Smallest multiple: Difference between revisions
Thundergnat (talk | contribs) (→{{header|Raku}}: more concisely, use built-in) |
(→{{header|Pascal}}: extended version) |
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<pre> |
<pre> |
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232792560 |
232792560 |
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</pre> |
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===extended=== |
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Find that the count of digits is nearly a constant x upper rangelimit.<br> The number of factors is the count of primes til limit.See GetFactorList.<br>No need for lcm or prime decomposition and other contortions.<BR> |
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Using prime sieve. |
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<lang pascal>{$IFDEF FPC} |
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{$MODE DELPHI} |
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{$ELSE} |
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{$APPTAYPE CONSOLE} |
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{$ENDIF} |
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{$DEFINE USE_GMP} |
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uses |
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{$IFDEF USE_GMP} |
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gmp, |
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{$ENDIF} |
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sysutils; //format |
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const |
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UpperLimit = 2*1000*1000; |
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MAX_UINT64 = 46; |
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type |
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tFactors = array of Uint32; |
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tprimelist = array of byte; |
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var |
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primelist : tPrimelist; |
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procedure Init_Primes; |
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var |
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pPrime : pByte; |
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p ,i: NativeUInt; |
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begin |
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setlength(primelist,UpperLimit+3*8+1); |
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pPrime := @primelist[0]; |
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//delete multiples of 2,3 |
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i := 0; |
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repeat |
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//take care of endianess //0706050403020100 |
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pUint64(@pPrime[i+0])^ := $0100010000000100; |
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pUint64(@pPrime[i+8])^ := $0000010001000000; |
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pUint64(@pPrime[i+16])^:= $0100000001000100; |
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inc(i,24); |
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until i>UpperLimit; |
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p := 5; |
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repeat |
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if pPrime[p] <> 0 then |
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begin |
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i := p*p; |
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if i > UpperLimit then |
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break; |
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repeat |
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pPrime[i] := 0; |
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inc(i,2*p); |
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until i>UpperLimit; |
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end; |
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inc(p,2); |
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until p*p>UpperLimit; |
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pPrime[1] := 0; |
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pPrime[2] := 1; |
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pPrime[3] := 1; |
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end; |
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{$IFDEF USE_GMP} |
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procedure ConvertToMPZ(const factors:tFactors); |
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var |
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mp : mpz_t; |
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s : AnsiString; |
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i : integer; |
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begin |
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mpz_init(mp); |
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mpz_set_ui(mp,1); |
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for i := 0 to high(factors) do |
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mpz_mul_ui(mp,mp,factors[i]); |
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i := mpz_sizeinbase(mp,10); |
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setlength(s,i+10); |
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mpz_get_str(@s[1],10,mp); |
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i := i+10; |
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while not(s[i] in['0'..'9']) do |
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dec(i); |
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setlength(s,i+1); |
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if length(s)> 22 then |
