On one bench here Monday night, when Indiana and North Carolina play for the NCAA basketball title, will be Bob Knight, whose brilliance often is overshadowed by his bizarre behavior, his inexplicable tantrums and outbursts, but who still, at age 40, has established his place among the sport's elite coaches.

On the other bench will be Dean Smith, 50, who has won an Olympic crown and has been to this tournament's final four six times, a record matched only by John Wooden. Like Knight, he would be on any list of all-time coaches. But he never has won the NCAA title, this is his third championship game, and it disturbs him.

Smith, in the Atlantic Coast, and Knight, in the Big Ten, have dominated two of the top conferences in the nation for many years, Smith averaging 24 victories a season, Knight 23, while each annually has played as tough a schedule as any in the country. Smith has won 436 games in 20 years as a head coach, Knight 332 in 16 years.

They are friends because they respect each other, the respect born of the knowledge of the game they share and the importance both put on ethics. Each despises cheating. Each takes as much pride in citing graduation statistics as won-lost figures.

They also share the ability to teach the game superbly, the drive to be successful coaching it, the near-obsession with seeing it treated right by players, fans, the media and coaches.

But away from the arena it is difficult to find two more diverse personalities. Knight, by his own admission, still is maturing, still trying to learn how to control his self-destructive tendencies. Even at a time when he has been working hard to improve his image, he could not avoid an imbroglio with a Louisiana State fan in his hotel Saturday night.

In many ways, Knight is very public person. Contrary to common belief, some of his closest friends are sportswriters. Those generally are granted access to his team meetings, his closed practices and his home.

There is nothing subtle about Knight. His favorite word is an obscenity. He always says what he is thinking no matter who it offends, no matter the circumstances.

Conversely, Smith is an enigma. Always, he deflects questions about himself, his personal feelings and his personal life. In a league where coaches and players constantly hear insults, he says he does not hear them.

"Except one time this year when the N.C. State fans starting chanting, 'Sit down Smith,'" he said today. "I made sure I didn't sit down."

While Knight's deeply competitive nature is written large on his face, Smith hides his. But it is there. About a year ago he and three good friends had to stop playing golf in set teams because they had all but stopped talking to one another while trying to win "friendly" matches. Smith is close to a very small group of people, and none of them are sportswriters. He discourages publicity. And, he doesn't curse.

Smith rarely says publicly what he is thinking. He says what sounds best. He never will criticize another coach or a player publicly. He is the master of the subtle shot.

Duke Coach Mike Krzyzewski, who played and coached under Knight, said of him today, "I think he's trying to change his image right now because he knows a lot of the things he says aren't listened to because of his image. He stands for a lot of good things. But he knows that some of the other stuff has kept a lot of people from paying attention to that."

Smith can remember every critical word written or said about him. In 1976, seconds after winning the Olympic gold medal, he stopped a writter who had suggested he had made a mistake by not picking Wally Walker for the team.

"Now do you think Wally Walker could have played for this team?" Smith asked coldly. In his moment of triumph, one of his first thoughts was to put down a critic.

Smith's memory of Carolina's last appearance in this championship game, four years ago against Marquette, still is vivid. He can remember the entire sequence of plays leading to his decision to go to the four-corner offense with the score tied. And he still can see, in his mind's eye, Bo Ellis blocking Bruce Buckley's backdoor layup while Mike O'Koren sat at the scorer's table waiting to come back in for Buckley.

For four years, Smith has lived with that memory and the hundreds of questions about his failure to win the national title. Perhaps only to himself will he admit how important Monday's game is to Dean Smith.

"It's his chance to get that last monkey off his back," said Tar Heel forward Al Wood, who must again be wondrous if that monkey is to be removed. "We all know how much he wants to win this."

For Knight there is no monkey. Five years ago, he won this championship in the building, the Spectrum, where Monday's game will be played. But he is 0-2 against Smith and he knows this will be as much a matchup of philosophies as players. Knight's teams never have played a zone defense, never will. He uses one defense, man to man. Much of Carolina's success is predicated on changing defenses frequently, and this year it has played more zone than ever before. Knight hates losing to a zone defense.

Perhaps Georgetown Coach John Thompson, a friend of both men, put it best.

"Knight against Smith," he said. "That's like two elephants going at it. The only loser in that one is the grass that gets trampled underneath."