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Here is one I have been playing with.

Factorials and Fibonacci numbers are traditionally used as examples of recursive functions.

Let's see them done without recursion with reasonable timing.

I apologize for not coming up with a new one this week, but I will post a few freebies.

I discovered discord, and I spent too much free time helping 8th graders do their home work :) Or so it would appear.

Okay, so my solution didn't meet the O(n+m) complexity. But Iound the correct algorithm, and both are in place and the code is updated. @freemo this was kind of interesting, reminds me of an old card trick I used to do.

Second Freebie!!! This one is marked as "easy"

This problem was asked by Google.

Given two singly linked lists that intersect at some point, find the intersecting node. The lists are non-cyclical.

For example, given A = 3 -> 7 -> 8 -> 10 and B = 99 -> 1 -> 8 -> 10, return the node with value 8.

In this example, assume nodes with the same value are the exact same node objects.

Do this in O(M + N) time (where M and N are the lengths of the lists) and constant space.

Freebie!! Here you go!
This problem was asked by Facebook.

A builder is looking to build a row of N houses that can be of K different colors. He has a goal of minimizing cost while ensuring that no two neighboring houses are of the same color.

Given an N by K matrix where the nth row and kth column represents the cost to build the nth house with kth color, return the minimum cost which achieves this goal.

Here's a freebie. They labeled it as "Hard"

This problem was asked by Google.

Suppose we represent our file system by a string in the following manner:

The string "dir\n\tsubdir1\n\tsubdir2\n\t\tfile.ext" represents:

dir
subdir1
subdir2
file.ext
The directory dir contains an empty sub-directory subdir1 and a sub-directory subdir2 containing a file file.ext.

The string "dir\n\tsubdir1\n\t\tfile1.ext\n\t\tsubsubdir1\n\tsubdir2\n\t\tsubsubdir2\n\t\t\tfile2.ext" represents:

dir
subdir1
file1.ext
subsubdir1
subdir2
subsubdir2
file2.ext
The directory dir contains two sub-directories subdir1 and subdir2. subdir1 contains a file file1.ext and an empty second-level sub-directory subsubdir1. subdir2 contains a second-level sub-directory subsubdir2 containing a file file2.ext.

We are interested in finding the longest (number of characters) absolute path to a file within our file system. For example, in the second example above, the longest absolute path is "dir/subdir2/subsubdir2/file2.ext", and its length is 32 (not including the double quotes).

Given a string representing the file system in the above format, return the length of the longest absolute path to a file in the abstracted file system. If there is no file in the system, return 0.

Note:

The name of a file contains at least a period and an extension.

The name of a directory or sub-directory will not contain a period.

Okay, this is a big one (description-wise) but basically the idea is to build a Monte Carlo simulation craps simulator to observe strategic differences between "Pass", "Don't Pass", with and without odds.

Here is a description of the necessary craps rules. Ask whatever questions that I haven't made clear.
git.qoto.org/Absinthe/crapssim

This one is super free! It is not a programming problem so much as a BASH problem.

Using bash parameter expansion only gnu.org/software/bash/manual/h

Given an arbitrarily long path, such as "/head/shoulders/knees/and/toes/eyes/ears/mouth" stored in a variable $TEMP construct a parameter expansion to render only the last two subdirectory and filename like "eyes/ears/mouth" such that you can simply offer the command "echo ${TEMP<stuff goes in here>}"

And yes I do know how much easier it is to do with grep, sed, python, perl, awk <insert your favorite alternate solution here> can do it better and easier. This is a real world problem, and someone on Reddit pointed me in the right direction.

I think I may have an idea for the problem this week. Who likes "Craps?" I will work on the specifics, and think of some additional what-ifs as well.

Here is my attempt in python

git.qoto.org/Absinthe/montecar

I tried it basing on a sample size of attempts, and also trying until I got so many successful points in circle.

c++ solution 

Here's another freebie, but I am not really sure how to solve it. Guess I wouldn't be getting that job at Google :)

This problem was asked by Google.

The area of a circle is defined as πr^2. Estimate π to 3 decimal places using a Monte Carlo method.

Hint: The basic equation of a circle is x2 + y2 = r2.

Here's a fun freebie! Only because I just recently saw a problem similar :)

This problem was asked by Facebook.

Given a stream of elements too large to store in memory, pick a random element from the stream with uniform probability.

Here's another freebie:

This problem was asked by Amazon.

Given an integer k and a string s, find the length of the longest substring that contains at most k distinct characters.

For example, given s = "abcba" and k = 2, the longest substring with k distinct characters is "bcb".

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