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begin |
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move(s[i-9],s[13],10); |
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s[11]:= '.';s[12]:= '.'; |
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setlength(s,22); |
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end; |
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writeln(s); |
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mpz_clear(mp); |
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end; |
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{$ENDIF} |
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procedure CheckDigits(const factors:tFactors); |
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var |
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digCnt : extended; |
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i : integer; |
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begin |
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digcnt := 0; |
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for i := 0 to high(factors) do |
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digcnt += ln(factors[i]); |
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i := trunc(digcnt/ln(10)+1); |
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writeln(' has ',length(factors):10,' factors and ',i:10,' digits'); |
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{$IFDEF USE_GMP} |
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If i < 10000 then |
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ConvertToMPZ(factors); |
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{$ENDIF} |
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end; |
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function ConvertToUint64(const factors:tFactors):Uint64; |
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var |
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i : integer; |
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begin |
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if length(factors) >15 then |
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Exit(0); |
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result := 1; |
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for i := 0 to high(factors) do |
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result *= factors[i]; |
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end; |
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function ConvertToStr(const factors:tFactors):Ansistring; |
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var |
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s : Ansistring; |
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i : integer; |
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begin |
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result := ''; |
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for i := 0 to high(factors)-1 do |
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begin |
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str(factors[i],s); |
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result += s+'*'; |
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end; |
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str(factors[High(factors)],s); |
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result += s; |
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end; |
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procedure GetFactorList(var factors:tFactors;max:Uint32); |
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var |
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pPrime : pByte; |
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n,f,lf : Uint32; |
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BEGIN |
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pPrime := @primeList[0]; |
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n := 2; |
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lf := 0; |
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setlength(factors,lf); |
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while n*n <= max do |
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Begin |
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if pPrime[n]<>0 then |
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begin |
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setlength(factors,lf+1); |
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f := n*n; |
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while f*n <= max do |
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f*= n; |
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factors[lf] := f; |
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inc(lf); |
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end; |
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inc(n); |
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end; |
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//the rest are all the primes up to max |
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For n := n to max do |
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if pPrime[n]<>0 then |
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Begin |
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setlength(factors,lf+1); |
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factors[lf] := n; |
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inc(lf); |
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end; |
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end; |
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procedure Check(var factors:tFactors;max:Uint32); |
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begin |
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GetFactorList(factors,max); |
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write(max:10,': '); |
