## Sunday, June 30, 2013

### Generalized Tower of Hanoi - K Pegs, N Disks

I recently found online that Facebook is giving a fast track job opportunity for those who would solve a specific problem which may be a little more complex than a simple interview question. The process happens online - you login with your Facebook id and have a specific amount of time to write a solution in the language you desire. Here's the url in case you want to try it. They also provide a sample problem and an allotted 45 minutes to solve it. The problem is the well known Tower of Hanoi puzzle but generalized to k pegs and n disks. Given an initial and final configuration of the pegs you have to output the minimal number of steps needed to reach the final configuration. To make it easier they bound the k and n to 1 <= n <= 8, 3 <= k <= 5 and let you assume that there's a solution that takes at least 7 steps.

One basic approach here is brute forcing all possible configurations which results in an undirected graph. And how do you find something in a graph ? Using a search strategy - in my case I chose Breath-First Search.

Before going into the details of this approach let's see what other approaches we can find. Brute forcing will generate in the worst case 5^8 (390625) different configurations and then we'll have to search through them. Is there any other way where we wouldn't do a brute force, but go through the minimal path the first time? It seems like we could use different strategies of navigating through the pegs of a Hanoi Tower. There's basically 3 configuration cases that will take different approaches in navigation. Those are n < k, n=k and n > k. The point is there's a specific move pattern for each of these cases, that you could do to achieve the desired configuration. This article goes into much detail on that. There's also the way of multi-threading - we could parallelize this in some way - for example we could start from both ends.

I chose the brute force this time. While coding this approach a few problems may arise; mainly the problem of how would you represent the pegs. I chose to use a byte array, where each cell represents a peg and each bit of a peg represents a disk (if set).

Code looks like this:

Note:
The findLowestBitSet method basically returns the number of trailing zeros. In Java there's a util method for that:

The method could be optimized to look like this:

1. Could you please explain the algorithm with some example , i am not able to follow it.In which order you are moving disks?
With what values searchPath() , start[] and end[] array are filled with while calling it?

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41. Holders Real Madrid will reach the UEFA Champions League semi-final provided they
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43. After a quick explosion in Game 4 where Isaiah Thomas knocked down his first five three-point attempts,
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After three subpar games, Beal showed up big time in Game 4 with a team-high 29 points including going 3-6 from three-point range.
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49. The United States Golf Association (USGA) has announced sectional qualifying sites for the 117th US Open 2017 Championship, which will be held at Erin Hills, in Erin, Wis., on June 15-18. Erin Hills is hosting its first U.S. Open and third USGA championship.

Sectional qualifying, conducted over 36 holes, will be held on Monday, June 5, at 10 sites in the U.S. For the 13th consecutive year, Japan and England will host international sectional qualifying, scheduled for May 22 and May 29, respectively.

50. The United States Golf Association (USGA) has announced sectional qualifying sites for the 117th US Open 2017 Championship, which will be held at Erin Hills, in Erin, Wis., on June 15-18. Erin Hills is hosting its first U.S. Open and third USGA championship.

Sectional qualifying, conducted over 36 holes, will be held on Monday, June 5, at 10 sites in the U.S. For the 13th consecutive year, Japan and England will host international sectional qualifying, scheduled for May 22 and May 29, respectively.

51. The long ushered super fight that fans dared Golden Boy promoter,
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Canelo Alvarez versus Gennady Golovkin is set for the 26th of September at the T-Mobile Arena, Las Vegas.
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Yee haw shouted ghosts of super fights gone by, one super fight in the mail, signed and sealed. Boxing fans
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53. The Wallabies must successfully target dynamic All Blacks second rowers Brodie Retallick and
Sam Whitelock when they attempt to turn their Bledisloe Cup fortunes around, says Australian backrower
Rory Arnold.The formidable duo of Retallick and Whitelock has been one of the great strengths of the world
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Whitelock has tasted defeat just three times in 20 games Tests against Australia and Retallick once in 15.
Rising Wallabies lock Rory ­Arnold said getting an edge over the duo was key for his team.“They’ve been world-class
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“We’re going to have to be at our best, the second-rowers, to take those blokes on.”
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While Whitelock and Retallick have been a constant force for New Zealand,
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Coach Michael Cheika used five starting second-row combinations in the first five Tests of 2016 and seven in total across the season as
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In the June Tests, Cheika started with Adam Coleman and Sam Carter and then brought in Arnold for the last match.
“He sort of swapped and changed a fair bit last year, so I’m not sure how he’s going to go this year with those second-row spots,” Arnold said.

