The book&#39;s website, [algorist.com][1] has a [wiki][2] with solutions.


  [1]: https://www.algorist.com/
  [2]: https://www.algorist.com/algowiki/index.php

How do you terminate a run in SBT without exiting?

I&#39;m trying CTRL+C but it exits SBT. Is there a way to only exit the running application while keeping SBT open?

SBT stop run without exiting

I have to invoke a PowerShell script from a batch file. One of the arguments to the script is a boolean value:

    C:\Windows\System32\WindowsPowerShell\v1.0\powershell.exe -NoProfile -File .\RunScript.ps1 -Turn 1 -Unify $false

The command fails with the following error:

    Cannot process argument transformation on parameter &#39;Unify&#39;. Cannot convert value &quot;System.String&quot; to type &quot;System.Boolean&quot;, parameters of this type only accept booleans or numbers, use $true, $false, 1 or 0 instead.

    At line:0 char:1
    +  &lt;&lt;&lt;&lt; &lt;br/&gt;
    + CategoryInfo          : InvalidData: (:) [RunScript.ps1], ParentContainsErrorRecordException &lt;br/&gt;
    + FullyQualifiedErrorId : ParameterArgumentTransformationError,RunScript.ps1

As of now I am using a string to boolean conversion inside my script. But how can I pass boolean arguments to PowerShell?


How to pass boolean values to a PowerShell script from a command prompt

The book is full of interesting questions, but since I am learning it myself, it would be a great help if I can find solutions to at least some of the questions. 

Anyone knows anything about this? 

Where can I find the solutions to &quot;The Algorithm Design Manual&quot;?

<p>The book is full of interesting questions, but since I am learning it myself, it would be a great help if I can find solutions to at least some of the questions.</p>
<p>Anyone knows anything about this?</p>


I tried writing an algorithm to simplify a decimal to a fraction and realized it wasn&#39;t too simple. 

Write `0.333333...` as `1/3` for example.

Or `0.1666667`, which is `1/6`.

Surprisingly I looked online and all the codes I found where either too long, or wouldn&#39;t work in some cases. What was even more annoying was that they didn&#39;t work for recurring decimals. I was wondering however whether there would be a mathematician/programmer here who understands all the involved processes in simplifying a decimal to a fraction. Anyone?

Algorithm for simplifying decimal to fractions

I had a look at [question][1] already which talk about algorithm to find loop in a linked list. I have read [Floyd&#39;s cycle-finding algorithm][2] solution, mentioned at lot of places that we have to take two pointers. One pointer( slower/tortoise ) is increased by one and other pointer( faster/hare ) is increased by 2. When they are equal we find the loop and if faster pointer reaches null there is no loop in the linked list.

Now my question is why we increase faster pointer by 2. Why not something else? Increasing by 2 is necessary or we can increase it by X to get the result. Is it necessary that we will find a loop if we increment faster pointer by 2 or there can be the case where we need to increment by 3 or 5 or x.


  [1]: https://stackoverflow.com/questions/2663115/interview-question-how-to-detect-a-loop-in-a-linked-list
  [2]: http://en.wikipedia.org/wiki/Cycle_detection#Tortoise_and_hare

Why increase pointer by two while finding loop in linked list, why not 3,4,5?

The famous Fisher-Yates shuffle algorithm can be used to randomly permute an array A of length N:

    For k = 1 to N
        Pick a random integer j from k to N
        Swap A[k] and A[j]

A common mistake that I&#39;ve been told over and over again not to make is this:

    For k = 1 to N
        Pick a random integer j from 1 to N
        Swap A[k] and A[j]

That is, instead of picking a random integer from k to N, you pick a random integer from 1 to N.

What happens if you make this mistake?  I know that the resulting permutation isn&#39;t uniformly distributed, but I don&#39;t know what guarantees there are on what the resulting distribution will be.  In particular, does anyone have an expression for the probability distributions over the final positions of the elements?

What distribution do you get from this broken random shuffle?

I&#39;m trying to find an efficient, numerically stable algorithm to calculate a rolling variance (for instance, a variance over a 20-period rolling window). I&#39;m aware of the [Welford algorithm][1] that efficiently computes the running variance for a stream of numbers (it requires only one pass), but am not sure if this can be adapted for a rolling window. I would also like the solution to avoid the accuracy problems discussed at the top of [this article][2] by John D. Cook. A solution in any language is fine.


  [1]: http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Online_algorithm
  [2]: http://www.johndcook.com/standard_deviation.html

Rolling variance algorithm

There are dozens of ways of computing F(n) for an arbitrary n, many of which have great runtime and memory usage.

However, suppose I wanted to ask the opposite question:

&gt; Given F(n) for n &gt; 2, what is n?

(The n &gt; 2 restriction is in there since F(1) = F(2) = 1 and there&#39;s no unambiguous inverse).

What would be the most efficient way of solving this problem?  It&#39;s easy to do this in linear time by enumerating the Fibonacci numbers and stopping when you hit the target number, but is there some way of doing this any faster than that?

**EDIT:** currently, the best solution posted here runs in O(log n) time using O(log n) memory, assuming that mathematical operations run in O(1) and that a machine word can hold any number in O(1) space.  I&#39;m curious if it&#39;s possible to drop the memory requirements, since you can compute Fibonacci numbers using O(1) space.

Content Type	Original Author	Original Content on Stackoverflow
Question	Steve	View Question on Stackoverflow
Solution 1 - Algorithm	corsiKa	View Answer on Stackoverflow

Where can I find the solutions to "The Algorithm Design Manual"?

Algorithm Problem Overview

Algorithm Solutions

Solution 1 - Algorithm

How to pass boolean values to a PowerShell script from a command prompt

SBT stop run without exiting

Attributions