I tried to find For a given positive integer Z, check if Z can be written as PQ, where P and Q are positive integers greater than 1. If Z can be written as PQ, return 1, else return 0
I tried lots with online solution,
Check if one integer is an integer power of another
Finding if a number is a power of 2
but it's not what i need , any hint or any tips?
Here's the naive method - try every combination:
function check($z) {
for($p = 2; $p < sqrt($z); $p++) {
if($z % $p > 0) {
continue;
}
$q = $p;
for($i = 1; $q < $z; $i++) {
$q *= $p;
}
if($q == $z) {
//print "$z = $p^$i";
return 1;
}
}
return 0;
}
Similarly, using php's built in log function. But it may not be as accurate (if there are rounding errors, false positives may occur).
function check($z) {
for($p = 2; $p < sqrt($z); $p++) {
$q = log($z,$p);
if($q == round($q)) {
return 1;
}
}
return 0;
}
Related
I had a need to generate a list of four-digit numbers for use as codes. The digits should not repeat, and each next digit should not be sequential. There were some questions that were similar but not enough for me to answer. I chose to share my function instead. It did not matter if reverse numbers were in the list e.g. 1357 > 7531.
It occurred to me that it there may be an opportunity for a recursive function, possibly to return five or six-digit numbers. Improvements to my function are most welcome.
public function codeList() {
$data = [];
for ($ii=0; $ii < 10; $ii++) {
for ($jj=0; $jj < 10; $jj++) {
for ($kk=0; $kk < 10; $kk++) {
for ($ll=0; $ll < 10; $ll++) {
$str = "{$ii}{$jj}{$kk}{$ll}";
$arr = str_split($str);
if (count($arr) === count(array_unique($arr))) {
if (($arr[0] + 1 != $arr[1]) && ($arr[1] + 1 != $arr[2]) && ($arr[2] + 1 != $arr[3])) {
$data[] = $str;
}
}
}
}
}
}
return $data;
} # END FUNCTION codeList
This code is working fine when the array length is 8 or 10 only. When we are checking this same code for more than 10 array length.it get loading not showing the results.
How do reduce my code. If you have algorithm please share. Please help me.
This program working flow:
$allowed_per_room_accommodation =[2,3,6,5,3,5,2,5,4];
$allowed_per_room_price =[10,30,60,40,30,50,20,60,80];
$search_accommodation = 10;
i am get subsets = [5,5],[5,3,2],[6,4],[6,2,2],[5,2,3],[3,2,5]
Show lowest price room and then equal of 10 accommodation; output like as [5,3,2];
<?php
$dp=array(array());
$GLOBALS['final']=[];
$GLOBALS['room_key']=[];
function display($v,$room_key)
{
$GLOBALS['final'][] = $v;
$GLOBALS['room_key'][] = $room_key;
}
function printSubsetsRec($arr, $i, $sum, $p,$dp,$room_key='')
{
// If we reached end and sum is non-zero. We print
// p[] only if arr[0] is equal to sun OR dp[0][sum]
// is true.
if ($i == 0 && $sum != 0 && $dp[0][$sum]) {
array_push($p,$arr[$i]);
array_push($room_key,$i);
display($p,$room_key);
return $p;
}
// If $sum becomes 0
if ($i == 0 && $sum == 0) {
display($p,$room_key);
return $p;
}
// If given sum can be achieved after ignoring
// current element.
if (isset($dp[$i-1][$sum])) {
// Create a new vector to store path
// if(!is_array(#$b))
// $b = array();
$b = $p;
printSubsetsRec($arr, $i-1, $sum, $b,$dp,$room_key);
}
// If given $sum can be achieved after considering
// current element.
if ($sum >= $arr[$i] && isset($dp[$i-1][$sum-$arr[$i]]))
{
if(!is_array($p))
$p = array();
if(!is_array($room_key))
$room_key = array();
array_push($p,$arr[$i]);
array_push($room_key,$i);
printSubsetsRec($arr, $i-1, $sum-$arr[$i], $p,$dp,$room_key);
}
}
// Prints all subsets of arr[0..n-1] with sum 0.