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if length(factors)>15 then |
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CheckDigits(factors) |
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else |
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writeln(ConvertToUint64(factors):21,' = ',ConvertToStr(factors)); |
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end; |
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var |
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factors:tFactors; |
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max: Uint32; |
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BEGIN |
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Init_Primes; |
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max := 200; |
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repeat |
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check(factors,max); |
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max *=10; |
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until max > UpperLimit; |
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For max := MAX_UINT64 downto 2 do |
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check(factors,max); |
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{$IFDEF WINDOWS} |
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READLN; |
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{$ENDIF} |
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END.</lang> |
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{{out}} |
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<pre style="height:300px"> |
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TIO.RUN Real time: 0.203 s User time: 0.147 s Sys. time: 0.054 s CPU share: 98.88 % |
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200: has 46 factors and 90 digits |
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3372935888..0066992000 |
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2000: has 303 factors and 867 digits |
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1511177948..5463680000 |
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20000: has 2262 factors and 8676 digits |
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4879325627..8112000000 |
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200000: has 17984 factors and 86871 digits |
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2000000: has 148933 factors and 868639 digits |
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46: 9419588158802421600 = 32*27*25*7*11*13*17*19*23*29*31*37*41*43 |
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45: 9419588158802421600 = 32*27*25*7*11*13*17*19*23*29*31*37*41*43 |
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44: 9419588158802421600 = 32*27*25*7*11*13*17*19*23*29*31*37*41*43 |
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43: 9419588158802421600 = 32*27*25*7*11*13*17*19*23*29*31*37*41*43 |
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42: 219060189739591200 = 32*27*25*7*11*13*17*19*23*29*31*37*41 |
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41: 219060189739591200 = 32*27*25*7*11*13*17*19*23*29*31*37*41 |
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40: 5342931457063200 = 32*27*25*7*11*13*17*19*23*29*31*37 |
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39: 5342931457063200 = 32*27*25*7*11*13*17*19*23*29*31*37 |
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38: 5342931457063200 = 32*27*25*7*11*13*17*19*23*29*31*37 |
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37: 5342931457063200 = 32*27*25*7*11*13*17*19*23*29*31*37 |
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36: 144403552893600 = 32*27*25*7*11*13*17*19*23*29*31 |
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35: 144403552893600 = 32*27*25*7*11*13*17*19*23*29*31 |
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34: 144403552893600 = 32*27*25*7*11*13*17*19*23*29*31 |
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33: 144403552893600 = 32*27*25*7*11*13*17*19*23*29*31 |
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32: 144403552893600 = 32*27*25*7*11*13*17*19*23*29*31 |
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31: 72201776446800 = 16*27*25*7*11*13*17*19*23*29*31 |
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30: 2329089562800 = 16*27*25*7*11*13*17*19*23*29 |
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29: 2329089562800 = 16*27*25*7*11*13*17*19*23*29 |
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28: 80313433200 = 16*27*25*7*11*13*17*19*23 |
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27: 80313433200 = 16*27*25*7*11*13*17*19*23 |
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26: 26771144400 = 16*9*25*7*11*13*17*19*23 |
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25: 26771144400 = 16*9*25*7*11*13*17*19*23 |
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24: 5354228880 = 16*9*5*7*11*13*17*19*23 |
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23: 5354228880 = 16*9*5*7*11*13*17*19*23 |
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22: 232792560 = 16*9*5*7*11*13*17*19 |
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21: 232792560 = 16*9*5*7*11*13*17*19 |
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20: 232792560 = 16*9*5*7*11*13*17*19 |
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19: 232792560 = 16*9*5*7*11*13*17*19 |
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18: 12252240 = 16*9*5*7*11*13*17 |
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17: 12252240 = 16*9*5*7*11*13*17 |
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16: 720720 = 16*9*5*7*11*13 |
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15: 360360 = 8*9*5*7*11*13 |
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14: 360360 = 8*9*5*7*11*13 |
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13: 360360 = 8*9*5*7*11*13 |
