Greatest product of five consecutive digits in a 1000-digit number_问答_开发者

I am working through the problems on project Euler and am not too certain if my understanding of the question is correct.

Problem 8 is as follows:

Find the greatest product of five c开发者_Go百科onsecutive digits in the 1000-digit number.

I have taken this to mean the following:

I need to find any five numbers that run consecutively in the 1000 digit number and then add these up to get the total. I am assuming that the size of the numbers could be anything, i.e. 1,2,3 or 12,13,14 or 123,124,124 or 1234,1235,1236 etc.

Is my understanding of this correct, or have I misunderstood the question?

Note: Please don't supply code or the solution, that I need to solve myself.

The number is:

73167176531330624919225119674426574742355349194934 96983520312774506326239578318016984801869478851843 85861560789112949495459501737958331952853208805511 12540698747158523863050715693290963295227443043557 66896648950445244523161731856403098711121722383113 62229893423380308135336276614282806444486645238749 30358907296290491560440772390713810515859307960866 70172427121883998797908792274921901699720888093776 65727333001053367881220235421809751254540594752243 52584907711670556013604839586446706324415722155397 53697817977846174064955149290862569321978468622482 83972241375657056057490261407972968652414535100474 82166370484403199890008895243450658541227588666881 16427171479924442928230863465674813919123162824586 17866458359124566529476545682848912883142607690042 24219022671055626321111109370544217506941658960408 07198403850962455444362981230987879927244284909188 84580156166097919133875499200524063689912560717606 05886116467109405077541002256983155200055935729725 71636269561882670428252483600823257530420752963450

The first five consecutive digits are: 73167. Their product is 7*3*1*6*7=882
The next five consecutive digits are: 31671. Their product is 3*1*6*7*1=126
The next five consecutive digits are: 16717. Their product is 1*6*7*1*7=294

And so on. Note the overlap. Now, find the five consecutive digits whose product is maximal over the whole 1000-digit number.

A digit is a single 0-9 in the string representing the number. So the number 12345 has 5 digits. 1234554321 has 10 digits.

The product is the multiplicative total, not the added total. So the product of 3, 5 and 7 is 105.

A (somewhat clunky) way of rephrasing the question would be:

Given a 1000-digit number, select 5 consecutive digits from it that, when taken as individual numbers and multiplied together, give the largest result.

Five single digits. 1, 5, 8... whatever shows up in the big number, all in a row. So if a chunk read "...47946285..." Then you could use "47946", "79462", "94628", "46285", etc.

Only improvisation in my solution is, avoiding unnecessary computations by looking ahead.

package com.euler;

public class Euler8 {
    public static void main(String[] ar) throws Exception {
        String s = 
                "73167176531330624919225119674426574742355349194934" + 
                "96983520312774506326239578318016984801869478851843" + 
                "85861560789112949495459501737958331952853208805511" + 
                "12540698747158523863050715693290963295227443043557" + 
                "66896648950445244523161731856403098711121722383113" + 
                "62229893423380308135336276614282806444486645238749" + 
                "30358907296290491560440772390713810515859307960866" + 
                "70172427121883998797908792274921901699720888093776" + 
                "65727333001053367881220235421809751254540594752243" + 
                "52584907711670556013604839586446706324415722155397" + 
                "53697817977846174064955149290862569321978468622482" + 
                "83972241375657056057490261407972968652414535100474" + 
                "82166370484403199890008895243450658541227588666881" + 
                "16427171479924442928230863465674813919123162824586" + 
                "17866458359124566529476545682848912883142607690042" + 
                "24219022671055626321111109370544217506941658960408" + 
                "07198403850962455444362981230987879927244284909188" + 
                "84580156166097919133875499200524063689912560717606" + 
                "05886116467109405077541002256983155200055935729725" + 
                "71636269561882670428252483600823257530420752963450" ;
        Integer[] tokens = new Integer[s.length()];
        for (int i = 0; i < s.length(); i++) {
            tokens[i] = (int) s.charAt(i)-48;
        }

