Today I'm going to go over three solutions to the popular leetcode question Two Sum.

The question is this: given an array of numbers and a target number, return the indices of two numbers that add up to the target number.

Solutions:

- O(n^2) time, O(1) space We can use two for loops to loop through the array and find the indices of the two numbers that add up to the target number.

```
class Solution:
def twoSum(self, nums: List[int], target: int) -> List[int]:
for i in range(len(nums)):
for j in range(i+1, len(nums)):
if nums[i] + nums[j] == target:
return [i, j]
```

- O(n) time, O(n) space We can use a hash table to store the numbers as keys and the indices as values. Then we check to see if the difference (target - number) is in the hash table. If it is, return both the index of the number and the index of the difference.

```
class Solution:
def twoSum(self, nums: List[int], target: int) -> List[int]:
values = {}
for i, num in enumerate(nums):
diff = target - num
if diff in values:
return [i, values[diff]]
values[num] = i
return []
```

- O(nlogn) time, O(1) space You can use the two pointer method. After sorting the array and creating an array of the numbers and their indices, create two pointers i and j where i = 0 and j = len(array)-1. If the sum is smaller than target, increment i, if larger, increment j. If equal, return the indices.

```
class Solution:
def twoSum(self, nums: List[int], target: int) -> List[int]:
i = 0
j = len(nums) - 1
sortedNums = sorted(zip(nums, range(len(nums))))
while i < j:
if sortedNums[i][0] + sortedNums[j][0] == target:
return [sortedNums[i][1], sortedNums[j][1]]
elif sortedNums[i][0] + sortedNums[j][0] < target:
i += 1
elif sortedNums[i][0] + sortedNums[j][0] > target:
j -= 1
```

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