1. Standard Binary Search (Find Target Index)

Use when:

• array is sorted
• you need to find exact value

Problems

• Binary Search
• Search Insert Position

def binary_search(nums, target):
    left, right = 0, len(nums) - 1

    while left <= right:
        mid = (left + right) // 2

        if nums[mid] == target:
            return mid
        elif nums[mid] < target:
            left = mid + 1
        else:
            right = mid - 1

    return -1

2. Leftmost / First or Rightmost / Last Occurrence

Use when:

• duplicates exist
• want first or last index
• Modify condition:
  • move left/right even after finding target

Problems

• Find First and Last Position of Element in Sorted Array

def left_most(nums, target):
    left, right = 0, len(nums) - 1
    ans = -1

    while left <= right:
        mid = (left + right) // 2

        if nums[mid] >= target:
            if nums[mid] == target:
                ans = mid
            # continue checking left half
            right = mid - 1
        else:
            left = mid + 1

    return ans

def right_most(nums, target):
    left, right = 0, len(nums) - 1
    ans = -1

    while left <= right:
        mid = (left + right) // 2

        if nums[mid] <= target:
            if nums[mid] == target:
                ans = mid
            # continue checking right half
            left = mid + 1
        else:
            right = mid - 1

    return ans

3. Binary Search on Answer (VERY IMPORTANT)