Szymański's algorithm
Okay, so have you ever played a game where you have to guess a secret number and the game tells you if your guess is too high or too low? Szymański's algorithm is a way to guess the secret number as fast as possible using a special trick.
Imagine you have to guess a number between 1 and 100. The first thing you would do is guess 50, right in the middle. If the game tells you the secret number is higher than 50, you can eliminate all the numbers from 1 to 50 and guess again in the middle of the remaining numbers (51 to 100). So now you guess 75. If the game says the number is lower than 75, you can eliminate all the numbers from 76 to 100 and guess again in the middle of the remaining numbers (51 to 75). This way, you keep eliminating half of the remaining numbers with each guess, until you find the secret number.
Szymański's algorithm takes this a step further by using a clever rule to determine which side of the remaining numbers to guess in. Instead of guessing exactly in the middle, it looks at the parity (whether a number is even or odd) of the remaining numbers. If there are more even numbers left, it guesses halfway between the highest even number and the lowest odd number. If there are more odd numbers left, it guesses halfway between the highest odd number and the lowest even number. This way, it eliminates more numbers with each guess and can find the secret number faster.
So basically, Szymański's algorithm uses a rule to guess the most efficient point for the next guess, instead of always guessing right in the middle. It's like a super-smart way to play a number-guessing game!
Imagine you have to guess a number between 1 and 100. The first thing you would do is guess 50, right in the middle. If the game tells you the secret number is higher than 50, you can eliminate all the numbers from 1 to 50 and guess again in the middle of the remaining numbers (51 to 100). So now you guess 75. If the game says the number is lower than 75, you can eliminate all the numbers from 76 to 100 and guess again in the middle of the remaining numbers (51 to 75). This way, you keep eliminating half of the remaining numbers with each guess, until you find the secret number.
Szymański's algorithm takes this a step further by using a clever rule to determine which side of the remaining numbers to guess in. Instead of guessing exactly in the middle, it looks at the parity (whether a number is even or odd) of the remaining numbers. If there are more even numbers left, it guesses halfway between the highest even number and the lowest odd number. If there are more odd numbers left, it guesses halfway between the highest odd number and the lowest even number. This way, it eliminates more numbers with each guess and can find the secret number faster.
So basically, Szymański's algorithm uses a rule to guess the most efficient point for the next guess, instead of always guessing right in the middle. It's like a super-smart way to play a number-guessing game!
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