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12: 27720 = 8*9*5*7*11 |
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11: 27720 = 8*9*5*7*11 |
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10: 2520 = 8*9*5*7 |
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9: 2520 = 8*9*5*7 |
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8: 840 = 8*3*5*7 |
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7: 420 = 4*3*5*7 |
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6: 60 = 4*3*5 |
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5: 60 = 4*3*5 |
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4: 12 = 4*3 |
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3: 6 = 2*3 |
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2: 2 = 2 |
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</pre> |
</pre> |
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Revision as of 13:47, 21 October 2021
- Task
Task desciption is taken from Project Euler
(https://projecteuler.net/problem=5)
2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.
What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?
ALGOL 68
Uses Algol 68G's LONG LONG INT which has specifiable precision.
<lang algol68>BEGIN # find the smallest number that is divisible by each of the numbers 1..n #
# translation of the Wren sample # PR precision 1000 PR # set the precision of LONG LONG INT # PR read "primes.incl.a68" PR # returns the lowest common multiple of the numbers 1 : n # PROC lcm = ( INT n )LONG LONG INT: BEGIN # sieve the primes to n # []BOOL prime = PRIMESIEVE n; LONG LONG INT result := 1; FOR p TO UPB prime DO IF prime[ p ] THEN LONG LONG INT f := p; # f will be set to the # WHILE f * p <= n DO f *:= p OD; # highest multiple of p <= n # result *:= f FI OD; result END # lcm # ; # returns a string representation of n with commas # PROC commatise = ( LONG LONG INT n )STRING: BEGIN STRING result := ""; STRING unformatted = whole( n, 0 ); INT ch count := 0; FOR c FROM UPB unformatted BY -1 TO LWB unformatted DO IF ch count <= 2 THEN ch count +:= 1 ELSE ch count := 1; "," +=: result FI; unformatted[ c ] +=: result OD; result END; # commatise # print( ( "The LCMs of the numbers 1 to N inclusive is:", newline ) ); []INT tests = ( 10, 20, 200, 2000 ); FOR i FROM LWB tests TO UPB tests DO print( ( whole( tests[ i ], -5 ), ": ", commatise( lcm( tests[ i ] ) ), newline ) ) OD
END</lang>
- Output:
10: 2,520 20: 232,792,560 200: 337,293,588,832,926,264,639,465,766,794,841,407,432,394,382,785,157,234,228,847,021,917,234,018,060,677,390,066,992,000 2000: 151,117,794,877,444,315,307,536,308,337,572,822,173,736,308,853,579,339,903,227,904,473,000,476,322,347,234,655,122,160,866,668,946,941,993,951,014,270,933,512,030,194,957,221,371,956,828,843,521,568,082,173,786,251,242,333,157,830,450,435,623,211,664,308,500,316,844,478,617,809,101,158,220,672,108,895,053,508,829,266,120,497,031,742,749,376,045,929,890,296,052,805,527,212,315,382,805,219,353,316,270,742,572,401,962,035,464,878,235,703,759,464,796,806,075,131,056,520,079,836,955,770,415,021,318,508,272,982,103,736,658,633,390,411,347,759,000,563,271,226,062,182,345,964,184,167,346,918,225,243,856,348,794,013,355,418,404,695,826,256,911,622,054,015,423,611,375,261,945,905,974,225,257,659,010,379,414,787,547,681,984,112,941,581,325,198,396,634,685,659,217,861,208,771,400,322,507,388,161,967,513,719,166,366,839,894,214,040,787,733,471,287,845,629,833,993,885,413,462,225,294,548,785,581,641,804,620,417,256,563,685,280,586,511,301,918,399,010,451,347,815,776,570,842,790,738,545,306,707,750,937,624,267,501,103,840,324,470,083,425,714,138,183,905,657,667,736,579,430,274,197,734,179,172,691,637,931,540,695,631,396,056,193,786,415,805,463,680,000
Go
<lang go>package main
import (
"fmt" "math/big" "rcu"
)
func lcm(n int) *big.Int {
lcm := big.NewInt(1) t := new(big.Int) for _, p := range rcu.Primes(n) { f := p for f*p <= n { f *= p } lcm.Mul(lcm, t.SetUint64(uint64(f))) } return lcm
}
func main() {
fmt.Println("The LCMs of the numbers 1 to N inclusive is:") for _, i := range []int{10, 20, 200, 2000} { fmt.Printf("%4d: %s\n", i, lcm(i)) }
}</lang>
- Output:
The LCMs of the numbers 1 to N inclusive is: 10: 2520 20: 232792560 200: 337293588832926264639465766794841407432394382785157234228847021917234018060677390066992000 2000: 151117794877444315307536308337572822173736308853579339903227904473000476322347234655122160866668946941993951014270933512030194957221371956828843521568082173786251242333157830450435623211664308500316844478617809101158220672108895053508829266120497031742749376045929890296052805527212315382805219353316270742572401962035464878235703759464796806075131056520079836955770415021318508272982103736658633390411347759000563271226062182345964184167346918225243856348794013355418404695826256911622054015423611375261945905974225257659010379414787547681984112941581325198396634685659217861208771400322507388161967513719166366839894214040787733471287845629833993885413462225294548785581641804620417256563685280586511301918399010451347815776570842790738545306707750937624267501103840324470083425714138183905657667736579430274197734179172691637931540695631396056193786415805463680000
Pascal
Here the simplest way, like Raku, check the highest exponent of every prime in range
Using harded coded primes.
<lang pascal>{$IFDEF FPC}
{$MODE DELPHI}
{$ELSE}
{$APPTAYPE CONSOLE}
{$ENDIF} const
smallprimes : array[0..10] of Uint32 = (2,3,5,7,11,13,17,19,23,29,31); MAX = 20;
function getmaxfac(pr: Uint32): Uint32; //get the pr^highest exponent of prime used in 2 .. MAX var
i,fac : integer;
Begin
result := pr; while pr*result <= MAX do result *= pr;
end;
var
n,pr,prIdx : Uint32;
BEGIN
n := 1; prIdx := 0; pr := smallprimes[prIdx]; repeat pr := smallprimes[prIdx]; n *= getmaxfac(pr); inc(prIdx); pr := smallprimes[prIdx]; until pr>MAX; writeln(n);
{$IFDEF WINDOWS}
READLN;
{$ENDIF} END. </lang>
- Output:
232792560
extended
Find that the count of digits is nearly a constant x upper rangelimit.
