Upgrade This Downtown Area

Computer Science Level 1

Many business owners in the downtown area of this town have decided that a central mall would drive more traffic to their stores. They want to build the biggest rectangular mall possible, but have discovered that there are several plots of land that can not be developed in this way.

If the black squares represent unavailable areas, what is the area of the largest possible shopping mall development?


The answer is 81.

Chung Gene Keun by Chung Gene Keun , 42, USA

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8 solutions

Chris Hambacher
Feb 4, 2014

You know that the region with the biggest area should be a square, or something that close to one. Looking at the picture, in the top right corner, you see a large rectangular region, which is actually a 9x9 square, making the answer 81.

11 Helpful 0 Interesting 0 Brilliant 0 Confused

I think you mean to say top left. If you plot it in a spread sheet with columns A-T (left to right) across the top and rows 1-20 (Top to bottom) along the side, the 9x9 box covers cells B2:J10

Craig Haydock - 7 years, 4 months ago

This is an incorrect solution. 

1
2
 
.....
..###

The largest square has size 2 × 2 2 \times 2 , but the largest rectangle has size 1 × 5 1 \times 5 .

Ivan Koswara - 5 years, 8 months ago
Luccas Mariano
Feb 12, 2014

Biggest area is 9 x 9, so 9*9 = 81

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Jiljith John
Feb 26, 2014

it is really a very simple question .From the given figure it can be quickly identify a 9x9 rectangle(or square)...which is the largest one

1 Helpful 0 Interesting 0 Brilliant 0 Confused

look at black point in the midle of square. Devided big square into four square and analys wich one have big area witout black square

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Vineeth Kartha
Mar 4, 2014

But How can we do this programatically?

0 Helpful 0 Interesting 0 Brilliant 0 Confused

dynamic programming

Faruk Alibasic - 7 years, 3 months ago
Sangram Gupta
Feb 22, 2014

It is always when the number of divisions in any terrain have numeric closest to each other and the largest of that possible set has to be checked. Eg: If a cube has to cut into 64 equal pieces the you cut it into 3 3 3 way.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Karan Mali
Feb 8, 2014

the black boxes display the places that cannot be used for building the mall. hence the shopping mall cannot be constructed at any area which has a black box in between.. the area on the top left corner of the given graph has no such black boxes in between.. there are 9 such boxes vertically and 9 boxes horizontally,, hence the area will be 9*9=81.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Saswat24 Das
Feb 5, 2014

that was easy but a little tricky because it had approximately similar looking and estimating plots of land.The solution is the top-left corner square with 81 sq unit being its area. #easy!

0 Helpful 0 Interesting 0 Brilliant 0 Confused

does it have anything to do with programming!!!!! i can see the ans in bare eyes

Reaz Mahmud - 7 years, 4 months ago

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