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The Rayo function of a natural number , notated as (), is the smallest number bigger than every finite number with the following property: there is a formula () in the language of first-order set-theory (as presented in the definition of ) with less than symbols and as its only free variable such that: (a) there is a variable assignment assigning to such that ([()],), and (b) for any variable ...
The multiples of a given prime are generated as a sequence of numbers starting from that prime, with constant difference between them that is equal to that prime. [1] This is the sieve's key distinction from using trial division to sequentially test each candidate number for divisibility by each prime. [ 2 ]
For example, for the array of values [−2, 1, −3, 4, −1, 2, 1, −5, 4], the contiguous subarray with the largest sum is [4, −1, 2, 1], with sum 6. Some properties of this problem are: If the array contains all non-negative numbers, then the problem is trivial; a maximum subarray is the entire array.
The smallest example of a number whose optimal expression is not of this form is 353942783. It is a prime number , and therefore also disproves a conjecture of Richard K. Guy that the complexity of every prime number p is one plus the complexity of p − 1 . [ 5 ]
A googol is the large number 10 100 or ten to the ... The word is notable for being the subject of the £1 million question in a 2001 episode of the British quiz ...
A further relaxation requiring only a list of the k smallest elements, but without requiring that these be ordered, makes the problem equivalent to partition-based selection; the original partial sorting problem can be solved by such a selection algorithm to obtain an array where the first k elements are the k smallest, and sorting these, at a total cost of O(n + k log k) operations.
A prime number is a natural number greater than 1 with no divisors other than 1 and itself. According to Euclid's theorem there are infinitely many prime numbers, so there is no largest prime. Many of the largest known primes are Mersenne primes , numbers that are one less than a power of two , because they can utilize a specialized primality ...
Min-max heaps are often represented implicitly in an array; [4] hence it's referred to as an implicit data structure. The min-max heap property is: each node at an even level in the tree is less than all of its descendants, while each node at an odd level in the tree is greater than all of its descendants .