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Refer to the sub cube containing nodes with a leading 0 as the 0-sub cube and the sub cube consisting of nodes with a leading 1 as 1-sub cube. Once both sub cubes have calculated the prefix sum, the sum over all elements in the 0-sub cube has to be added to the every element in the 1-sub cube, since every processing element in the 0-sub cube ...
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 ...
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.
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 ...
A planar graph and its minimum spanning tree. Each edge is labeled with its weight, which here is roughly proportional to its length. A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected, edge-weighted undirected graph that connects all the vertices together, without any cycles and with the minimum possible total edge weight. [1]
Shortest path (A, C, E, D, F), blue, between vertices A and F in the weighted directed graph. In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized.
A tree consisting of only a root node has a height of 0. The least number of nodes is obtained by adding only two children nodes per adding height so + (1 for counting the root node). The maximum number of nodes is obtained by fully filling nodes at each level, i.e., it is a perfect tree.
Root nodes provide set representatives: Two nodes are in the same set if and only if the roots of the trees containing the nodes are equal. Nodes in the forest can be stored in any way convenient to the application, but a common technique is to store them in an array. In this case, parents can be indicated by their array index.