95 lines
3.9 KiB
Text
95 lines
3.9 KiB
Text
BEGIN # find some esthetic numbers: numbers whose successive digits differ by 1 #
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# returns TRUE if n is esthetic in the specified base, FALSE otherwise #
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PRIO ISESTHETIC = 1;
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OP ISESTHETIC = ( INT n, base )BOOL:
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BEGIN
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INT v := ABS n;
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BOOL is esthetic := TRUE;
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INT prev digit := v MOD base;
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v OVERAB base;
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WHILE v > 0 AND is esthetic
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DO
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INT next digit := v MOD base;
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is esthetic := ABS ( next digit - prev digit ) = 1;
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prev digit := next digit;
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v OVERAB base
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OD;
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is esthetic
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END # ISESTHETIC # ;
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# returns an array of the first n esthetic numbers in the specified base #
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PRIO ESTHETIC = 1;
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OP ESTHETIC = ( INT n, base )[]INT:
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BEGIN
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[ 1 : n ]INT result;
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INT e count := 0;
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FOR i WHILE e count < n DO
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IF i ISESTHETIC base THEN result[ e count +:= 1 ] := i FI
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OD;
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result
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END # ESTHETIC # ;
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# returns a string erpresentation of n in the specified base, 2 <= base <= 16 must be TRUE #
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PRIO TOBASESTRING = 1;
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OP TOBASESTRING = ( INT n, base )STRING:
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IF base < 2 OR base > 16
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THEN # invalid vbase #
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"?" + whole( n, 0 ) + ":" + whole( base, 0 ) + "?"
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ELSE
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INT v := ABS n;
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STRING digits = "0123456789abcdef";
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STRING result := digits[ ( v MOD base ) + 1 ];
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WHILE ( v OVERAB base ) > 0 DO
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digits[ ( v MOD base ) + 1 ] +=: result
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OD;
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IF n < 0 THEN "-" +=: result FI;
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result
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FI # TOBASESTRING # ;
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# sets count to the number of esthetic numbers with length digits in base b less than max #
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# also displays the esthetic numbers #
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PROC show esthetic = ( INT number, base, length, max, REF INT count )VOID:
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IF length = 1
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THEN # number is esthetic #
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IF number <= max THEN
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# number is in the required range #
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print( ( " ", whole( number, 0 ) ) );
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IF ( count +:= 1 ) MOD 9 = 0 THEN print( ( newline ) ) FI
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FI
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ELSE
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# find the esthetic numbers that start with number #
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INT digit = number MOD base;
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INT prefix = number * base;
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IF digit > 0 THEN # can have a lower digit #
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show esthetic( prefix + ( digit - 1 ), base, length - 1, max, count )
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FI;
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IF digit < base - 1 THEN # can have a higher digit #
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show esthetic( prefix + ( digit + 1 ), base, length - 1, max, count )
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FI
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FI # show esthetic # ;
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# task #
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# esthetic numbers from base * 4 to base * 6 for bases 2 to 16 #
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FOR base FROM 2 TO 16 DO
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INT e from = base * 4;
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INT e to = base * 6;
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print( ( "Esthetic numbers ", whole( e from, 0 ), " to ", whole( e to, 0 ), " in base ", whole( base, 0 ), newline ) );
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[]INT e numbers = e to ESTHETIC base;
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print( ( " " ) );
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FOR n FROM e from TO e to DO
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print( ( " ", e numbers[ n ] TOBASESTRING base ) )
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OD;
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print( ( newline ) )
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OD;
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# esthetic base 10 numbers between 1000 and 9999 #
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print( ( "Base 10 eshetic numbers between 1000 and 9999", newline ) );
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INT e count := 0;
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FOR i FROM 1000 TO 9999 DO
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IF i ISESTHETIC 10 THEN
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print( ( " ", whole( i, 0 ) ) );
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IF ( e count +:= 1 ) MOD 16 = 0 THEN print( ( newline ) ) FI
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FI
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OD;
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print( ( newline, newline ) );
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print( ( "Esthetic numbers between 100 000 000 and 130 000 000:", newline ) );
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e count := 0;
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show esthetic( 1, 10, 9, 130 000 000, e count );
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print( ( newline ) );
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print( ( "Found ", whole( e count, 0 ), " esthetic numbers", newline ) )
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END
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