function printAllSubsets($arr, $n, $sum,$get=[])
{
if ($n == 0 || $sum < 0)
return;
// Sum 0 can always be achieved with 0 elements
// $dp = new bool*[$n];
$dp = array();
for ($i=0; $i<$n; ++$i)
{
// $dp[$i][$sum + 1]=true;
$dp[$i][0] = true;
}
// Sum arr[0] can be achieved with single element
if ($arr[0] <= $sum)
$dp[0][$arr[0]] = true;
// Fill rest of the entries in dp[][]
for ($i = 1; $i < $n; ++$i) {
for ($j = 0; $j < $sum + 1; ++$j) {
// echo $i.'d'.$j.'.ds';
$dp[$i][$j] = ($arr[$i] <= $j) ? (isset($dp[$i-1][$j])?$dp[$i-1][$j]:false) | (isset($dp[$i-1][$j-$arr[$i]])?($dp[$i-1][$j-$arr[$i]]):false) : (isset($dp[$i - 1][$j])?($dp[$i - 1][$j]):false);
}
}
if (isset($dp[$n-1][$sum]) == false) {
return "There are no subsets with";
}
$p;
printSubsetsRec($arr, $n-1, $sum, $p='',$dp);
}
$blockSize = array('2','3','6','5','3','5','2','5','4');
$blockvalue = array('10','30','60','40','30','50','20','60','80');
$blockname = array("map","compass","water","sandwich","glucose","tin","banana","apple","cheese");
$processSize = 10;
$m = count($blockSize);
$n = count($processSize);
// sum of sets in array
printAllSubsets($blockSize, $m, $processSize);
$final_subset_room = '';
$final_set_room_keys = '';
$final_set_room =[];
if($GLOBALS['room_key']){
foreach ($GLOBALS['room_key'] as $set_rooms_key => $set_rooms) {
$tot = 0;
foreach ($set_rooms as $set_rooms) {
$tot += $blockvalue[$set_rooms];
}
$final_set_room[$set_rooms_key] = $tot;
}
asort($final_set_room);
$final_set_room_first_key = key($final_set_room);
$final_all_room['set_room_keys'] = $GLOBALS['room_key'][$final_set_room_first_key];
$final_all_room_price['set_room_price'] = $final_set_room[$final_set_room_first_key];
}
if(isset($final_all_room_price)){
asort($final_all_room_price);
$final_all_room_first_key = key($final_all_room_price);
foreach ($final_all_room['set_room_keys'] as $key_room) {
echo $blockname[$key_room].'---'. $blockvalue[$key_room];
echo '<br>';
}
}
else
echo 'No Results';
?>
I'm assuming your task is, given a list rooms, each with the amount of people it can accommodate and the price, to accommodate 10 people (or any other quantity).
This problem is similar to 0-1 knapsack problem which is solvable in polynomial time. In knapsack problem one aims to maximize the price, here we aim to minimize it. Another thing that is different from classic knapsack problem is that full room cost is charged even if the room is not completely occupied. It may reduce the effectiveness of the algorithm proposed at Wikipedia. Anyway, the implementation isn't going to be straightforward if you have never worked with dynamic programming before.
If you want to know more, CLRS book on algorithms discusses dynamic programming in Chapter 15, and knapsack problem in Chapter 16. In the latter chapter they also prove that 0-1 knapsack problem doesn't have trivial greedy solution.
How can I calculate the n-th root of an integer using PHP/GMP?
Although I found a function called gmp_root(a, nth) in the PHP source, it seems that this function has not been published in any release yet*: http://3v4l.org/8FjU7
*) 5.6.0alpha2 being the most recent one at the time of writing
Original source: Calculating Nth root with bcmath in PHP – thanks and credits to HamZa!