The number of factors is the count of primes til limit.See GetFactorList.
No need for lcm or prime decomposition and other contortions.
Using prime sieve.
<lang pascal>{$IFDEF FPC}
{$MODE DELPHI}
{$ELSE}
{$APPTAYPE CONSOLE}
{$ENDIF} {$DEFINE USE_GMP} uses
{$IFDEF USE_GMP} gmp, {$ENDIF} sysutils; //format
const
UpperLimit = 2*1000*1000; MAX_UINT64 = 46;
type
tFactors = array of Uint32; tprimelist = array of byte;
var
primelist : tPrimelist;
procedure Init_Primes; var
pPrime : pByte; p ,i: NativeUInt;
begin
setlength(primelist,UpperLimit+3*8+1); pPrime := @primelist[0]; //delete multiples of 2,3 i := 0; repeat //take care of endianess //0706050403020100 pUint64(@pPrime[i+0])^ := $0100010000000100; pUint64(@pPrime[i+8])^ := $0000010001000000; pUint64(@pPrime[i+16])^:= $0100000001000100; inc(i,24); until i>UpperLimit; p := 5; repeat if pPrime[p] <> 0 then begin i := p*p; if i > UpperLimit then break; repeat pPrime[i] := 0; inc(i,2*p); until i>UpperLimit; end; inc(p,2); until p*p>UpperLimit; pPrime[1] := 0; pPrime[2] := 1; pPrime[3] := 1;
end;
{$IFDEF USE_GMP} procedure ConvertToMPZ(const factors:tFactors); var
mp : mpz_t; s : AnsiString; i : integer;
begin
mpz_init(mp); mpz_set_ui(mp,1); for i := 0 to high(factors) do mpz_mul_ui(mp,mp,factors[i]); i := mpz_sizeinbase(mp,10); setlength(s,i+10); mpz_get_str(@s[1],10,mp); i := i+10; while not(s[i] in['0'..'9']) do dec(i); setlength(s,i+1); if length(s)> 22 then begin move(s[i-9],s[13],10); s[11]:= '.';s[12]:= '.'; setlength(s,22); end; writeln(s); mpz_clear(mp);
end; {$ENDIF}
procedure CheckDigits(const factors:tFactors); var
digCnt : extended; i : integer;
begin
digcnt := 0; for i := 0 to high(factors) do digcnt += ln(factors[i]); i := trunc(digcnt/ln(10)+1); writeln(' has ',length(factors):10,' factors and ',i:10,' digits'); {$IFDEF USE_GMP} If i < 10000 then ConvertToMPZ(factors); {$ENDIF}
end;
function ConvertToUint64(const factors:tFactors):Uint64; var
i : integer;
begin
if length(factors) >15 then Exit(0); result := 1; for i := 0 to high(factors) do result *= factors[i];
end;
function ConvertToStr(const factors:tFactors):Ansistring; var
s : Ansistring; i : integer;
begin
result := ; for i := 0 to high(factors)-1 do begin str(factors[i],s); result += s+'*'; end; str(factors[High(factors)],s); result += s;
end;
procedure GetFactorList(var factors:tFactors;max:Uint32); var
pPrime : pByte; n,f,lf : Uint32;
BEGIN
pPrime := @primeList[0]; n := 2; lf := 0; setlength(factors,lf);
while n*n <= max do Begin if pPrime[n]<>0 then begin setlength(factors,lf+1); f := n*n; while f*n <= max do f*= n; factors[lf] := f; inc(lf); end; inc(n); end; //the rest are all the primes up to max For n := n to max do if pPrime[n]<>0 then Begin setlength(factors,lf+1); factors[lf] := n; inc(lf); end;
