Project Euler Problem 8 (PHP)

Posted on August 15, 2011 by

Problem 8

Find the greatest product of five consecutive digits in the 1000-digit number.

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

Script

Execution Time: 0.0129 seconds

$n = "7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450";

$s = 0;
$l = 5;
$a = array();

for ($p = $s; $p < strlen($n)-$l; $p++) {
    $a[] = array_product(str_split(substr($n, $p, $l)));
}

rsort($a);

echo $a[0].PHP_EOL;
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Project Euler Problem 7 (PHP)

Posted on August 15, 2011 by

Problem 7

By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.

What is the 10,001st prime number?

Script

Execution Time: 1.3918 seconds

function isPrime($n)
{
    $m = floor(sqrt($n));
    for ($x=2; $x<=$m; $x++) {
        if ($n%$x == 0) {
            return false;
        }
    }

    return true;
}

$n = 3;
$k = 2;
$kMax = 10001;

while ($k <= $kMax) {
    if (isPrime($n)) {
        if ($k == $kMax) {
            echo $n.PHP_EOL;
            break;
        }
        $k++;
    }
    $n=$n+2;
}
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Project Euler Problem 6 (PHP)

Posted on August 15, 2011 by

Problem 6

The sum of the squares of the first ten natural numbers is,
12 + 22 + … + 102 = 385

The square of the sum of the first ten natural numbers is,
(1 + 2 + … + 10)2 = 552 = 3025

Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 − 385 = 2640.

Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.

Script

Execution Time: 0.0013 seconds

$sum = 0;
$squareSum = 0;

for($x = 1; $x<=100; $x++) {
    $sum += $x;
    $squareSum += ($x*$x);
}
$diff = $squareSum-($sum*$sum);

echo abs($diff).PHP_EOL;
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Project Euler Problem 5 (PHP)

Posted on August 9, 2011 by

Problem 5

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?

Script

Execution Time: 19.8054 seconds

$stop = false;

for($x=20; $stop == false; $x=$x+20) {
    for ($y=2; $y<=19; $y++) {
        if($x%$y == 0) {
            $stop = true;
        } else {
            $stop = false;
            $y = 21;
        }
    }
    if ($stop == true) {
        echo $x.PHP_EOL;
    }
}
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Project Euler Problem 4 (PHP)

Posted on August 9, 2011 by

Problem 4

A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99.

Find the largest palindrome made from the product of two 3-digit numbers.

Script

Execution Time: 1.3709 seconds

$start = 999;
$r = array();

for ($x = $start; $x >= 100; $x--) {
    for ($y=$start; $y >= 100; $y--) {
        $p = $x*$y;
        if ($p == strrev($p)) {
            $r[] = $p;
        }
    }
}

rsort($r, SORT_NUMERIC);

echo $r[0].PHP_EOL;
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Project Euler Problem 3 (PHP)

Posted on July 14, 2011 by

Problem 3

The prime factors of 13195 are 5, 7, 13 and 29.

What is the largest prime factor of the number 600851475143 ?

Answer Show ▼

Script

Execution Time: 18.15 seconds

function isPrime($n)
{
    for ($x=2; $x<=floor($n/2); $x++) {
        if ($n%$x == 0) {
            return false;
        }
    }

    return true;
}

$comp = 600851475143;

for ($x = 3; $x <= ceil($comp/2); $x = $x+2) {
    if ($comp%$x == 0) {
        $y = $comp / $x;
        if (isPrime($y)) {
            echo $y.PHP_EOL;
            break;
        }
    }
}
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