Problem 8

Largest product in a series

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?

https://projecteuler.net/problem=8

Brute Force

The naive approach is to compare the product of each 13 element window starting at the beginning, keeping track of the max.

function arrProduct(arr) {
  return arr.reduce(function(n, prod) { return n * prod; }, 1);
}

function euler8() {
  var data = '7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450',
      arr = data.split('').map(Number),
      WINDOW_SIZE = 13,
      i = arr.length - WINDOW_SIZE,
      max = 0;
  while (i--) {
    var subArr = arr.slice(i, i+WINDOW_SIZE);
    max = Math.max(max, arrProduct(subArr));
  }
  return max;
}
timer(euler8, 1000);
// euler8 x 1000: 724.827ms
// 23514624000

This approach creates an array containing all the digits. What if this isn’t possible? For example you get the digits in a stream or there are too many digits to fit in memory.

Streaming Data

function DataStream() {
  var data = '7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450',
      i = -1;

  this.next = function() {
    return data.charAt(++i);
  };
};

function euler8() {
  var dataStream = new DataStream(),
      WINDOW_SIZE = 13,
      max = 0,
      d,
      arr = [];
  d = dataStream.next();
  while (d) {
    arr.push(Number(d));
    if (arr.length > WINDOW_SIZE) {
      arr.shift();
    }
    max = Math.max(max, arrProduct(arr));
    d = dataStream.next();
  }
  return max;
}
timer(euler8, 1000);
// euler8 x 1000: 486.864ms
// 23514624000

Less Array Ops

function digitProduct(n) {
  var d, p = 1;
  if (n === 0) {
    return 0;
  }
  while (n) {
    p = p * (n % 10);
    n = Math.floor(n / 10);
  }
  return p;
}

function euler8() {
  var dataStream = new DataStream(),
      WINDOW_SIZE = 13,
      MOD = Math.pow(10, WINDOW_SIZE),
      DIV = Math.pow(10, WINDOW_SIZE-1),
      max = 0,
      n = 0,
      d = dataStream.next();
  while (d) {
    d = Number(d);
    if (d !== 0) {
      n = n * 10 + d;
      n = n % MOD;
      if (Math.floor(n / DIV)) {
        max = Math.max(max, digitProduct(n));
      }
    } else {
      n = d;
    }
    d = dataStream.next();
  }
  return max;
}
timer(euler8, 1000);
// euler8 x 1000: 262.848ms
// 23514624000