target: 15 return i + 1, mid + 1 16 elif numbers[i] + numbers[mid] < target: 17 p = mid 18 else: 19 q = mid
思路4：使用两个坐标，朝中间遍历
1 class Solution(object): 2 def twoSum(self, numbers, target): 3 """ 4 :type numbers: List[int] 5 :type target: int 6 :rtype: List[int] 7 """ 8 length = len(numbers) 9 i = 0 10 j = length - 1 11 while j - i >= 1: 12 if numbers[i] + numbers[j] == target: 13 return i + 1, j + 1 14 elif numbers[i] + numbers[j] < target: 15 i = i + 1 16 else: 17 j = j - 1