Keivan Borna
Abstract
Convex hull of some given points is the intersection of all convex sets containing them. It is used as primary structure in many other problems in computational geometry and other areas like image processing, model identification, geographical data systems, and triangular computation of a set of points ...
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Convex hull of some given points is the intersection of all convex sets containing them. It is used as primary structure in many other problems in computational geometry and other areas like image processing, model identification, geographical data systems, and triangular computation of a set of points and so on. Computing the convex hull of a set of point is one of the most fundamental and important problems of computational geometry. In this paper a new algorithm is presented for computing the convex hull of a set of random points in the plane by using a sweep-line strategy. The sweep-line is a horizontal line that is moved from top to bottom on a map of points. Our algorithm is optimal and has time complexity $O(nlogn)$ where $n$ is the size of input.
N. Aghaieabiane; H. Koppelaar; Peyman Nasehpour
Abstract
Binary trees are essential structures in Computer Science. The leaf (leaves) of a binary tree is one of the most significant aspects of it. In this study, we prove that the order of a leaf (leaves) of a binary tree is the same in the main tree traversals; preorder, inorder, and postorder. Then, we prove ...
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Binary trees are essential structures in Computer Science. The leaf (leaves) of a binary tree is one of the most significant aspects of it. In this study, we prove that the order of a leaf (leaves) of a binary tree is the same in the main tree traversals; preorder, inorder, and postorder. Then, we prove that given the preorder and postorder traversals of a binary tree, the leaf (leaves) of a binary tree can be determined. We present the algorithm BT-LEAF, a novel one, to detect the leaf (leaves) of a binary tree from its preorder and postorder traversals in quadratic time and linear space.
Niloofar Aghaieabiane; Henk Koppelaar; Peyman Nasehpour
Abstract
It is well-known that, given inorder traversal along with one of the preorder or postorder traversals of a binary tree, the tree can be determined uniquely. Several algorithms have been proposed to reconstruct a binary tree from its inorder and preorder traversals. There is one study to reconstruct a ...
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It is well-known that, given inorder traversal along with one of the preorder or postorder traversals of a binary tree, the tree can be determined uniquely. Several algorithms have been proposed to reconstruct a binary tree from its inorder and preorder traversals. There is one study to reconstruct a binary tree from its inorder and postorder traversals, and this algorithm takes running time of $ \BigO{\emph{n}^2} $. In this paper, we present $ \proc{InPos} $ an improved algorithm to reconstruct a binary tree from its inorder and postorder traversals. The running time and space complexity of the algorithm are an order of $ \BigTheta{\emph{n}} $ and $ \BigTheta{\emph{n}} $ respectively, which we prove to be optimal. The $ \proc{InPos} $ algorithm not only reconstructs the binary tree, but also it determines different types of the nodes in a binary tree; nodes with two children, nodes with one child, and nodes with no child. At the end, the $ \proc{InPos} $ returns a matrix-based structure to represent the binary tree, and enabling access to any structural information of the reconstructed tree in linear time with any given tree traversals.
