From: Mart Lubbers Date: Wed, 16 Dec 2015 19:32:39 +0000 (+0100) Subject: update code' X-Git-Url: https://git.martlubbers.net/?a=commitdiff_plain;h=cd29bc230f39614f057810c37520ce20f75d76d0;p=ar1516.git update code' git pus"g --- diff --git a/a2/1.tex b/a2/1.tex index b294ecc..94a01cb 100644 --- a/a2/1.tex +++ b/a2/1.tex @@ -1,5 +1,5 @@ \section{Problem 1} -{\em Three non-self-supporting villages $A$, $B$ and $C$ in the middle of +\emph{Three non-self-supporting villages $A$, $B$ and $C$ in the middle of nowhere consume one food package each per time unit. The required food packages are delivered by a truck, having a capacity of $300$ food packages. The locations of the villages are given in the following picture, in which the @@ -19,28 +19,30 @@ city $B$, city $C$, the truck, the trucks location and a help variable to record how much food is dumped in the city. The distance between two cities is described with the function $dist(x, y)$. For all cities except $S$ a variable is defined that states the maximum capacity. -$$a_{max}=120\wedge b_{max}=120\wedge c_{max}=200$$ +$$a_{\max}=120\wedge b_{\max}=120\wedge c_{\max}=200$$ Iteration $0$ depicts the initial state and can be described with a simple conjuction: -$$a_0=40\wedge b_0=30\wedge c_0=145\wedge t_0=300\wedge l_0=S\wedge d_0=0$$. +$$a_0=40\wedge b_0=30\wedge c_0=145\wedge t_0=300\wedge l_0=S\wedge d_0=0$$ After that all iteration can be formalized as -\begin{align} +$$\begin{array}{lrl} \bigwedge_{i\in I} \Bigg( % Bent in S - & \Bigg[l_i=S\wedge d_i=0\wedge t_i=300\wedge - \bigvee_{k\in\{A,B\}}\bigg(l_{i-1}=k\wedge - \bigwedge_{s\in\{A,B,C\}}s_i=s_{i-1}-dist(S, k)\bigg)\Bigg]\vee\\ + & \Bigg[ & l_i=S\wedge d_i=0\wedge t_i=300\wedge\\ + & & \bigvee_{k\in\{A,B\}} + \bigg(l_{i-1}=k\wedge + \bigwedge_{s\in\{A,B,C\}} + s_i=s_{i-1}-dist(S, k)\bigg)\Bigg]\vee\\ % Bent in A,B,C - & \bigvee_{k\in\{a,b,c\}} - \Bigg[l_i=k\wedge d_i>0\wedge d_i0\wedge d_i