问题
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 consecutive 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.
回答1:
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.
回答2:
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.
回答3:
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.
回答4:
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] + ")");
}
}
回答5:
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;
回答6:
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... ;-)
回答7:
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");
}
}
}
回答8:
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?
回答9:
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);
}
来源：https://stackoverflow.com/questions/2167339/greatest-product-of-five-consecutive-digits-in-a-1000-digit-number