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In the most balanced case, each time we perform a partition we divide the list into two nearly equal pieces. This means each recursive call processes a list of half the size. Consequently, we can make only log 2 n nested calls before we reach a list of size 1. This means that the depth of the call tree is log 2 n.
function merge_sort(list m) is // Base case. A list of zero or one elements is sorted, by definition. if length of m ≤ 1 then return m // Recursive case. First, divide the list into equal-sized sublists // consisting of the first half and second half of the list.
Double dabble: convert binary numbers to BCD; Hash function: convert a large, possibly variable-sized amount of data into a small datum, usually a single integer that may serve as an index into an array Fowler–Noll–Vo hash function: fast with low collision rate; Pearson hashing: computes 8-bit value only, optimized for 8-bit computers
The following pseudocode demonstrates an algorithm that merges input lists (either linked lists or arrays) A and B into a new list C. [1] [2]: 104 The function head yields the first element of a list; "dropping" an element means removing it from its list, typically by incrementing a pointer or index.
In computer science, divide and conquer is an algorithm design paradigm. A divide-and-conquer algorithm recursively breaks down a problem into two or more sub-problems of the same or related type, until these become simple enough to be solved directly. The solutions to the sub-problems are then combined to give a solution to the original problem.
Perl, Python (only modern versions) choose the remainder with the same sign as the divisor d. [6] Scheme offer two functions, remainder and modulo – Ada and PL/I have mod and rem, while Fortran has mod and modulo; in each case, the former agrees in sign with the dividend, and the latter with the divisor.
Python supports normal floating point numbers, which are created when a dot is used in a literal (e.g. 1.1), when an integer and a floating point number are used in an expression, or as a result of some mathematical operations ("true division" via the / operator, or exponentiation with a negative exponent).
Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.