[Solved] COMP9101 Assignment 4

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1. Boolean operators NAND and NOR are defined as follows

NAND true true

f alse true

f alse true true

NOR

true f alse

true f alse

f alse f alse true

false

false

You are given a boolean expression consisting of a string of the symbols true, false, separated by operators AND, OR, NAND and NOR but without any parentheses. Count the number of ways one can put parentheses in the ex- pression such that it will evaluate to true. (20 pts)

2. You are given a 2D map consisting of an R C grid of squares; in each square there is a number representing the elevation of the terrain at that square. Find a path going from square (1, R) which is the top left corner of the map to square (C, 1) in the lower right corner which from every square goes only to the square immediately below or the square immediately to the right so that the number of moves from lower elevation to higher elevation along such a path is as small as possible. (20 pts)
3. You are on vacation for N days at a resort that has three possible activities. For each day, for each activity, youve determined how much enjoyment you will get out of that activity. However, you are not allowed to do the same activity two days in a row. What is the maximum total enjoyment possible? (30 pts)
4. Given a weighted directed graph G(V,E), find a path in G (possibly self- intersecting) of length exactly K that has the maximum total weight. (30 pts)1