本次澳洲代写主要为算法相关的assignment

1. Boolean operators NAND and NOR are dened as follows

NAND true false

true false true

false true true

NOR true false

true false false

false false true

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 RC 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 to 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. In a pond there is a sequence on n lily pads arranged in a straight line:

1; 2; 3 : : : n . On lily pad i there are fi 0 ies. On lily pad 1 there is a

frog sitting. The frog can only jump forward from a lily pad i to either lily

pad i+3 or lily pad i+4. Find the largest number of ies that the frog can

catch. (20 pts)

Hint: be careful: not all lily pads are accessible to the frog; the frog can only

jump from the starting lily pad 1 to lily pads 4 and 5 but cannot access lily

pads 2 and 3. Also, for some i there might be no ies on that lily pad (i.e.,

fi = 0). So you want to distinguish between lily pads without ies but which

are accessible and lily pads which are not accessible.

4. You are on vacation for N days at a resort that has three possible activities

1,2 and 3. For each day i, for each activity 1,2 or 3, you’ve determined how

much enjoyment e(i; j) (1 i n; 1 j 3) you will get out of that

activity if you do it on that particular day (the same activity might give you

a dierent amounts of enjoyment at dierent days). However, you are not

allowed to do the same activity two days in a row. Design an algorithm for

determining the maximum total enjoyment possible over the entire stay of

N days and the sequence of activities you should do at each day. (20 pts)

5. Given a weighted directed graph G(V;E), nd a path in G (possibly self-

intersecting) of length exactly K that has the maximum total weight. The

path can visit a vertex multiple times and can traverse an edge also multiple

times. It can also start and end at arbitrary vertices or even start and end

at the same vertex. (20 pts)

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