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With the help of disjoints sets, you can keep a track of the existence of elements in a particular group. Find — It helps determine which subset a particular element belongs to. It also helps determine if the element is in more than one subset. Union — It helps check whether a graph is cyclic or not.

For the disjoint set, we keep a single representative for each node. If we search for any element in a particular node, it lead us to the parent of that particular node. Therefore, when you search for D, the answer would be B. If B is not a representative, we can move up the tree to find the parent or representative for the tree.

You can read more here about Basics of Disjoint sets. Spanning tree is the sum of weights of all the edges in a tree. Step 1 — Remove all loops and parallel edges. Step 2 — Arrange all the edges in ascending order of cost. Step 3 — Add edges with least weight. On your trip to Venice, you plan to visit all the important world heritage sites but are short on time.

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What Makes Wheels Appear to Spin Backward?

Mark Basilica J , which is of length 2. We will remove the parallel road and keep the 1. Step 2 — Arrange all the edges on the graph in ascending order. Hence, B, C is connected first considering their edge cost only 1. I, J has cost 1; it is the edge connected next. He felt for a moment uncreated. Another kind of awake. Aug 18, Debbie rated it really liked it Shelves: I was only looking at words in a book, but the image gives me instant vertigo! But how can just reading about this bizarre and incredible feat affect me physically, make me dizzy and nauseous?

The power of books. Just blows me away. This book is cool. It starts with a chapter about people looking up at the madman in the sky. The story is based on the real s event of a guy who walked on a wire between the two insanely tall buildings. Sort of eerie reading about these buildings that no longer exist.

Despite my vertigo, the story pulled me right in. But now I have to go directly to my complaint board. Who says I want to hang out with two brothers in Ireland? The contrast was too fast. The brothers bored me to tears and I felt no connection to them. They ended up in New York, and one of them was a priest who helped hookers.

I usually like reading about squalor and down-and-outers, but for some reason their story left me cold. What a downer, after the excitement of the first chapter. But never fear, the next story had me mesmerized and mostly I liked all the other stories. I signed up for a novel, but for a long while it read like a collections of short stories, too independent. I wanted dependence, I wanted connection, damn it. It took a while for the stories to meld. Finally, a little later than I liked, the stories were woven into a nice tapestry; in fact, a beautiful tapestry.

All the sudden I was in love with the book. The language is to die for, lyrical and intense. The story so juicy meaty, the characters so interesting and complex. The interwoven plot is intense and heart-wrenching. And McCann is so damn profound, I was highlighting text like mad—sometimes whole paragraphs, in fact. A cool thing is that McCann is able to use different styles of writing, and they all work.

Here are a few quotes. It was hard to pick among the zillion gems. They got businessmen come in for a day. They lift up their shirts, you can smell the husband panic off them, like their wife is gonna come out of the TV set. From a Park Avenue woman whose son died in the Vietnam War: No newspapers big enough to paste him back together in Saigon. She takes another long haul, lets the smoke settle in her lungs—she has heard somewhere that cigarettes are good for grief. One long drag and you forget how to cry. The body too busy dealing with the poison.

No wonder they gave them out free to the soldiers. Afterward, Gloria said to her that it was necessary to love silence, but before you could love silence you had to have noise. I loved it too, which led me to this book. I want to read more more more of his stuff. So even though I got bored occasionally with a character who left me cold, mostly I loved this book to pieces.

View all 20 comments. Jan 04, Matt rated it liked it Shelves: The terrorist attacks of September 11, are almost ten years old, and yet, the wound is still very raw for those not directly involved, I mean; for those that were there, the wound is forever. Books and films that have dared touch the subject have done so in one of two ways: There's a good reason for this: These have nothing to do with the actual events, yet have everything to do with the actual events. It is a collection of interlocking stories strung together natch! This event had been mostly forgotten until the Towers fell, when suddenly Petit's walk became unbelievably poignant.

This is made clear right at the start, when McCann describes the tumult caused by the wire-walker: It's almost as though he was describing something else And if the point isn't hammered home enough, McCann later includes a photo of the wire-walker suspended between the Towers, with an airplane in the background. Yeah, it's not too subtle. But I'm not really sure what to make of the allusion, just as I'm not really sure what to make of the book.

