## Problem 8: Largest product in a series

*Difficulty: Easy

Problem

The four adjacent digits in the 1000-digit number that have the greatest product are 9 × 9 × 8 × 9 = 5832.

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

Find the thirteen adjacent digits in the 1000-digit number that have the greatest product. What is the value of this product?

How to solve:

Just loop all substrings from 0 to 1000-13 (exclusive) , convert those substrings into digits, and calculate the product of all those digits.

Implementation: Java

public class Prob8 {

private static final String input =

“73167176531330624919225119674426574742355349194934”

+ “96983520312774506326239578318016984801869478851843”

+ “85861560789112949495459501737958331952853208805511”

+ “12540698747158523863050715693290963295227443043557”

+ “66896648950445244523161731856403098711121722383113”

+ “62229893423380308135336276614282806444486645238749”

+ “30358907296290491560440772390713810515859307960866”

+ “70172427121883998797908792274921901699720888093776”

+ “65727333001053367881220235421809751254540594752243”

+ “52584907711670556013604839586446706324415722155397”

+ “53697817977846174064955149290862569321978468622482”

+ “83972241375657056057490261407972968652414535100474”

+ “82166370484403199890008895243450658541227588666881”

+ “16427171479924442928230863465674813919123162824586”

+ “17866458359124566529476545682848912883142607690042”

+ “24219022671055626321111109370544217506941658960408”

+ “07198403850962455444362981230987879927244284909188”

+ “84580156166097919133875499200524063689912560717606”

+ “05886116467109405077541002256983155200055935729725”

+ “71636269561882670428252483600823257530420752963450”;

private static final intTHIRTEEN = 13;

public static void main(String[] args) {

long cur = System.currentTimeMillis();

long max = Long.MIN_VALUE;

for(int i = 0; i < input.length()THIRTEEN; ++i) {

long product = productOfThirteenAdjacents(input.substring(i, i+13));

if(product > max) {

max= product;

}

}

System.out.println(max);

System.out.println(“Took “ + (System.currentTimeMillis()cur) + ” ms”);

}

long result = 1;

int[] digits = new int[adjacents.length()];

for(int i = 0; i < adjacents.length(); ++i) {

digits[i] = Integer.valueOf(adjacents.charAt(i) + “”);

result*= digits[i];

}

return result;

}

}

Took 15 ms