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holmescn

½ð³æ (ÕýʽдÊÖ)

[½»Á÷] Euler ¹¤³Ì µÚÎåÌ⣺Äܱ»1µ½20ËùÓеÄÊý¶¼Õû³ýµÄ×îСÕýÊý ÒÑÓÐ11È˲ÎÓë

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?

2520ÊÇÒ»¸öÄܱ»1µ½10ÖеÄÿ¸öÊý¶¼³ý¾¡µÄ×îСµÄÊý¡£
ÄÇôÄܱ»1µ½20ËùÓеÄÊýµÄÕû³ýµÄ×îСµÄÕýÊýÊǶàÉÙÄØ£¿
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libralibra

ÖÁ×ðľ³æ (ÖøÃûдÊÖ)

æôÆï½«¾ü

¡ï ¡ï ¡ï ¡ï
Сľ³æ(½ð±Ò+0.5):¸ø¸öºì°ü£¬Ð»Ð»»ØÌû
ÓàÔó³É(½ð±Ò+3): ¹ÄÀø½»Á÷£¡ 2011-05-12 19:11:36
ÓàÔó³É(³ÌÐòÇ¿Ìû+1): 2011-05-12 19:12:13
CODE:
%% evenly divided by 1:20
% Elapsed time is 173.211097 seconds.
% ans =
%    232792560
function result = euler5()
tic;
flag = 0;
result = 2520; % Äܱ»1-20Õû³ý,¿Ï¶¨±ÈÄܱ»1-10Õû³ýµÄ2520´ó
while flag==0
    result = result+10; % Äܱ»10Õû³ý,ËùÒÔÿ´ÎÔö¼Ó10
    flag = ~any(mod(result,2:20)); % ¼ì²â2-20,Èç¹ûÈ«²¿¿ÉÒÔÕû³ý,¸Ä±äflag½áÊøÑ­»·
end
toc;
end

ЧÂÊÓеãµÍ,170¶àÃë°¡,
matlab/VB/python/c++/Javaд³ÌÐòÇë·¢QQÓʼþ:790404545@qq.com
2Â¥2011-05-12 16:36:07
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

holmescn

½ð³æ (ÕýʽдÊÖ)

ÒýÓûØÌû:
Originally posted by libralibra at 2011-05-12 16:36:07:
[code] %% evenly divided by 1:20
% Elapsed time is 173.211097 seconds.
% ans =
%    232792560
function result = euler5()
tic;
flag = 0;
result = 2520; % Äܱ»1-20Õû³ý,¿Ï¶¨±ÈÄܱ»1-10Õû³ýµÄ2520 ...

1. Ϊʲô²»ÓÃall£¬ÒªÓÃanyÄØ£¿
2. ÎÊÌâºÜ¼òµ¥°¡£¬Ë㷨̫´Ö±©ÁË¡£
3Â¥2011-05-12 16:45:10
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

΢³¾¡¢ÃÎÏë

ľ³æ (ÖªÃû×÷¼Ò)

¡ï ¡ï ¡ï ¡ï
Сľ³æ(½ð±Ò+0.5):¸ø¸öºì°ü£¬Ð»Ð»»ØÌû
ÓàÔó³É(½ð±Ò+3, ³ÌÐòÇ¿Ìû+1): лл²ÎÓë½»Á÷£¡ 2011-05-12 19:12:02
CODE:
#include
#include
int x(int i);
void main(void)
{
        int i;
        float dif;
        time_t start,end;

        time(&start);
        for(i=1;1;i++)
                if(x(i))
                {
                        printf("%d\n",i);
                        break;
                }
        time(&end);
        dif=difftime(end,start);
        printf("ÔËËãʱ¼ä£º%.1fÃë\n",dif);
}
int x(int i)
{
        int j,k=0;
        for(j=2;j<21;j++)
                if(i%j==0)
                        k++;
        if(k==19)
                return 1;
        else return 0;
}

´ð°¸£º232792560
ÔËÐÐʱ¼ä£º37s

Ëã·¨£º×µÄÄÇÖÖ£¡

[ Last edited by ΢³¾¡¢ÃÎÏë on 2011-5-12 at 17:20 ]
ÈηçÔÆ±ä»Ã£¬ÎÒЦ¶ÔÈËÉú£¡
4Â¥2011-05-12 17:19:14
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libralibra

ÖÁ×ðľ³æ (ÖøÃûдÊÖ)

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Сľ³æ(½ð±Ò+0.5):¸ø¸öºì°ü£¬Ð»Ð»»ØÌû
ÓàÔó³É(½ð±Ò+2): ¹ÄÀøÌÖÂÛ£¡ 2011-05-13 21:13:19
ÒýÓûØÌû:
Originally posted by holmescn at 2011-05-12 16:45:10:
1. Ϊʲô²»ÓÃall£¬ÒªÓÃanyÄØ£¿
2. ÎÊÌâºÜ¼òµ¥°¡£¬Ë㷨̫´Ö±©ÁË¡£

