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Base case may refer to: Base case (recursion) , the terminating scenario in recursion that does not use recursion to produce an answer Base case (induction) , the basis in mathematical induction, showing that a statement holds for the lowest possible value of n
Short-circuiting the base case, also known as arm's-length recursion, consists of checking the base case before making a recursive call – i.e., checking if the next call will be the base case, instead of calling and then checking for the base case. Short-circuiting is particularly done for efficiency reasons, to avoid the overhead of a ...
A recursive step — a set of rules that reduces all successive cases toward the base case. For example, the following is a recursive definition of a person's ancestor. One's ancestor is either: One's parent (base case), or; One's parent's ancestor (recursive step). The Fibonacci sequence is another classic example of recursion: Fib(0) = 0 as ...
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The first, the base case, proves the statement for = without assuming any knowledge of other cases. The second case, the induction step , proves that if the statement holds for any given case n = k {\displaystyle n=k} , then it must also hold for the next case n = k + 1 {\displaystyle n=k+1} .
Base32 is an encoding method based on the base-32 numeral system.It uses an alphabet of 32 digits, each of which represents a different combination of 5 bits (2 5).Since base32 is not very widely adopted, the question of notation—which characters to use to represent the 32 digits—is not as settled as in the case of more well-known numeral systems (such as hexadecimal), though RFCs and ...
This popular sorting algorithm has an average-case performance of O(n log(n)), which contributes to making it a very fast algorithm in practice. But given a worst-case input, its performance degrades to O(n 2). Also, when implemented with the "shortest first" policy, the worst-case space complexity is instead bounded by O(log(n)).
In arithmetic, a complex-base system is a positional numeral system whose radix is an imaginary (proposed by Donald Knuth in 1955 [1] [2]) or complex number (proposed by S. Khmelnik in 1964 [3] and Walter F. Penney in 1965 [4] [5] [6]).