My enjoyment - and my internal Goodreads star-meter - ebbed and flowed as I made my way through. The book is designed to frustrate in this manner. In a way, it's more a collection of short stories than a novel. Each chapter is told from the point of view of a different character, utilizing first person and third person storytelling, and even a little second person for good measure.

Among the various characters are Irish brothers Ciaran and John "Corrie" Corrigan, who live among the prostitutes of New York City; Claire and her husband Solomon, an upper middle class couple who have lost a son in Vietnam Claire spends time with a support group, while Solomon is the Judge who arraigns an unnamed Philippe Petit ; a South American nurse who's in love with Corrie; a black prostitute whom Corrie attempts to save; a young white girl named Lara who left her privileged upbringing to make time with a too-serious artist; and so forth.

Petit shows up a couple times, in chapters that end the first two sections of the novel. Everything had purpose, signal, meaning. But in the end he knew that it all came down to the wire. Him and the cable. Two hundred and ten feet and the distance it bridged.

The towers had been designed to sway a full three feet in a storm. A violent gust or even a sudden change in temperature would force the buildings to sway and the wire could tighten and bounce. It was one of the few things that came down to chance The structure of this novel is nothing, well, novel. It employs the kind of set up utilized by any number of cut-rate books and movies I'm looking askance at you, the Academy Award-winning Crash. Unsurprisingly, many of these characters meet and intertwine, in ways that are meant to surprise and enlighten; others share only a passing connection, perhaps as ephemeral as having both witnessed Petit's wire-walk.

I'm not trying to be too down, here, because great care is taken in assembling thsi mosaic. Indeed, one of the enjoyments of the book is meeting a character, and later seeing that person through another character's eyes. I'm not a big short story guy, so that should factor into the relevance of this review. I prefer three acts and full arcs, rather than the precious snippets of illumination short stories ostensibly provide. Just as I was getting into a character and actually figuring out who they were the chapter would end and you'd jump into someone else's life.

Often times, you never go back, and many character threads are left dangling forever. And, as with any short story collection, there is good and bad. Some chapters were really powerful, others felt like padding.

And the ending, which flashes forward to , for a blah-blah-blah epilogue, is particularly bad. He also won the National Book Award, while Ferris was only a finalist, so go figure. Maybe this is bitterness, but the book felt too perfect. To paraphrase Melville, I saw the author's foot on the treadle of the loom. There are times when you really notice the care taken with each word, but I don't mean this as a compliment. Despite having different characters narrate each chapter, all the voices sounded suspiciously the same: This is a problem when you skip from an Irishman, to a prostitute, to a judge.

Sure, there's an idiom here, and some slang there, and a little patois in the corner, but in general, everyone sounded the same. Moreover, McCann doesn't really play by his own rules. In one chapter, the narrator is describing his day at the beach, but then intercuts his story with a deadly car crash happening elsewhere.


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Now, this narrator wasn't in the car, so he wouldn't know what was happening, yet he describes the event as though he were in the passenger seat. Back and forth like this. It's seamless and powerful writing, but it's supposedly coming from a guy who never made it far past high school. It's a quibble, to be sure, but it speaks to the lingering sensation I had, with every page, that I was reading something "important. View all 14 comments. Feb 09, Deborah Edwards rated it it was amazing Shelves: Life is full of unexpected synchronicities. The kinds of things that occasionally make you feel that you are connected to a greater web of being, a little sign to let you know that you are not in this alone.

Philippe Petit, more angel than human, strung a cable across the Twin Towers in and performed on it for over half Life is full of unexpected synchronicities. Philippe Petit, more angel than human, strung a cable across the Twin Towers in and performed on it for over half an hour, walking, reclining, and literally dancing for the tiny human specks below and for the gods above who could see him better, after all.

It is a breathtaking sight, a man who has become art, who has made of himself something otherworldly and glorious. Like walking into a forest and seeing a unicorn or looking at the seashore and spotting a mermaid on a rock. It is therefore no wonder that the thread that ties together the vignettes in "Let the Great World Spin" is Petit's momentous tightrope walk as witnessed by the various residents of New York City.

