# Posts

• ## Leetcode: Square root of x

The task is to implement a square root method without using `math.sqrt` or `**` or `pow` or any similar function. Any digits after the decimal point do not to be returned. This is effectively the `floor(sqrt(n))` function. The first idea is to simply try out every number and multiply it with itself until the square root is found. If the next number is greater than `n`, return the previous number. This is however not very efficient as it has a time complexity of `O(sqrt(n))` in every case. To speed this process up, we can use binary search. The idea is to always double the size of the steps until we reach the target number or overshoot. If we overshoot, take half of the number and start at `1` again, then double, and so on.

The task is to add two binary numbers of various length. There is more than one possible solution. First, the basic solution which doesn’t use too many builtin Python functions works as follows: Reverse the strings containing the numbers. Then Iterate in a loop as long as we didn’t reach the end of both strings. Write the current position to a temporary variable if it’s still in the boundaries of the string. Then add a potential overflow and handle it if the sum of `a + b + overflow > 1`. Finally, check for the overflow at the end and add a `1` and reverse the string again before returning it. This can be solved much simpler with builtin Python functions.

• ## Leetcode: Plus one

A decimal number is given as a list of integers. The number should be incremented by `1`. The idea here is to iterate backwards through the list and start with the smallest digit. This way, this challenge can be solved in `O(n)`. If after adding `1`, the `mod(10)` is `0` it means we had an overflow and need to add one. If we didn’t we’re done and can break the loop. As a final check we need to make sure that there is no overflow in the end which would cause us to prepend the list.

• ## Leetcode: Climbing stairs

There is a given number of stairs `n`. Stairs can be either taken two steps at a time or one step at a time. For a height of `1`, there is only one possible solution: `1`. For a height of `2`, there are two solutions: `1-1` or `2`.

• ## Leetcode: Best time to buy and sell stock

The task is to find out of a series of stock prices the best time to buy and sell the stock. Only one stock can be owned at the time and it can be sold and bought at the same time.

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