        int prod = 1;
        int[] numberSet = new int[5];
        int prodCounter = 1;
        for (int i=0; i<tokens.length-4; i++) {
            // Look ahead: if they are zeros in next 5 numbers, just jump.
            if ( tokens[i] == 0) {
                i = i+1;
                continue;
            } else if ( tokens[i+1] == 0) {
                i = i+2;                
                continue;
            } else if ( tokens[i+2] == 0) {
                i = i+3;
                continue;
            } else if ( tokens[i+3] == 0) {
                i = i+4;                
                continue;                           
            } else if ( tokens[i+4] == 0) {
                i = i+5;                
                continue;               
            }           
            int localProd = tokens[i] * tokens[i+1] * tokens[i+2] * tokens[i+3] * tokens[i+4];
            System.out.println("" + (prodCounter++) + ")" + tokens[i] + "*" + tokens[i+1] + "*" + tokens[i+2] + "*" + tokens[i+3] + "*" + tokens[i+4] + " = " + localProd);
            if (localProd > prod) {
                prod = localProd;
                numberSet[0] = tokens[i];
                numberSet[1] = tokens[i+1];
                numberSet[2] = tokens[i+2];
                numberSet[3] = tokens[i+3];
                numberSet[4] = tokens[i+4];
            }
        }
        System.out.println("Largest Prod = " + prod  + " By: (" + numberSet[0] + " , " + numberSet[1] + " ,  " + numberSet[2] + " , " + numberSet[3] + " , " + numberSet[4] + ")");
    }
}

You will get: Numbers: 99879 Product: 40824

$no = "7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450";
$x = 0;
$a = 0;
$max = 0;
while($a != 63450){
    $a = substr($no, $x, 5);
    $prod = substr($a, 0, 1) * substr($a, 1, 1) * substr($a, 2, 1)* substr($a, 3, 1) * substr($a, 4, 1);
    if($prod >= $max){
        $max = $prod;
        $theno = $a;
    }
    $x++;
}
echo 'Numbers: '.$theno.'<br>';
echo 'Product: '.$max;

This is my personal solution, using a bit of the brutal force:

