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\$\begingroup\$ Your initial board generation does not guarantee a board that has the input density. I guess it's OP's choice whether to allow that or not. \$\endgroup\$

JungHwan Min
– JungHwan Min

2016-12-27 16:02:22 +00:00
Commented Dec 27, 2016 at 16:02
\$\begingroup\$ Oh, @JarkoDubbeldam asked that already. \$\endgroup\$

JungHwan Min
– JungHwan Min

2016-12-27 16:03:58 +00:00
Commented Dec 27, 2016 at 16:03
\$\begingroup\$ @JungHwanMin How so? Let the density be d. Every position gets a value between 0 and 1. If between 0 and ᵈ⁄₂ it becomes a ↓,. If between ᵈ⁄₂ and d it becomes a →. If between d and 1 it stays empty. \$\endgroup\$

Adám
– Adám

2016-12-27 17:15:55 +00:00
Commented Dec 27, 2016 at 17:15
\$\begingroup\$ Well, an extreme case would be: every position somehow gets the value 0 (because they're (pseudo)-randomly generated (pseudo)-independently; very improbable but possible). Then your board is full of ↓s. \$\endgroup\$

JungHwan Min
– JungHwan Min

2016-12-27 17:19:09 +00:00
Commented Dec 27, 2016 at 17:19
\$\begingroup\$ @JungHwanMin Ah, I see what you mean. \$\endgroup\$

Adám
– Adám

2016-12-27 17:25:23 +00:00
Commented Dec 27, 2016 at 17:25

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