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~anyÖ»ÒªÓÐ2:20ÈÎÒâÒ»¸ö²»Õû³ý,¾Íbreak,
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Õâ¸öÎÊÌâºÃÏñûÓÐÆäËû°ì·¨,¹þ¹þ,Ö»ÄÜ´Ö±©½â¾ö

[ Last edited by libralibra on 2011-5-12 at 19:21 ]
matlab/VB/python/c++/Javaд³ÌÐòÇë·¢QQÓʼþ:790404545@qq.com
5Â¥2011-05-12 19:10:13
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

΢³¾¡¢ÃÎÏë

ľ³æ (ÖªÃû×÷¼Ò)

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ÓàÔó³É(½ð±Ò+3, ³ÌÐòÇ¿Ìû+1): ¹ÄÀøÌÖÂÛ£¡ 2011-05-13 21:13:39
CODE:
#include
#define n 30
static int a=1;
void fun(int i);
void main(void)
{
        int i;
        for(i=2;i<=n;i++)
                fun(i);
        printf("%d\n",a);
}
void fun(int i)
{
        int j,k=i,m=a;
        for(j=2;j         {
                if((m%j==0)&&(k%j==0))
                {
                        k/=j;
                        m/=j;
                        j--;
                }
        }
        a*=k;
}

ÓиÐÓÚ2Â¥µÄÏë·¨£¬¸Ä½øÁËÒ»ÏÂËã·¨£¬Çó³öÁËÄܱ»1µ½20ËùÓеÄÊýµÄÕû³ýµÄ×îСµÄÕýÊý£¬ÆäÔËËãʱ¼ä²»µ½1Ã룬Æä½á¹ûÊÇ£º232792560
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ps:²»ÄÜÇó³öÄܱ»1µ½30ËùÓеÄÊýµÄÕû³ýµÄ×îСµÄÕýÊý£¬ÒòΪ»á²úÉúÊý¾ÝÒç³öÎÊÌ⣬×î´óÖ»ÄÜÇóµ½22£¬µ«Ëã·¨ÊÇÕýÈ·µÄ¡£

[ Last edited by ΢³¾¡¢ÃÎÏë on 2011-5-13 at 07:56 ]
ÈηçÔÆ±ä»Ã£¬ÎÒЦ¶ÔÈËÉú£¡
6Â¥2011-05-12 21:35:50
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

zzy870720z

ÈÙÓþ°æÖ÷ (ÎÄ̳¾«Ó¢)

ÓÅÐã°æÖ÷ÓÅÐã°æÖ÷ÓÅÐã°æÖ÷ÓÅÐã°æÖ÷

¡ï ¡ï ¡ï ¡ï
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ÓàÔó³É(½ð±Ò+3, ³ÌÐòÇ¿Ìû+1): ¹ÄÀøÌÖÂÛ£¡ 2011-05-13 21:13:58
FORTRAN³ÌÐò£¬20ÄÚµÄÕûÊýµÄ»°Ò²²»µ½1s
ºÜ³¤£¬ÓÐЩÂé·³

½á¹û232792560

30ÒÔÄÚ2329089562800
CODE:
        PROGRAM MAIN
        IMPLICIT NONE
        INTEGER N,I,J,K,M,FLAG
        INTEGER(8) SUM
        DIMENSION K(10)
        DO I=1,10
        K(I)=1
        END DO
        READ(*,*)N
        J=1
        DO I=2,N
                CALL ZS(I,FLAG)
                IF(FLAG.EQ.1)THEN
                        K(J)=I
                        J=J+1
                END IF
        END DO       
        DO I=1,J-1
                CALL KN(K(I),N)
        END DO
        SUM=1
        DO I=1,J-1
                SUM=SUM*K(I)
        END DO
        WRITE(*,*)SUM
        END

C        ÅжÏÖÊÊý£¬FLAG=1ΪÖÊÊý£¬·ñÔò²»ÎªÖÊÊý¡£
        INTEGER        FUNCTION ZS(II,FLAG)
        INTEGER II,I,J,K,FLAG
        K=INT(II/2)
        FLAG=1
        DO I=2,K
        IF(MOD(II,I).EQ.0)THEN
                FLAG=0
                GOTO 10
        END IF
        END DO
10        RETURN
        END

C        ÅжÏij¸öÖÊÊýµÄn´Î·½Ôڹ涨·¶Î§ÒÔÄÚ
        INTEGER FUNCTION KN(X,N)
        IMPLICIT NONE
        INTEGER X,Y,N,SUM
        Y=1
        SUM=X
        DO WHILE(SUM.LT.N)
                SUM=SUM*X
                Y=Y+1
C        WRITE(*,*)X,N
        END DO
        X=SUM/X
        END

