85 lines
3.5 KiB
Text
85 lines
3.5 KiB
Text
# mode to hold details of a Heronian triangle #
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MODE HERONIAN = STRUCT( INT a, b, c, area, perimeter );
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# returns the details of the Heronian Triangle with sides a, b, c or nil if it isn't one #
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PROC try ht = ( INT a, b, c )REF HERONIAN:
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BEGIN
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REF HERONIAN t := NIL;
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REAL s = ( a + b + c ) / 2;
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REAL area squared = s * ( s - a ) * ( s - b ) * ( s - c );
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IF area squared > 0 THEN
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# a, b, c does form a triangle #
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REAL area = sqrt( area squared );
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IF ENTIER area = area THEN
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# the area is integral so the triangle is Heronian #
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t := HEAP HERONIAN := ( a, b, c, ENTIER area, a + b + c )
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FI
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FI;
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t
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END # try ht # ;
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# returns the GCD of a and b #
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PROC gcd = ( INT a, b )INT: IF b = 0 THEN a ELSE gcd( b, a MOD b ) FI;
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# prints the details of the Heronian triangle t #
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PROC ht print = ( REF HERONIAN t )VOID:
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print( ( whole( a OF t, -4 ), whole( b OF t, -5 ), whole( c OF t, -5 ), whole( area OF t, -5 ), whole( perimeter OF t, -10 ), newline ) );
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# prints headings for the Heronian Triangle table #
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PROC ht title = VOID: print( ( " a b c area perimeter", newline, "---- ---- ---- ---- ---------", newline ) );
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BEGIN
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# construct ht as a table of the Heronian Triangles with sides up to 200 #
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[ 1 : 1000 ]REF HERONIAN ht;
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REF HERONIAN t;
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INT ht count := 0;
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FOR c TO 200 DO
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FOR b TO c DO
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FOR a TO b DO
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IF NOT ODD ( a + b + c ) THEN
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IF gcd( gcd( a, b ), c ) = 1 THEN
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t := try ht( a, b, c );
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IF REF HERONIAN(t) ISNT REF HERONIAN(NIL) THEN
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ht[ ht count +:= 1 ] := t
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FI
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FI
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FI
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OD
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OD
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OD;
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# sort the table on ascending area, perimeter and max side length #
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# note we constructed the triangles with c as the longest side #
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BEGIN
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INT lower := 1, upper := ht count;
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WHILE upper := upper - 1;
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BOOL swapped := FALSE;
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FOR i FROM lower TO upper DO
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REF HERONIAN h := ht[ i ];
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REF HERONIAN k := ht[ i + 1 ];
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IF area OF k < area OF h OR ( area OF k = area OF h
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AND ( perimeter OF k < perimeter OF h
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OR ( perimeter OF k = perimeter OF h
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AND c OF k < c OF h
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)
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)
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)
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THEN
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ht[ i ] := k;
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ht[ i + 1 ] := h;
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swapped := TRUE
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FI
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OD;
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swapped
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DO SKIP OD;
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# display the triangles #
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print( ( "There are ", whole( ht count, 0 ), " Heronian triangles with sides up to 200", newline ) );
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ht title;
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FOR ht pos TO 10 DO ht print( ht( ht pos ) ) OD;
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print( ( " ...", newline ) );
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print( ( "Heronian triangles with area 210:", newline ) );
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ht title;
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FOR ht pos TO ht count DO
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REF HERONIAN tr := ht[ ht pos ];
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IF area OF tr = 210 THEN ht print( tr ) FI
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OD
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END
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END
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