start to 0 and end to len(nums) - 1.start is less than or equal to end:
a. Calculate mid as the midpoint between start and end.
b. If nums[mid] equals target, return true.
c. If nums[start] is less than nums[mid], the left half is sorted:
i. If target is between nums[start] and nums[mid], search the left half by setting end to mid - 1.
ii. Otherwise, search the right half by setting start to mid + 1.
d. If nums[start] is greater than nums[mid], the right half is sorted:
i. If target is between nums[mid] and nums[end], search the right half by setting start to mid + 1.
ii. Otherwise, search the left half by setting end to mid - 1.
e. If nums[start], nums[mid], and nums[end] are equal, we cannot determine the correct half, so we increment start and decrement end.false.