[ Last edited by zzy870720z on 2011-5-12 at 22:46 ]
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7Â¥2011-05-12 22:36:14
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

holmescn

½ð³æ (ÕýʽдÊÖ)

¡ï ¡ï ¡ï
ÓàÔó³É(½ð±Ò+3): ¹ÄÀøÌÖÂÛ£¡ 2011-05-13 21:14:16
΢³¾¡¢ÃÎÏë(³ÌÐòÇ¿Ìû+1): 2011-05-14 19:29:31
OK,ÌùËã·¨ÁË£¡

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Matlab:
CODE:
clear;
tic;
primes  = [2 3 5 7 11 13 17 19];
factors = [];
numbers = 1:20;

for i = 1:length(primes)
    while any(mod(numbers, primes(i)) == 0)
        for j = 1:length(numbers)
            if mod(numbers(j), primes(i)) == 0
                numbers(j) = numbers(j) / primes(i);
            end
        end
        factors = [factors primes(i)];
    end
end

result = 1;
for i = 1:length(factors)
    result = result * factors(i);
end
disp(num2str(result));
toc;

Fortran:
CODE:
Program Euler5
    Implicit None
    Integer, Dimension(8) :: Primes
    Integer, Dimension(100) :: Factors
    Integer, Dimension(20)  :: Numbers
    Integer I, J, N
    Real(8) :: Res

    Primes = (/2, 3, 5, 7, 11, 13, 17, 19/)
    Numbers = (/(I, I=1, 20)/)
    N = 1

    Do I = 1, Size(Primes)
        Do While(Any(Mod(Numbers, Primes(I)) == 0))
            Do J = 1, Size(Numbers)
                If(Mod(Numbers(J), Primes(I)) == 0) Then
                    Numbers(J) = Numbers(J) / Primes(I)
                EndIF
            EndDo
            Factors(N) = Primes(I)
            N = N + 1
        EndDo
    EndDo

    Res = 1.0
    Do I = 1, N - 1
        Print '(I2)', Factors(I)
        Res = Res * Factors(I)
    EndDo

    Print '(F20.0)', Res

EndProgram Euler5

C:
CODE:
#include

int any(int Numbers[], int n, int Prime){
    int i;
    for(i = 0; i < n; i++){
        if(Numbers[i] % Prime == 0)
            return 1;
    }

    return 0;
}

int main(int argc, char** argv){
    int Primes[] = {2, 3, 5, 7, 11, 13, 17, 19};
    int Factors[100];
    int Numbers[20];
    int sizeOfNumbers = sizeof(Numbers)/sizeof(int);
    int sizeOfPrimes  = sizeof(Primes)/sizeof(int);
    int i, j, n = 0;
    double result = 1;

    for(i = 0; i < sizeOfNumbers; i++) Numbers[i] = i + 1;

    for(i = 0; i < sizeOfPrimes; i++) {
        while(any(Numbers, sizeOfNumbers, Primes[i])) {
            for(j = 0; j < sizeOfNumbers; j++){
                if(Numbers[j] % Primes[i] == 0){
                    Numbers[j] /= Primes[i];
                }
            }
            Factors[n++] = Primes[i];
        }

    }

    for(i = 0; i < n; i++){
        result *= Factors[i];
    }
    printf("%18.0f\n", result);

    return 0;
}

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[ Last edited by holmescn on 2011-5-13 at 12:51 ]
8Â¥2011-05-13 11:31:07
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

huycwork

½ð³æ (ÖøÃûдÊÖ)

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ÓàÔó³É(½ð±Ò+3, ³ÌÐòÇ¿Ìû+1): ¹ÄÀøÌÖÂÛ£¡ 2011-05-13 21:14:37
ÒýÓûØÌû:
Originally posted by holmescn at 2011-05-13 11:31:07:
OK,ÌùËã·¨ÁË£¡

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9Â¥2011-05-13 19:58:36
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ming.su

Òø³æ (³õÈëÎÄ̳)

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ÓàÔó³É(½ð±Ò+2): ¹ÄÀøÌÖÂÛ£¡ 2011-05-13 21:14:52
tic;
result=2520*11*13*17*19*2;
toc;


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https://drwater.rcees.ac.cn
10Â¥2011-05-13 20:29:02
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû
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[¿¼ÑÐ] Ò»Ö¾Ô¸»ªÖÐũ΢ÉúÎ288·Ö£¬ÈýÄêʵÑé¾­Àú +11 ´úfish 2026-04-09 11/550 2026-04-12 10:21 by Hayaay
[¿¼ÑÐ] 305Çóµ÷¼Á +7 Â꿨°Í¿¨boom 2026-04-11 7/350 2026-04-12 07:35 by zhouxiaoyu
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