49 lines
1.9 KiB
Racket
49 lines
1.9 KiB
Racket
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;; Text from a semicolon to the end of a line is ignored
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;; This lets the racket engine know it is running racket
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#lang racket
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;; “define” defines a function in the engine
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;; we can use an English name for the function
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;; a number ends in 269696 when its remainder when
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;; divided by 1000000 is 269696 (we omit commas in
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;; numbers... they are used for another reason).
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(define (ends-in-269696? x)
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(= (remainder x 1000000) 269696))
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;; we now define another function square-ends-in-269696?
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;; actually this is the composition of ends-in-269696? and
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;; the squaring function (which is called “sqr” in racket)
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(define square-ends-in-269696? (compose ends-in-269696? sqr))
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;; a for loop lets us iterate (it’s a long Latin word which
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;; Victorians are good at using) over a number range.
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;;
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;; for/first go through the range and break when it gets to
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;; the first true value
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;;
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;; (in-range a b) produces all of the integers from a (inclusive)
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;; to b (exclusive). Because we know that 99736² ends in 269696,
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;; we will stop there. The add1 is to make in-range include 99736
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;;
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;; we define a new variable, so that we can test the verity of
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;; our result
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(define first-number-that-when-squared-ends-in-269696
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(for/first ((i ; “i” will become the ubiquetous looping variable of the future!
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(in-range 1 (add1 99736)))
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; when returns when only the first one that matches
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#:when (square-ends-in-269696? i))
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i))
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;; display prints values out; newline writes a new line (otherwise everything
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;; gets stuck together)
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(display first-number-that-when-squared-ends-in-269696)
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(newline)
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(display (sqr first-number-that-when-squared-ends-in-269696))
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(newline)
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(newline)
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(display (ends-in-269696? (sqr first-number-that-when-squared-ends-in-269696)))
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(newline)
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(display (square-ends-in-269696? first-number-that-when-squared-ends-in-269696))
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(newline)
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;; that all seems satisfactory
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