Module Module1

    Sub Main()
        Dim v() As Integer = {7, 3, 1, 6, 7, 1, 7, 6, 5, 3, 1, 3, 3, 0, 6, 2, 4, 9, 1, 9, 2, 2, 5, 1, 1, 9, 6, 7, 4, 4, 2, 6, 5, 7, 4, 7, 4, 2, 3, 5, 5, 3, 4, 9, 1, 9, 4, 9, 3, 4, 9, 6, 9, 8, 3, 5, 2, 0, 3, 1, 2, 7, 7, 4, 5, 0, 6, 3, 2, 6, 2, 3, 9, 5, 7, 8, 3, 1, 8, 0, 1, 6, 9, 8, 4, 8, 0, 1, 8, 6, 9, 4, 7, 8, 8, 5, 1, 8, 4, 3, 8, 5, 8, 6, 1, 5, 6, 0, 7, 8, 9, 1, 1, 2, 9, 4, 9, 4, 9, 5, 4, 5, 9, 5, 0, 1, 7, 3, 7, 9, 5, 8, 3, 3, 1, 9, 5, 2, 8, 5, 3, 2, 0, 8, 8, 0, 5, 5, 1, 1, 1, 2, 5, 4, 0, 6, 9, 8, 7, 4, 7, 1, 5, 8, 5, 2, 3, 8, 6, 3, 0, 5, 0, 7, 1, 5, 6, 9, 3, 2, 9, 0, 9, 6, 3, 2, 9, 5, 2, 2, 7, 4, 4, 3, 0, 4, 3, 5, 5, 7, 6, 6, 8, 9, 6, 6, 4, 8, 9, 5, 0, 4, 4, 5, 2, 4, 4, 5, 2, 3, 1, 6, 1, 7, 3, 1, 8, 5, 6, 4, 0, 3, 0, 9, 8, 7, 1, 1, 1, 2, 1, 7, 2, 2, 3, 8, 3, 1, 1, 3, 6, 2, 2, 2, 9, 8, 9, 3, 4, 2, 3, 3, 8, 0, 3, 0, 8, 1, 3, 5, 3, 3, 6, 2, 7, 6, 6, 1, 4, 2, 8, 2, 8, 0, 6, 4, 4, 4, 4, 8, 6, 6, 4, 5, 2, 3, 8, 7, 4, 9, 3, 0, 3, 5, 8, 9, 0, 7, 2, 9, 6, 2, 9, 0, 4, 9, 1, 5, 6, 0, 4, 4, 0, 7, 7, 2, 3, 9, 0, 7, 1, 3, 8, 1, 0, 5, 1, 5, 8, 5, 9, 3, 0, 7, 9, 6, 0, 8, 6, 6, 7, 0, 1, 7, 2, 4, 2, 7, 1, 2, 1, 8, 8, 3, 9, 9, 8, 7, 9, 7, 9, 0, 8, 7, 9, 2, 2, 7, 4, 9, 2, 1, 9, 0, 1, 6, 9, 9, 7, 2, 0, 8, 8, 8, 0, 9, 3, 7, 7, 6, 6, 5, 7, 2, 7, 3, 3, 3, 0, 0, 1, 0, 5, 3, 3, 6, 7, 8, 8, 1, 2, 2, 0, 2, 3, 5, 4, 2, 1, 8, 0, 9, 7, 5, 1, 2, 5, 4, 5, 4, 0, 5, 9, 4, 7, 5, 2, 2, 4, 3, 5, 2, 5, 8, 4, 9, 0, 7, 7, 1, 1, 6, 7, 0, 5, 5, 6, 0, 1, 3, 6, 0, 4, 8, 3, 9, 5, 8, 6, 4, 4, 6, 7, 0, 6, 3, 2, 4, 4, 1, 5, 7, 2, 2, 1, 5, 5, 3, 9, 7, 5, 3, 6, 9, 7, 8, 1, 7, 9, 7, 7, 8, 4, 6, 1, 7, 4, 0, 6, 4, 9, 5, 5, 1, 4, 9, 2, 9, 0, 8, 6, 2, 5, 6, 9, 3, 2, 1, 9, 7, 8, 4, 6, 8, 6, 2, 2, 4, 8, 2, 8, 3, 9, 7, 2, 2, 4, 1, 3, 7, 5, 6, 5, 7, 0, 5, 6, 0, 5, 7, 4, 9, 0, 2, 6, 1, 4, 0, 7, 9, 7, 2, 9, 6, 8, 6, 5, 2, 4, 1, 4, 5, 3, 5, 1, 0, 0, 4, 7, 4, 8, 2, 1, 6, 6, 3, 7, 0, 4, 8, 4, 4, 0, 3, 1, 9, 9, 8, 9, 0, 0, 0, 8, 8, 9, 5, 2, 4, 3, 4, 5, 0, 6, 5, 8, 5, 4, 1, 2, 2, 7, 5, 8, 8, 6, 6, 6, 8, 8, 1, 1, 6, 4, 2, 7, 1, 7, 1, 4, 7, 9, 9, 2, 4, 4, 4, 2, 9, 2, 8, 2, 3, 0, 8, 6, 3, 4, 6, 5, 6, 7, 4, 8, 1, 3, 9, 1, 9, 1, 2, 3, 1, 6, 2, 8, 2, 4, 5, 8, 6, 1, 7, 8, 6, 6, 4, 5, 8, 3, 5, 9, 1, 2, 4, 5, 6, 6, 5, 2, 9, 4, 7, 6, 5, 4, 5, 6, 8, 2, 8, 4, 8, 9, 1, 2, 8, 8, 3, 1, 4, 2, 6, 0, 7, 6, 9, 0, 0, 4, 2, 2, 4, 2, 1, 9, 0, 2, 2, 6, 7, 1, 0, 5, 5, 6, 2, 6, 3, 2, 1, 1, 1, 1, 1, 0, 9, 3, 7, 0, 5, 4, 4, 2, 1, 7, 5, 0, 6, 9, 4, 1, 6, 5, 8, 9, 6, 0, 4, 0, 8, 0, 7, 1, 9, 8, 4, 0, 3, 8, 5, 0, 9, 6, 2, 4, 5, 5, 4, 4, 4, 3, 6, 2, 9, 8, 1, 2, 3, 0, 9, 8, 7, 8, 7, 9, 9, 2, 7, 2, 4, 4, 2, 8, 4, 9, 0, 9, 1, 8, 8, 8, 4, 5, 8, 0, 1, 5, 6, 1, 6, 6, 0, 9, 7, 9, 1, 9, 1, 3, 3, 8, 7, 5, 4, 9, 9, 2, 0, 0, 5, 2, 4, 0, 6, 3, 6, 8, 9, 9, 1, 2, 5, 6, 0, 7, 1, 7, 6, 0, 6, 0, 5, 8, 8, 6, 1, 1, 6, 4, 6, 7, 1, 0, 9, 4, 0, 5, 0, 7, 7, 5, 4, 1, 0, 0, 2, 2, 5, 6, 9, 8, 3, 1, 5, 5, 2, 0, 0, 0, 5, 5, 9, 3, 5, 7, 2, 9, 7, 2, 5, 7, 1, 6, 3, 6, 2, 6, 9, 5, 6, 1, 8, 8, 2, 6, 7, 0, 4, 2, 8, 2, 5, 2, 4, 8, 3, 6, 0, 0, 8, 2, 3, 2, 5, 7, 5, 3, 0, 4, 2, 0, 7, 5, 2, 9, 6, 3, 4, 5, 0}
        Dim n = v.Length - 1
        Console.WriteLine(ElementoMax(v))
        Console.ReadKey()
    End Sub