end;
procedure Check(var factors:tFactors;max:Uint32); begin
GetFactorList(factors,max); write(max:10,': '); if length(factors)>15 then CheckDigits(factors) else writeln(ConvertToUint64(factors):21,' = ',ConvertToStr(factors));
end;
var
factors:tFactors; max: Uint32;
BEGIN
Init_Primes;
max := 200; repeat check(factors,max); max *=10; until max > UpperLimit; For max := MAX_UINT64 downto 2 do check(factors,max);
{$IFDEF WINDOWS}
READLN;
{$ENDIF} END.</lang>
- Output:
TIO.RUN Real time: 0.203 s User time: 0.147 s Sys. time: 0.054 s CPU share: 98.88 % 200: has 46 factors and 90 digits 3372935888..0066992000 2000: has 303 factors and 867 digits 1511177948..5463680000 20000: has 2262 factors and 8676 digits 4879325627..8112000000 200000: has 17984 factors and 86871 digits 2000000: has 148933 factors and 868639 digits 46: 9419588158802421600 = 32*27*25*7*11*13*17*19*23*29*31*37*41*43 45: 9419588158802421600 = 32*27*25*7*11*13*17*19*23*29*31*37*41*43 44: 9419588158802421600 = 32*27*25*7*11*13*17*19*23*29*31*37*41*43 43: 9419588158802421600 = 32*27*25*7*11*13*17*19*23*29*31*37*41*43 42: 219060189739591200 = 32*27*25*7*11*13*17*19*23*29*31*37*41 41: 219060189739591200 = 32*27*25*7*11*13*17*19*23*29*31*37*41 40: 5342931457063200 = 32*27*25*7*11*13*17*19*23*29*31*37 39: 5342931457063200 = 32*27*25*7*11*13*17*19*23*29*31*37 38: 5342931457063200 = 32*27*25*7*11*13*17*19*23*29*31*37 37: 5342931457063200 = 32*27*25*7*11*13*17*19*23*29*31*37 36: 144403552893600 = 32*27*25*7*11*13*17*19*23*29*31 35: 144403552893600 = 32*27*25*7*11*13*17*19*23*29*31 34: 144403552893600 = 32*27*25*7*11*13*17*19*23*29*31 33: 144403552893600 = 32*27*25*7*11*13*17*19*23*29*31 32: 144403552893600 = 32*27*25*7*11*13*17*19*23*29*31 31: 72201776446800 = 16*27*25*7*11*13*17*19*23*29*31 30: 2329089562800 = 16*27*25*7*11*13*17*19*23*29 29: 2329089562800 = 16*27*25*7*11*13*17*19*23*29 28: 80313433200 = 16*27*25*7*11*13*17*19*23 27: 80313433200 = 16*27*25*7*11*13*17*19*23 26: 26771144400 = 16*9*25*7*11*13*17*19*23 25: 26771144400 = 16*9*25*7*11*13*17*19*23 24: 5354228880 = 16*9*5*7*11*13*17*19*23 23: 5354228880 = 16*9*5*7*11*13*17*19*23 22: 232792560 = 16*9*5*7*11*13*17*19 21: 232792560 = 16*9*5*7*11*13*17*19 20: 232792560 = 16*9*5*7*11*13*17*19 19: 232792560 = 16*9*5*7*11*13*17*19 18: 12252240 = 16*9*5*7*11*13*17 17: 12252240 = 16*9*5*7*11*13*17 16: 720720 = 16*9*5*7*11*13 15: 360360 = 8*9*5*7*11*13 14: 360360 = 8*9*5*7*11*13 13: 360360 = 8*9*5*7*11*13 12: 27720 = 8*9*5*7*11 11: 27720 = 8*9*5*7*11 10: 2520 = 8*9*5*7 9: 2520 = 8*9*5*7 8: 840 = 8*3*5*7 7: 420 = 4*3*5*7 6: 60 = 4*3*5 5: 60 = 4*3*5 4: 12 = 4*3 3: 6 = 2*3 2: 2 = 2
Raku
Exercise with some larger values as well.
