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The string spelled by the edges from the root to such a node is a longest repeated substring. The problem of finding the longest substring with at least k {\displaystyle k} occurrences can be solved by first preprocessing the tree to count the number of leaf descendants for each internal node, and then finding the deepest node with at least k ...
The longest repeated substring problem for a string of length can be solved in () time using both the suffix array and the LCP array. It is sufficient to perform a linear scan through the LCP array in order to find its maximum value v m a x {\displaystyle v_{max}} and the corresponding index i {\displaystyle i} where v m a x {\displaystyle v ...
The longest common substrings of a set of strings can be found by building a generalized suffix tree for the strings, and then finding the deepest internal nodes which have leaf nodes from all the strings in the subtree below it. The figure on the right is the suffix tree for the strings "ABAB", "BABA" and "ABBA", padded with unique string ...
The operation (v & -v) zeros all bits except the least-significant bit set, resulting in a new value which is a power of 2. This power of 2 is multiplied (arithmetic modulo 2 32 ) by the de Bruijn sequence, thus producing a 32-bit product in which the bit sequence of the 5 MSBs is unique for each power of 2.
Their exact values are not known, but upper and lower bounds on their values have been proven, [15] and it is known that they grow inversely proportionally to the square root of the alphabet size. [16] Simplified mathematical models of the longest common subsequence problem have been shown to be controlled by the Tracy–Widom distribution. [17]
Run-length encoding (RLE) is a form of lossless data compression in which runs of data (consecutive occurrences of the same data value) are stored as a single occurrence of that data value and a count of its consecutive occurrences, rather than as the original run. As an imaginary example of the concept, when encoding an image built up from ...
In mathematics, a recurrence relation is an equation according to which the th term of a sequence of numbers is equal to some combination of the previous terms. Often, only previous terms of the sequence appear in the equation, for a parameter that is independent of ; this number is called the order of the relation.
Support for multi-dimensional arrays may also be provided by external libraries, which may even support arbitrary orderings, where each dimension has a stride value, and row-major or column-major are just two possible resulting interpretations. Row-major order is the default in NumPy [19] (for Python).