McCann introduces us to a number of these residents, some living gritty lives in the projects, others living lives of quiet luxury in a Park Avenue penthouse, still others trying to survive somewhere between the two extremes, in addresses less prone to preconception. And all of these residents are tied to the story and tied to the events of the day in ways that are sometimes obvious but more often as tenuous as a wire strung between buildings.

But a wire that stretches. McCann's brilliance lies in the fact that each individual we meet is a revelation, a wholly expressed and vivid entity burnt onto our brain cells for all time. When we first meet the young Irish monk, Corrigan, living in a pit in the projects in order to try to protect the downtrodden, the hookers, and the elderly of the neighborhood, we jump into his world without a thought for our own safety, because we are smitten by his desire to bring goodness to bad places.

As it turns out, he - and we - should have considered our safety a bit more carefully. So we learn straight off that some stories are not connected by so much as common addresses or economic status as they are by loss, by grief, by people left behind to trudge on when another's goals are left unfulfilled. Other characters will learn similar lessons, some by choice and others by circumstance, but McCann does not leave us behind like onlookers in a theater. He tells us these stories to make us look at our own and to consider the effect our lives have on the lives around us.

Add to this ingenious structure the most perfect prose in modern literature and you have not a book, not a work of fiction, but an experience. McCann's stories are startlingly beautiful in many ways - their description, their construct, their gorgeous dissection of the dreams and memories of their characters. But the windows McCann opens, the doors he peers through, are just as often opening onto heartbreak as they are onto joy. Somehow, though, the grief and loss make the small tribulations and unexpected beauty that much more meaningful, the way a small remembrance can give us an inner photograph of our own unique definition of happiness.

McCann's characters allow us a glimpse of their sorrow and their happiness and let us decide if a balance has been achieved. That is, if the living of a life matters in the world, which is what McCann ultimately appears to be weighing in his fiction. Which is why he has allowed us glimpses into lives connected to other lives, and connected to other lives still, like the branches of an ever-expanding tree limb.

How does this new person have an impact on the soul I have just become acquainted with, how can this person across town make a mark on the life of the one I just met in the Bronx? Late in the book one of our characters says, "It had never occurred to me before but everything in New York is built upon another thing, nothing is entirely by itself, each thing as strange as the last, and connected. And every so often something stunning and remarkable happens that can bind us all together in sorrow or in joy.

Like two planes hitting the Twin Towers. Or an angel walking between them. Sep 17, Fabian rated it it was amazing. A city with so much life in it that just a sliver of a fleeting moment--a man atop a wire suspended between ill-fated twin building--suffices to display the budding emotion of the general populace.

And not one emotion but a hundred. A true valentine to NYC--a jisgaw puzzle of faces that come from different places. They all look up in awe; we look down in equal amazement at the power of this grand American e A city with so much life in it that just a sliver of a fleeting moment--a man atop a wire suspended between ill-fated twin building--suffices to display the budding emotion of the general populace.

They all look up in awe; we look down in equal amazement at the power of this grand American epic. Feb 19, Christopher Ryan rated it did not like it. I despise this book on so many levels. It's as if some foreign writer came in to write about America and wanted to come away with all its dark secrets by scanning ne I despise this book on so many levels. It's as if some foreign writer came in to write about America and wanted to come away with all its dark secrets by scanning newspaper headlines and popular magazines from the past thirty-five years.

Which is exactly what happened. The writing is cloying and overwritten to the point of complete transparency. It feels excessively edited, as if done by committee. So often I wanted to throw this book at something hard and sharp, because the book lacked any edge. It avoided tension by making everyone into a martyr of some sort, which robbed them of their vitality. Lines that drove me insane: If you play a saxophone beautifully, it does none of these things.

It settled into the corner, a small bubble of blood at its tip. This person did not see a dab of blood on a needletip on the other side of a room in which the bulbs have been painted black. Just tell the story. There were so many other examples but I just want to forget this book now.

View all 6 comments.

I had a difficult time getting into this book but in the end I am glad I persevered. It is really a story about New York City in centered around Phillippe Petit's historic tight rope walk between the two towers of the World Trade Center. But the story itself trancends all that and takes us into the lives of some of the people whose days are coloured by this incredible feat and what unfolds is a powerful,complex tale of life, love, loss and redemption.

