CLRS 22.3-1, How Come Solutions Online State There Can’t Be Edges From WHITE to GRAY nodes “at any point… during search”?

The exercise (from the book Introduction To Algorithms) states

Make a 3-by-3 chart with row and column labels WHITE, GRAY,and BLACK. In each cell (i, j) indicate whether, at any point during a depth-first search of a di- rected graph, there can be an edge from a vertex of color i to a vertex of color j . For each possible edge, indicate what edge types it can be. Make a second such chart for depth-first search of an undirected graph.

The colors WHITE, GRAY, BLACK correspond to Undiscovered, discovered but not finished, and finished. The following solution is what multiple sites & universities have posted(such as: walkccc, Rutgers University):

 |       | WHITE         | GRAY                | BLACK                | |-------|---------------|---------------------|----------------------| | WHITE | All kinds     | Cross, Back         | Cross                | | GRAY  | Tree, Forward | Tree, Forward, Back | Tree, Forward, Cross | | BLACK | -             | Back                | All kinds            | 

I will draw a minimal counter example as it helps understand my conflict:


  • Start at node 0: 0 is GRAY
  • At this point, 3 is still white and has an edge to 0
  • Resume and keep going, eventually the edge from 3 to 0 will be discovered as a tree edge

This contradicts the solutions saying you can only have Cross/Back edges going form WHITE->GRAY. This example can be easily modified to contradict many of the elements in the table. I think the solutions are doing one of the following:

  • Assuming that the graph is a tree and that we start at its root. (Wrong as DFS doesn’t need a tree graph and any node can be started from).
  • More likely (Just thought of this), interpreting the question of "can there be an edge" as "can there be an edge that we have discovered". In which case, the solutions work, as although the edge from 3->0 was a WHITE->GRAY edge at one point, we hadn’t discovered it yet.

Discover People by Phone Number – Should You Use a Reverse Phone Trace, Search Engine

The short answer is that converse telephone follow administrations or opposite mobile phone queries are the most effective of the three hunt techniques. At the point when you have to find somebody with their telephone number, the primary response is to go to the web crawlers and interpersonal interaction locales and either run name follow or number follow. Mobile Database Yet, in the event that you don’t have the foggiest idea, this is just about the most wasteful way to deal with attempt and discover individuals by telephone number. Most likely, the web indexes will run an extensive rundown of results, however the better piece of the rundown is excess with disconnected data you needn’t bother with. You will likewise need to know the name, epithet or number to follow the individual, As we as a whole know, not every person utilize their genuine names on these locales which actually makes scanning for the genuine character troublesome.

Utilizing open telephone indexes could likewise present challenges for your undertakings to discover individuals by telephone number. You have to initially characterize the sort of telephone numbers you are following. On the off chance that you are searching for proprietor data ashore lines, you will show signs of improvement results with the free open telephone catalogs as land lines are open space and thus naturally turns out to be free open data. Be that as it may, should you be looking for versatile number subtleties, you won’t get any outcome from open telephone indexes. This is basically because of the way that these are not arranged as free open data. To follow hand telephone numbers, you will require the opposite mobile phone queries.

So since you know the motivation behind why you have not been fruitful you would at long last understand that the best strategy is to utilize the converse telephone follow. The administration basically permits you to enter a number into the inquiry box and the framework will run a match with its database to create a full report for you on the hand telephone proprietor subtleties. Any legitimate assistance ought to have the option to give the necessary data in practically no time and not need to make you hang tight 24 hours for it. There is a little expense when you join the enrollment which actually costs not exactly a decent feast.

Google Search Console: Content wider than screen [closed]

The Google Search Console says that my website content is wider than the screen. That’s very weird because I checked everything, the only element it may out of the screen (the navigation bar (nav tag more exactly)) is default inside, and after JavaScript execution, it may be outside (but with display: none).

How I should debug it? It doesn’t give me any information about the element or where is this happening.

2 Super Easy Ways To Save Money On Paid Captcha Services When Using GSA Search Engine Ranker

Many GSA Search Engine Ranker Users are making use of 3rd party captcha solving services which they have to pay for the number of solved captchas. If you are running allot of GSA SER projects with multiple tiers then paying for these paid captchas  can be very expensive, very quickly.

So since we all can do with saving a bit of money where possible, i will show you 2 very easy ways you can reduce the cost of captchas your paid captchas. Some of you might already be aware of these methods and many of you are not aware of them, so read further to see how to save money with your paid captchas and GSA Search Engine Ranker.

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Range search in a max-heap


I am having trouble with coming up for a suitable algorithm for this question. A max-heap is essentially visualized as a binary tree not a binary search tree. Also the runtime of the algorithm must depend only on the number of elements in the output. I was thinking of doing a preorder traversal on the max heap. While doing the preorder traversal, if the value of a node is less than the given value x, we return to the previous recursive call. All child nodes in a max heap are less than the parent node. Otherwise we output current node and recur on the children.

I am not sure however if the runtime of this algorithm depends only on the number of elements in the output.

Anybody have other suggestions/thoughts? Thanks.

Izito and similar sites keeps appearing in my search results

Izito and similar sites keep appearing on my search engine results. It started a few weeks ago. It has been happening on both – my Ubuntu and Windows computer, and even on a new Windows computer. It has been happening on Chrome and Microsoft Edge and on Google and Bing. I have since installed Bitdefender AV and done factory resets and it still keeps coming back after a while. I was wondering if someone could please advise on what might be causing it, what damage / impact it might (have) caused, and how I could get rid of it.

Runtime for Search in Unordered_map C++ [closed]

I have come across lot of articles and questions suggesting that unordered_map is a lookup table that offers O(1) search time complexity. And I wonder how this is possible, And they say it is amortized to O(1) and worst case is O(n) for lookup. Now, even though after an extensive search I haven’t found when this lookup time hits O(n) and how actually unordered_map is implemented under the hood?