37 lines
1.2 KiB
Tcl
Executable File
37 lines
1.2 KiB
Tcl
Executable File
#!/usr/bin/env tclsh
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package require Tcl 8.6
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set input stdin
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regexp {Time: (.*)} [gets $input] _ time
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regexp {Distance: (.*)} [gets $input] _ dist
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proc solve {t d} {
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# the distance traveled if the boat is released at time i
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# is equal to (t-i)*i
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# we want to know the range of values of i for which this
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# exceeds the best time (d)
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# (t-i)*i > d
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# a little rearranging gets us the quadratic equation
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# i^2 - ti + d <= 0
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# which we can determine the crossing points for
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# using the quadratic formula (the good one, not the
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# one you learned in school)
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#puts "solve $t $d"
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set h [expr {$t / 2.0}]
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set s [expr {sqrt($h*$h - $d)}]
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set a [expr {int($h-$s)}]
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set b [expr {int($h+$s)}]
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# in general these will not be at integer values,
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# so we probe the floor and ceiling of each crossing
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# point to determine exactly where the condition is met
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if {($t-$a)*$a <= $d} { incr a }
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if {($t-$b)*$b > $d} { incr b }
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#puts "a=$a b=$b"
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return [expr {$b - $a}]
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}
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proc lmul {list} { return [expr [join $list *]] }
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proc smush {list} { return [join $list ""] }
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puts "Part 1: [lmul [lmap t $time d $dist {solve $t $d}]]"
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puts "Part 2: [solve [smush $time] [smush $dist]]"
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