I don't think I realized just how profo I had a difficult time getting into this book but in the end I am glad I persevered. I don't think I realized just how profound and deeply felt this story was until I had finished it. It will be some time, no doubt, before I am done thinking about all this book brings to bear. View all 11 comments. May 12, Saffron rated it it was amazing Shelves: It is enough" I am not one for literary fiction.

I mean, the life is profound enough, why read about it? It's just depressing, you know. This book is depressing too because it's just so, so beautiful. I read the first page and I stopped, and rubbed my face in it. Crazy, I know but sometimes you need to feel the texture of the words that touch you so deeply. This book is a masterpiece portrayal of New York City that is tied together by one tightrope walker. I don't know how to describe this book other than saying that this book is complicated, layered. But it is also simple and true. There a million people out there we don't know and we will never get to know them.

But they touch our lives in a million ways. This book is about those people. This book is about connections we will never make but still, we have them. This book is about ordinary people who are special in their own way. This book is alive with people who die, who live and who move on. This book is perfect! Thank you, Professor for making me read this I can't stop crying! View all 46 comments.

How did he do it? How did he get the wire across? That's the question that intrigues those who saw or heard of Philippe Petit's daring tightrope walk on August 7, Not who, not why. How he bridged the unbridgeable, the chasm between those two monolithic structures. Spider-like, sending a thread that looks as delicate as silk from afar, but is strong enough to carry a man, a thread that connects the two separate giants. This took a wee while to work its magic.

It is oblique, which I li How? It is oblique, which I like, but it can be unsettling , there are some oddly ugly metaphors - a sunset the colour of muscle. But there I was thrown the lifeline of some breathtakingly well executed writing, which persuaded me to struggle back on board.

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There are more - a whole ensemble. And they start to come together, all these people, in unexpected ways. There are gossamer thin threads thrown across the void, threads that are delicate and easily broken, and as strong as a wire that can carry a man. They cross the void between those different worlds.

View all 16 comments. An ambitious and complex novel set in New York in Each chapter tells the story of a different character, and it gradually becomes clear that they are much more linked than seems the case early on. McCann's characters are rounded and sympathetic, covering a wide cross section of New York society. The central inspiration is Philippe Petit's high wire walk between the towers of the World Trade Centre, and his story has a symbolic resonance that links the remaining tales of survival.

If I have An ambitious and complex novel set in New York in If I have a slight criticism it is that the last chapter, set in , ties up the loose ends a little too neatly, but overall this was a very rewarding read. Jan 17, Nate rated it really liked it Shelves: I wanted to remember some of the lines from this book so I wrote them in my journal. I haven't read anything in a while that has made me ache. The loss in this book and the admiration the narrators have for the central figure is overwhelming as you read it.

The author has obviously lost someone special and has captured that loss on paper. Just gorgeously written, especially the chapters titled Miro, Miro on the Wall and Centavos. It is I wanted to remember some of the lines from this book so I wrote them in my journal. It is a tale of interwoven characters who don't know how they connect, each chapter is written from a different point of view, and there's some play with the chronology of the plot.

Pretty standard fiction fare nowadays. We never hear from Maris or McCann's character Corrigan directly, but we get a fully fleshed out character from hearsay.

Let the Great World Spin

In Corrigan's case, he just keeps getting more and more wholesome and that wholesomeness radiates through the other characters in the novel. That delicate kind of wholesome that isn't preachy or judgmental. To me, the character Corrigan illustrates the reason I dislike Oprah. He felt no need to wear his good deeds like a medallion - he did not do the tremendously kind things he did for his own self-esteem or for an audience.

He did them because it was right. The fact that the reader learns of Corrie's philanthropy is solely because we hear it from other characters. He would never tell us these things if he were to narrate. He was a reminder to people who most needed reminding that there is still good in the world.

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Similarities can easily be drawn between him and the unnamed tightrope walker. I would like to write about the tightrope walker and Corrie's differences. We are told the tightrope walker's intentions for walking out between the Twin Towers were because the Towers were there to be walked between. Since this stunt took place before reality tv shows and 24 hour news channels, I can somewhat believe it. But somewhere in there he must have done it for notoriety, don't we all have some wish to be remembered, or at least have our 15 minutes of fame? That's the main difference to me between the tightrope walker and Corrie.