    Function ElementMax(vett() As Integer)

    Dim MAX, temp1, temp2, temp

    MAX = vett(0) * vett(1) * vett(2) * vett(3) * vett(4) * vett(5) * vett(6) * vett(7) * vett(8) * vett(9) * vett(10) * vett(11) * vett(12)
        For i = 1 To (vett.Length - 13)

            temp1 = vett(i) * vett(i + 1) * vett(i + 2) * vett(i + 3) * vett(i + 4) *       vett(i + 5) * vett(i + 6) * vett(i + 7) * vett(i + 8) * vett(i + 9) * vett(i + 10)* vett(i + 11) * vett(i + 12)
            temp2 = vett(i + 5) * vett(i + 6) * vett(i + 7) * vett(i + 8) * vett(i + 9) * vett(i + 10) * vett(i + 11) * vett(i + 12)
            temp = temp1 * temp2

            If temp > MAX Then
                MAX = temp
            End If
        Next
        Return MAX
    End Function

End Module

and the result is... ;-)

public class Problem008
{
    public static int checkInt(String s)
    {
        int product = 1;
        for (int i = 0; i < 5; i++)
        {
            Character c = new Character(s.charAt(i));
            String tmp = c.toString();
            int temp = Integer.parseInt(tmp);
            product *= temp;
        }
        return product;
    }

    public static void main(String[] args)
    {
        long begin = System.currentTimeMillis();
        String BigNum = "7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450";
        String snip;
        int largest = 0;

        for (int i = 0; i <= (BigNum.length()-5); i++)
        {
            snip = null;

            for (int j = 0; j < 5; j++)
            {
                char c = BigNum.charAt(i+j);
                snip += c;
            }
            if (checkInt(snip) > largest)
                largest = checkInt(snip);
            }
            long end = System.currentTimeMillis();
            System.out.println(largest);
            System.out.println(end-begin + "ms");
        }
    }
}

public class ProjectEuler8
{
    public static void main(String[] args)
    {
        int list[] = new int[1000];
        int max = 0;
        String str = "7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450";
        for (int index = 0; index < 1000; index++)
            list[index] = str.charAt(index) - 48;
        for (int count = 0; count < 996; count++)
        {
            int product = list[count] * list[count + 1] * list[count + 2] * list[count + 3] * list[count + 4];
            if (product > max) max = product;
        }
        System.out.println(max);
    }
}

Simple is better, isn't it?

In C I copied it in a txt file and read from it, or you can just initialise string at the beginning.

#include <stdio.h>
#include <stdlib.h>

int main()
{
    FILE *a;
    a=fopen("Long.txt","r");
    char s[1001];
    fscanf(a,"%s",s);
char p[6];

int i=0,x,prdmax=1,m,n;
while(s[i]!='\0')
{
    p[0]=s[i];
    p[1]=s[i+1];
    p[2]=s[i+2];
    p[3]=s[i+3];
    p[4]=s[i+4];
    p[5]='\0';

    x=atoi(p);
    n=x;
    int prd=1;
    while(x!=0)
    {
        int q=x%10;
        prd*=q;
        x/=10;
    }

    if(prd>prdmax)
    {
        prdmax=prd;
        m=n;
    }
    i++;
}

printf("Numbers are: %d\n Largest product is: %d",m,prdmax);

fclose(a);
}