Knuth’s Method

Knuth’s method is a recursive algorithm for dividing two large numbers. It is named after Donald Knuth, who published it in his 1968 book The Art of Computer Programming.

The algorithm works by repeatedly dividing the dividend by the divisor, starting with the largest power of 10 that is smaller than the dividend. For each division, the quotient is stored in a temporary variable, and the remainder is added to the previous remainder. The algorithm terminates when the remainder is 0.

Knuth’s method is a very efficient algorithm for dividing large numbers. It is often used in computer programs that need to divide large numbers, such as programs that perform financial calculations or scientific calculations.

Here is a step-by-step example of how Knuth’s method works:

1. Divide the dividend by the divisor, starting with the largest power of 10 that is smaller than the dividend. For example, if the dividend is 1234567890 and the divisor is 100, then the first division would be 1234567890 / 100 = 123456.789.
2. Store the quotient in a temporary variable. In this example, the temporary variable would be 123456.789.
3. Add the remainder to the previous remainder. In this example, the previous remainder is 0, so the remainder is added to 0 to get 0.
4. Repeat steps 1-3 until the remainder is 0. In this example, the remainder is 0 after the first step, so the algorithm terminates.

The following pseudocode shows the algorithm in a more formal way:

function divide(dividend, divisor) {
  if (dividend < divisor) {
    throw new Error("Dividend must be greater than or equal to divisor");
  }
  quotient = 0;
  remainder = 0;
  while (dividend > 0) {
    quotient = quotient * 10 + dividend % divisor;
    dividend = dividend / divisor;
    remainder = quotient - dividend;
  }
  return quotient;
}

Knuth’s method is a very efficient algorithm for dividing large numbers. It is often used in computer programs that need to divide large numbers, such as programs that perform financial calculations or scientific calculations.thumb_upthumb_downrefreshGoogle itmore_vert