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The set ret can be saved efficiently by just storing the index i, which is the last character of the longest common substring (of size z) instead of S[(i-z+1)..i]. Thus all the longest common substrings would be, for each i in ret, S[(ret[i]-z)..(ret[i])]. The following tricks can be used to reduce the memory usage of an implementation:
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.
Given a function that accepts an array, a range query (,) on an array = [,..,] takes two indices and and returns the result of when applied to the subarray [, …,].For example, for a function that returns the sum of all values in an array, the range query (,) returns the sum of all values in the range [,].
Because the "Old" palindrome is the largest possible palindrome centered on OldCenter, we know the characters before and after it are different. Thus, the palindrome at Center will run exactly up to the border of the "Old" palindrome, because the next character will be different than the one inside the palindrome at MirroredCenter .
In computer science, the longest common prefix array (LCP array) is an auxiliary data structure to the suffix array.It stores the lengths of the longest common prefixes (LCPs) between all pairs of consecutive suffixes in a sorted suffix array.
A one-dimensional array (or single dimension array) is a type of linear array. Accessing its elements involves a single subscript which can either represent a row or column index. As an example consider the C declaration int anArrayName[10]; which declares a one-dimensional array of ten integers.
An algorithm is fundamentally a set of rules or defined procedures that is typically designed and used to solve a specific problem or a broad set of problems.. Broadly, algorithms define process(es), sets of rules, or methodologies that are to be followed in calculations, data processing, data mining, pattern recognition, automated reasoning or other problem-solving operations.
An even simpler linear-time sequential algorithm (Barbay, Fischer & Navarro (2012), Lemma 1) does not even need a stack; it assumes that the input sequence is given as an array A[1,n] of size n, and stores the index j of the preceding smaller value of the i th value A[i] in P[i].