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Episode 19 – How to cut a square grid ? European section – Season 3

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(1)

Episode 19 – How to cut a square grid ?

European section – Season 3

(2)

The problem

n + 1

m + 1

(3)

The problem

n + 1 m + 1

What is the best way to cut a rectangular grid ?

(4)

Problem #1

How should you cut the grid so that the

total length cut is minimal ?

(5)

Problem #1

n + 1

m + 1

(6)

Problem #1

n + 1 m + 1

Solution :

(7)

Problem #1

n + 1 m + 1

Solution : The total cut length is always 2mn + m + n.

(8)

Problem #2

How should you cut the grid so that the

number of cuts is minimal ?

(9)

Problem #2

n + 1

m + 1

(10)

Problem #2

n + 1 m + 1

Solution :

(11)

Problem #2

n + 1 m + 1

Solution : The total number of cuts is always mn + m + n.

(12)

Problem #3

How should you cut the grid so that the

time needed to cut it is minimal ?

(13)

Problem #3

n + 1

m + 1

(14)

Problem #3

n + 1 m + 1

Solution :

(15)

Problem #3

n + 1 m + 1

Solution : The minimal cutting time is mn + 2m + n + 1.

(16)

Problem #3

n + 1 m + 1

Solution : The minimal cutting time is mn + 2m + n + 1.

The solution is to start with a vertical grid

and cut into into strips.

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How to cut a square grid ?

If we start by utting all the vertial lines in the urrent position, then we will have to rotate. eah of the n + 1 strips of squares and ut them one