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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 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]
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 query algorithm visits one node per level of the tree, so O(log n) nodes in total. On the other hand, at a node v, the segments in I are reported in O(1 + k v) time, where k v is the number of intervals at node v, reported. The sum of all the k v for all nodes v visited, is k, the number of reported segments. [5]
A Fenwick tree or binary indexed tree (BIT) is a data structure that stores an array of values and can efficiently compute prefix sums of the values and update the values. It also supports an efficient rank-search operation for finding the longest prefix whose sum is no more than a specified value.
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 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 subset sum problem (SSP) is a decision problem in computer science. In its most general formulation, there is a multiset S {\displaystyle S} of integers and a target-sum T {\displaystyle T} , and the question is to decide whether any subset of the integers sum to precisely T {\displaystyle T} . [ 1 ]