54. The Wallabies must successfully target dynamic All Blacks second rowers Brodie Retallick and
Sam Whitelock when they attempt to turn their Bledisloe Cup fortunes around, says Australian backrower
Rory Arnold.The formidable duo of Retallick and Whitelock has been one of the great strengths of the world
champion All Blacks’ forward ­machine in recent years and both are used to winning against the Wallabies.
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Whitelock has tasted defeat just three times in 20 games Tests against Australia and Retallick once in 15.
Rising Wallabies lock Rory ­Arnold said getting an edge over the duo was key for his team.“They’ve been world-class
locks now for a number of years, so if we want to dominate up front we know we’ve got to go at those blokes,” said Arnold.
“We’re going to have to be at our best, the second-rowers, to take those blokes on.”
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While Whitelock and Retallick have been a constant force for New Zealand,
Australia have chopped and changed their second-row combinations since the 2015 World Cup final against the All Blacks.
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Coach Michael Cheika used five starting second-row combinations in the first five Tests of 2016 and seven in total across the season as
six different locks got an opportunity in the run-on side.
In the June Tests, Cheika started with Adam Coleman and Sam Carter and then brought in Arnold for the last match.
“He sort of swapped and changed a fair bit last year, so I’m not sure how he’s going to go this year with those second-row spots,” Arnold said.

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59. The McGregor vs Mayweather is on! The worst kept secret in the fight has finally been revealed with the superclassification that will take place later this summer.
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Mayweather vs McGregor Fight Date, Time and TV Channel: Our guide reveals what you really need to know about the year’s biggest boxing showdown.

60. The SummerSlam 2017 is an upcoming professional wrestling pay-per-view (PPV)

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61. deserves any and all criticism levied against him in regards to his personal conduct, but one thing that can never be put in doubt is his near-divine boxing talents.
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It’s almost unfair how gifted Mayweather is as a boxer. Like a video game character, the 40-year-old possesses god-like hand speed, quick feet, an almost-psychic ability to predict what his opponent wants to do, otherworldly spatial awareness and impossible reactions.

62. Mayweather deserves any and all criticism levied against him in regards to his personal conduct, but one thing that can never be put in doubt is his near-divine boxing talents.
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It’s almost unfair how gifted Mayweather is as a boxer. Like a video game character, the 40-year-old possesses god-like hand speed, quick feet, an almost-psychic ability to predict what his opponent wants to do, otherworldly spatial awareness and impossible reactions.

63. With the late withdrawal of second-seeded Andy Murray, Zverev was the highest seed in his half of the draw, and he had a golden opportunity to make a deep run at a Grand Slam tournament for the first time.
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But he still has not made it past the second round at the United States Open. And his best result at a Grand Slam event is reaching the fourth round at Wimbledon this year.

64. American Made 2017 Full Movie Watch Online, American Made is a 2017 American biographical crime film directed by Doug Liman, written by Gary Spinelli and starring Tom Cruise.

Watch American Made full Movie 2017 is more interesting as a showcase for the dateless elasticity of Cruise’s star power. It feels, for better or worse, like a film he could have made at almost any point in the last 30 years.

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Next month, Tom Cruise is reteaming with his Edge of Tomorrow director Doug Liman for American Made. Based on a true story, the film finds the three-time Academy Award nominee playing the part of Barry Seal, a pilot-turned-drug runner who, in 1984, was recruited to be an undercover CIA informant for one of the biggest drug busts in history. While Seal may not be one of the most virtuous of real life figures, Cruise says that it was Seal's incredible true story that was just too interesting to pass up. Cruise said.

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66. Fast forward to the conclusion of Jedrzejczyk's scrum along with a reporter reunite into asking her to get a prediction. When Jedrzejczyk disclosed she was 50/50, the reporter subsequently shifted to asking her about McGregor's behavior.
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67. For your convenient gadgets, for example, iPad, iPhone or iPod Touch there are some equipment and in addition programming confinements. iCloud works basically with iOS 5, the most recent working framework for Apple gadgets.