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[1] [2] [3] It is a divide-and-conquer algorithm that reduces the multiplication of two n-digit numbers to three multiplications of n/2-digit numbers and, by repeating this reduction, to at most single-digit multiplications.
More formally, multiplying two n-digit numbers using long multiplication requires Θ(n 2) single-digit operations (additions and multiplications). When implemented in software, long multiplication algorithms must deal with overflow during additions, which can be expensive.
Take half of the neighbor, then, if the current digit is odd, add 5. Example: 42×5=210 Half of 2's neighbor, the trailing zero, is 0. Half of 4's neighbor is 1. Half of the leading zero's neighbor is 2. 43×5 = 215 Half of 3's neighbor is 0, plus 5 because 3 is odd, is 5. Half of 4's neighbor is 1. Half of the leading zero's neighbor is 2. 93 ...
Operation Input Output Algorithm Complexity Addition: Two -digit numbers : One +-digit number : Schoolbook addition with carry ()Subtraction: Two -digit numbers : One +-digit number
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As an example, consider the multiplication of 58 with 213. After writing the multiplicands on the sides, consider each cell, beginning with the top left cell. In this case, the column digit is 5 and the row digit is 2. Write their product, 10, in the cell, with the digit 1 above the diagonal and the digit 0 below the diagonal (see picture for ...
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