<lang perl6>say "$_: ", [lcm] 2..$_ for <10 20 200 2000></lang>
- Output:
10: 2520 20: 232792560 200: 337293588832926264639465766794841407432394382785157234228847021917234018060677390066992000 2000: 151117794877444315307536308337572822173736308853579339903227904473000476322347234655122160866668946941993951014270933512030194957221371956828843521568082173786251242333157830450435623211664308500316844478617809101158220672108895053508829266120497031742749376045929890296052805527212315382805219353316270742572401962035464878235703759464796806075131056520079836955770415021318508272982103736658633390411347759000563271226062182345964184167346918225243856348794013355418404695826256911622054015423611375261945905974225257659010379414787547681984112941581325198396634685659217861208771400322507388161967513719166366839894214040787733471287845629833993885413462225294548785581641804620417256563685280586511301918399010451347815776570842790738545306707750937624267501103840324470083425714138183905657667736579430274197734179172691637931540695631396056193786415805463680000
Ring
<lang ring> see "working..." + nl see "Smallest multiple is:" + nl n = 0
while true
n++ flag = 0 for m = 1 to 20 if n % m = 0 flag += 1 ok next if flag = 20 see "" + n + nl exit ok
end
see "done..." + nl </lang>
- Output:
working... Smallest multiple is: 232792560 done...
Wren
We don't really need a computer for the task as set because it's just the product of the maximum prime powers <= 20 which is : 16 x 9 x 5 x 7 x 11 x 13 x 17 x 19 = 232,792,560.
More formally and quite quick by Wren standards at 0.017 seconds: <lang ecmascript>import "./math" for Int import "./big" for BigInt import "./fmt" for Fmt
var lcm = Fn.new { |n|
var primes = Int.primeSieve(n) var lcm = BigInt.one for (p in primes) { var f = p while (f * p <= n) f = f * p lcm = lcm * f } return lcm
}
System.print("The LCMs of the numbers 1 to N inclusive is:") for (i in [10, 20, 200, 2000]) Fmt.print("$,5d: $,i", i, lcm.call(i))</lang>
- Output:
The LCMs of the numbers 1 to N inclusive is: 10: 2,520 20: 232,792,560 200: 337,293,588,832,926,264,639,465,766,794,841,407,432,394,382,785,157,234,228,847,021,917,234,018,060,677,390,066,992,000 2,000: 151,117,794,877,444,315,307,536,308,337,572,822,173,736,308,853,579,339,903,227,904,473,000,476,322,347,234,655,122,160,866,668,946,941,993,951,014,270,933,512,030,194,957,221,371,956,828,843,521,568,082,173,786,251,242,333,157,830,450,435,623,211,664,308,500,316,844,478,617,809,101,158,220,672,108,895,053,508,829,266,120,497,031,742,749,376,045,929,890,296,052,805,527,212,315,382,805,219,353,316,270,742,572,401,962,035,464,878,235,703,759,464,796,806,075,131,056,520,079,836,955,770,415,021,318,508,272,982,103,736,658,633,390,411,347,759,000,563,271,226,062,182,345,964,184,167,346,918,225,243,856,348,794,013,355,418,404,695,826,256,911,622,054,015,423,611,375,261,945,905,974,225,257,659,010,379,414,787,547,681,984,112,941,581,325,198,396,634,685,659,217,861,208,771,400,322,507,388,161,967,513,719,166,366,839,894,214,040,787,733,471,287,845,629,833,993,885,413,462,225,294,548,785,581,641,804,620,417,256,563,685,280,586,511,301,918,399,010,451,347,815,776,570,842,790,738,545,306,707,750,937,624,267,501,103,840,324,470,083,425,714,138,183,905,657,667,736,579,430,274,197,734,179,172,691,637,931,540,695,631,396,056,193,786,415,805,463,680,000