The only reason this book didn't get a 5 star from me is because of the phreakers chapter. I'm still wrapping my head around it. I wouldn't say it was a mismatch to the rest of the book; but its reason for being included isn't as obvious. Communication and distance are definite themes of the novel.

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The beginnings of the internet seem like a good locale for that discussion - but the rest of the book was so tightly written; much more obvious in its motives. Plus there was always a tie in to other characters of the novel somehow in other chapters. Maybe I should read it again, because I don't think any of the people the phreakers got a hold of tied in. View all 8 comments. Oct 17, Cheryl rated it really liked it Shelves: Let the great world spin. And the great world of New York did indeed spin in this book. How do you view melancholy and heartbreak as something pure and beautiful and riveting and just plain astounding?

You read Colum McCann's work, that's how. It was an orchestra of sorts--the many different voices and narratives. McCann writes with so much lyricism, he makes you want to dance with the tightrope walker the book opens with taken from the true story of Philippe Petit, by the way. Three word Let the great world spin.

Three word sentences and then one-page paragraph. Almost no dialogue and then a three-page dialogue-only scene. Simply-structured sentences combined with complex word vines. The prose is a web of bemusement, much like the characters. Ireland, a city I love reading about ever since Frank McCourt made tales of Ireland and what one might call the 'Irish dialect' in literature alluring. Yet McCann does not even come close to writing about Ireland the way in which he writes about New York. The New York he describes, I see clearly. I was a teenaged immigrant when I lived in New York City.

Though I was fortunate to have parents who swore to keep us out of the projects even though they had lost everything when they emigrated, I walked the streets of the projects with my high school friends in Queens, where I lived. I visited the Bronx with them, where mothers leaned out of windows speaking in code, asking their sons to buy things I had no idea of then until I saw small bags exchanged through palms. Walked the projects of Staten Island with friends who had just moved there after escaping war in their homelands.

Went to church in the middle of what was then Brooklyn's worst projects; Bedsty. Watched while some of my friends never made it through high school and some were deported for bad behavior. Sometimes it all seems unnerving, as if someone handed me a skateboard and I skated through all of it in slow motion. Now here goes McCann, illuminating it all, reminding me. He speaks of prostitution, drugs, death, etc. But mostly, the book probes about life and consequences, life and the decisions we make, life--the good, the ugly, the beautiful, the painful.

Ciaran Corrigan was my favorite character. Then Jaslyn; the daughter of Jazzlyn the prostitute. Ciaran told the twisted story of his brother, John Corrigan, who was a priest living in the projects with prostitutes, and somehow he became their best friend and angel. But even a priest has struggles and even his family must deal with tragedy. Through Ciaran's narration, I wanted to move with the book and never let it go. Until about 80 pages in when the parallel narration took Ciaran away from me and introduced another character.

And this is the only problem I had. The parallel narratives seemed almost like short stories that were later stringed into a novel. And since McCann was a short story writer, that theory may not be too far off. There was the overarching theme of New York, yes, and there were characters whose lives were later intertwined yes, but don't look to be driven by some plot alignment. I love short stories but I hate when I'm reading a novel and it starts to feel like a short story collection. You come across so many characters--which, I admit, seems befitting for New York.

Though when I got to Tillie's narration the older prostitute it seemed a bit inauthentic because the New York-African American dialect was off. Great book and an author whose masterful prose I will gladly seek. Apr 06, Catherine Siemann rated it it was amazing Shelves: New York City in was a run-down, uneasy place, trapped in a spiral of decay.

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Colum McCann's novel captures the spirit of the place and the people eloquently and movingly, the despair and isolation, the community and the hope. The stories of a disparate group of New Yorkers are linked together by Philippe Petit's tightrope walk between the Twin Towers: While a few of the sections particularly one of computer hackers working on the early Arpanet are weaker than the others, overall, this beautifully written book was one that I never wanted to end.

Aug 16, Joe rated it it was ok.


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