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Maximum subarray problems arise in many fields, such as genomic sequence analysis and computer vision.. Genomic sequence analysis employs maximum subarray algorithms to identify important biological segments of protein sequences that have unusual properties, by assigning scores to points within the sequence that are positive when a motif to be recognized is present, and negative when it is not ...
The sum-product problem is particularly well-studied over finite fields. Motivated by the finite field Kakeya conjecture , Wolff conjectured that for every subset A ⊆ 픽 p , where p is a (large) prime, that max(| A + A |, | AA |) ≥ min( p , | A | 1+ ε ) for an absolute constant ε > 0 .
The clique decision problem is not of practical importance; it is formulated in this way in order to apply the theory of NP-completeness to clique-finding problems. [19] The clique problem and the independent set problem are complementary: a clique in G is an independent set in the complement graph of G and vice versa. [20]
function lookupByPositionIndex(i) node ← head i ← i + 1 # don't count the head as a step for level from top to bottom do while i ≥ node.width[level] do # if next step is not too far i ← i - node.width[level] # subtract the current width node ← node.next[level] # traverse forward at the current level repeat repeat return node.value end ...
The above example would have a child nodes at each non-leaf node. Each node does an amount of work that corresponds to the size of the subproblem n passed to that instance of the recursive call and given by (). The total amount of work done by the entire algorithm is the sum of the work performed by all the nodes in the tree.
The static optimality problem is the optimization problem of finding the binary search tree that minimizes the expected search time, given the + probabilities. As the number of possible trees on a set of n elements is ( 2 n n ) 1 n + 1 {\displaystyle {2n \choose n}{\frac {1}{n+1}}} , [ 2 ] which is exponential in n , brute-force search is not ...
The MAX-SAT problem is OptP-complete, [1] and thus NP-hard (as a decision problem), since its solution easily leads to the solution of the boolean satisfiability problem, which is NP-complete. It is also difficult to find an approximate solution of the problem, that satisfies a number of clauses within a guaranteed approximation ratio of the ...
Then as the search pointer proceeds past the search window and forward, as far as the run pattern repeats in the input, the search and input pointers will be in sync and match characters until the run pattern is interrupted. Then L characters have been matched in total, L > D, and the code is [D, L, c]. Upon decoding [D, L, c], again, D = L R.