hw3 - Computer Science 130B Winter 2007 Homework#3 Due 4pm...

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Computer Science 130B Winter 2007 Homework #3 Due: 4pm, February 23th, Friday Problem 1 Consider a square lattice structure. A square lattice of size n 2 is a directed labeled graph G = ( V, E ), where | V | = n 2 . Vertices in a lattice are arranged in a grid pattern, i.e., each vertex has a unique address ( i, j ), where 1 i n , and 1 j n . There are two types of edges in a lattice: horizontal and vertical. Horizontal edges go from vertex ( i, j ) to vertex ( i, j +1), for 1 i n , and 1 j n - 1, while vertical edges go from vertex ( i, j ) to vertex ( i + 1 , j ), for 1 i n - 1, and 1 j n . Label of an edge indicates the cost of traversing the particular edge. The goal here is to find a directed path of 2 × ( n - 1) edges ( n - 1 vertical and n - 1 horizontal) leading from vertex (1,1) to vertex ( n, n ) such that the total cost of the path is minimized. a. Explain why divide-and-conquer method is not feasible in finding the optimal path.
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