two_sum.py

"""
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 two_sum
should return indices of the two numbers such that they add up to the target,
where index1 must be less than index2. Please note that 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.

Input: numbers = [2, 7, 11, 15], target=9
Output: index1 = 1, index2 = 2

Solution:
two_sum: using binary search
two_sum1: using dictionary as a hash table
two_sum2: using two pointers
"""

def two_sum(numbers, target):
    """
    Given a list of numbers sorted in ascending order, find the indices of two
    numbers such that their sum is the given target.

    Using binary search.
    """
    for i, number in enumerate(numbers):
        second_val = target - number
        low, high = i+1, len(numbers)-1
        while low <= high:
            mid = low + (high - low) // 2
            if second_val == numbers[mid]:
                return [i + 1, mid + 1]

            if second_val > numbers[mid]:
                low = mid + 1
            else:
                high = mid - 1
    return None

def two_sum1(numbers, target):
    """
    Given a list of numbers, find the indices of two numbers such that their
    sum is the given target.

    Using a hash table.
    """
    dic = {}
    for i, num in enumerate(numbers):
        if target - num in dic:
            return [dic[target - num] + 1, i + 1]
        dic[num] = i
    return None

def two_sum2(numbers, target):
    """
    Given a list of numbers sorted in ascending order, find the indices of two
    numbers such that their sum is the given target.

    Using a bidirectional linear search.
    """
    left = 0                      # pointer 1 holds from left of array numbers
    right = len(numbers) - 1       # pointer 2 holds from right of array numbers
    while left < right:
        current_sum = numbers[left] + numbers[right]
        if current_sum == target:
            return [left + 1, right + 1]

        if current_sum > target:
            right = right - 1
        else:
            left = left + 1