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             ________                         ________
            |        |____                   |        |____    
...
|                         |      |_________________________|   
|                         |      |     a single strip      |   
|_________________________|      |_________________________|

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             ________                         ________
            |        |____                   |        |____    
...
|                         |      |           | subproblem  |   
|                         |      | subproblem|             |   
|_________________________|      |___________|_____________|

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             ________                            ________
            |        |____                      |________|____    
...
|                         |         |___________|             |   
|                         |         |           |_____________|   
|_________________________|         |___________|_____________|

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use List::Util qw(min sum);
use strict;
...
        reconstruct($split+1, $right, $height);
    }
}

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you can solve this with 5 strips
strip of length 55, height 16
...
strip of length 15, height 8
strip of length 20, height 32
strip of length 10, height 24