https://ameblo.jp/eugene-y/ The collection of computer science problems(And answers from me! hahahwehahaha duh meh yhwh wer) ja
和訳はまだ

Question1:

T or F?
Let G be an arbitrary connected, undirected graph with a distinct cost c(e) on every edge e. Suppose
e* is the cheapest edge in G. Then there is a minimum spanning tree T of G that contains the edge e*.

Answer:
True. Refer to the proof of correctness of Prim's alg.

Q2:
(a)Suppose we are given an instance of the minimum spanning tree problem on a graph G with edge costs that are all positive and distinct. Let T be a minimum spanning tree for this instance. Now suppose we replace each edge cost by its square, thereby creating a new instance the problem with the same graph but different costs.
T or F? T must still be a minimum spanning tree for this new instance.

Answer:
True. When a >= b and c >= d(all positive integers), a^2 + c^2 > b^2 + d^2. This shows T's cost must still be minimum.

(b)Suppose we are given an instance of the shortest s-t path problem on a directed graph G. We assume that all edge costs are positive and distinct. Let P be a minimum-cost s-t path for this instance. Now suppose we replace each edge cost c(e) by its square c(e)^2, thereby creating a instance of the problem with the same graph but different costs.
T or F? P must still be a minimum-cost s-t path for this new instance.

Answer:
False. Suppose it is true. Then when a+b>=c+d, a^2+b^2>=c^2+d^2. This is simply false(consider the case where a = 3, b = 1, c = 2 and d = 2).



]]> https://ameblo.jp/eugene-y/entry-10752250752.html Thu, 30 Dec 2010 07:16:10 +0900
C言語により記述された次の関数fがある。ここで、display()は
画面に1個の文字Aを書く手続きであるとする。
Consider the following function f written in C. Here, display() is a function
that prints an 'A'.

int f(int x){
display();
if(x==0)return 1;
if(x==1)return 3;
if(x==2)return 5;
return(f(x-1)+f(x-2)+f(x-3));
}

いま、f(x)を呼び出したとき、値105が返された。このf(x)が呼び出されてから
値を返すまでの間に、文字Aは画面にいくつ書かれたか。
Upon a call to f(x), 105 is returned. How many A's have been printed since this call?

１．43　２．44　３．45　４．46　５．47

(Source: 2ch)

Answer:

Naive approach:
x f(x) #A's
7 105 46
6 57 25
5 31 13
4 17 7
3 9 4
2 5 1
1 3 1
0 1 1




]]> https://ameblo.jp/eugene-y/entry-10752207393.html Thu, 30 Dec 2010 05:21:54 +0900 The main objective is to help me improve my rotten brain by making it a rule to think about how to solve problems.

]]> https://ameblo.jp/eugene-y/entry-10752205914.html Thu, 30 Dec 2010 05:11:47 +0900