Computer Science 170 - Spring 1997 - Vazirani - Midterm 1

# Computer Science 170 - Spring 1997 - Vazirani - Midterm 1 -...

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CS 170, Midterm #1, Spring 1997) CS 170, Spring 1997 Midterm #1 Problem #1 (50 points) Let T be a binary tree with root r. The height of a vertex v is 0 if v is a leaf vertex, and otherwise it is the height of the subtree rooted at v; i.e. it is the distance between v and the farthest leaf in the subtree rooted at v. The balance factor of a vertex v is defined to be the difference between the height of v's left child and the height of its right child. By convention, the balance factor of leaf vertex is defined to be 0. Give a linear time algorithm that given as input a binary tree T and its root vertex r, computes the balance factor of all vertices in T. Problem #2 (50 points) You are given a directed graph G(V,E) with associated weights w:E->Z on the edges. Moreover you know that there is only one edge (u, v) whose weight is negative -- all other edges weight are positive. (30 points) Show how to use Dijkstra's algorithm to determine whether G(V,E) has negative cycle.

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