Problem 45415. Find an optimal placement of coolers on a grid

Created by Karl Ezra Pilario

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In a certain chemical plant, 6 new pieces of cooling equipment (coolers) are to be installed in a vacant space. This vacant space was divided into a grid of 6 cells by 6 cells. Your task is to assign the 6 coolers to 6 cells in this grid with the following requirements:<ol><li>There must be one cooler for every column in the grid.</li><li>If you decide to install a cooler at row R, column C, then the cooler at column C+1 must be installed either on row R-1, R, or R+1 only. This is done to ease the connection of coolers by piping.</li><li>The total installation cost for the 6 coolers must be minimum.</li></ol>For this problem, you are given a cost matrix (COST) in relation to the third requirement above. COST is a 6 x 6 matrix where the r,c-th element is the cost of assigning any cooler to row r, column c (All the coolers are identical). Write a function that accepts the matrix COST, and output the value of the minimum cost of installation. You are ensured that all elements of COST are integers in the range [1,1000].In the sample test case below, the optimal placement is at the following rows: 4,3,3,2,2,2.<pre class="language-matlab">&gt;&gt; COST = [695 766 710 119 752 548;
 318 796 755 499 256 139;
 951 187 277 960 506 150;
 35 490 680 341 700 258;
 439 446 656 586 891 841;
 382 647 163 224 960 255];
&gt;&gt; coolers(COST)
ans = 
 1393
</pre>Meanwhile, the optimal placement for the case below is at rows: 5,6,5,6,5,6<pre class="language-matlab">&gt;&gt; COST = [815 617 918 76 569 312;
 244 474 286 54 470 529;
 930 352 758 531 455 988;
 350 831 754 780 12 602;
 197 586 381 935 163 263;
 252 550 568 130 795 100];
&gt;&gt; coolers(COST)
ans = 
 1521
</pre>

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49 Solutions
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Last Solution submitted on Nov 11, 2020

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Alfonso Nieto-Castanon on 19 Aug 2020

nice problem (hint: viterbi) and overall an excellent series / problem-group!

Jimmy Sølvsteen Nielsen on 10 Sep 2020

I wish I had done a clever solution but I resorted to brute forcing it!

Solution Comments

Solution 2188958

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3 Comments

Karl Ezra Pilario on 2 Apr 2020

This passed because the grid is small. I knew I should have changed the problem to a 20 x 20 or 100 x 100 grid haha. Anyway, I'll make a harder version of this problem in the next series. :)

Nikolaos Nikolaou on 3 Apr 2020

And i ll prove to you then it will still work :)

Karl Ezra Pilario on 3 Apr 2020

Yeah probably so. I don't even know if Cody has a memory limit or time limit so one can create test cases that can really filter unwanted solutions. oh well.

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Problem 45415. Find an optimal placement of coolers on a grid

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Problem 45415. Find an optimal placement of coolers on a grid

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