I've rewritten the code to use GMP instead of BCMath:
function gmp_nth_root($num, $n) {
if ($n < 1) return 0; // we want positive exponents
if ($num <= 0) return 0; // we want positive numbers
if ($num < 2) return 1; // n-th root of 1 or 2 give 1
// g is our guess number
$g = 2;
// while (g^n < num) g=g*2
while (gmp_cmp(gmp_pow($g, $n), $num) < 0) {
$g = gmp_mul($g, 2);
}
// if (g^n==num) num is a power of 2, we're lucky, end of job
if (gmp_cmp(gmp_pow($g, $n), $num) == 0) {
return $g;
}
// if we're here num wasn't a power of 2 :(
$og = $g; // og means original guess and here is our upper bound
$g = gmp_div($g, 2); // g is set to be our lower bound
$step = gmp_div(gmp_sub($og, $g), 2); // step is the half of upper bound - lower bound
$g = gmp_add($g, $step); // we start at lower bound + step , basically in the middle of our interval
// while step != 1
while (gmp_cmp($step, 1) > 0) {
$guess = gmp_pow($g, $n);
$step = gmp_div($step, 2);
$comp = gmp_cmp($guess, $num); // compare our guess with real number
if ($comp < 0) { // if guess is lower we add the new step
$g = gmp_add($g, $step);
} else if ($comp == 1) { // if guess is higher we sub the new step
$g = gmp_sub($g, $step);
} else { // if guess is exactly the num we're done, we return the value
return $g;
}
}
// whatever happened, g is the closest guess we can make so return it
return $g;
}
We are looking for the Nth root in PHP. We need to do this with a very large number, and the windows calculator returns 2. With the following code we are getting 1. Does anybody have an idea how this works?
echo bcpow(18446744073709551616, 1/64);
Well it seems that PHP and the BC lib has some limits, and after searching on the internet i found this interesting article/code:
So you should use this function:
<?php
function NRoot($num, $n) {
if ($n<1) return 0; // we want positive exponents
if ($num<=0) return 0; // we want positive numbers
if ($num<2) return 1; // n-th root of 1 or 2 give 1
// g is our guess number
$g=2;
// while (g^n < num) g=g*2
while (bccomp(bcpow($g,$n),$num)==-1) {
$g=bcmul($g,"2");
}
// if (g^n==num) num is a power of 2, we're lucky, end of job
if (bccomp(bcpow($g,$n),$num)==0) {
return $g;
}
// if we're here num wasn't a power of 2 :(
$og=$g; // og means original guess and here is our upper bound
$g=bcdiv($g,"2"); // g is set to be our lower bound
$step=bcdiv(bcsub($og,$g),"2"); // step is the half of upper bound - lower bound
$g=bcadd($g,$step); // we start at lower bound + step , basically in the middle of our interval
// while step!=1
while (bccomp($step,"1")==1) {
$guess=bcpow($g,$n);
$step=bcdiv($step,"2");
$comp=bccomp($guess,$num); // compare our guess with real number
if ($comp==-1) { // if guess is lower we add the new step
$g=bcadd($g,$step);
} else if ($comp==1) { // if guess is higher we sub the new step
$g=bcsub($g,$step);
} else { // if guess is exactly the num we're done, we return the value
return $g;
}
}
// whatever happened, g is the closest guess we can make so return it
return $g;
}
echo NRoot("18446744073709551616","64");
?>
Hope this was helpful ...
I had problems with HamZa's solution getting to work with arbitrary precission, so i adopted it a little.
<?php
function NthRoot($Base, $NthRoot, $Precision = 100) {
if ($NthRoot < 1) return 0;
if ($Base <= 0) return 0;
if ($Base < 2) return 1;
$retVal = 0;
$guess = bcdiv($Base, 2, $Precision);
$continue = true;
$step = bcdiv(bcsub($Base, $guess, $Precision), 2, $Precision);
while ($continue) {
$test = bccomp($Base, bcpow($guess, $NthRoot, $Precision), $Precision);
if ($test == 0) {
$continue = false;
$retVal = $guess;
}
else if ($test > 0) {
$step = bcdiv($step, 2, $Precision);
$guess = bcadd($guess, $step, $Precision);
}
else if ($test < 0) {
$guess = bcsub($guess, $step, $Precision);
}
if (bccomp($step, 0, $Precision) == 0) {
$continue = false;
$retVal = $guess;
}
}
return $retVal;
}
I'm trying to program my own Sine function implementation for fun but I keep getting :
Fatal error: Maximum execution time of 30 seconds exceeded
I have a small HTML form where you can enter the "x" value of Sin(x) your looking for and the number of "iterations" you want to calculate (precision of your value), the rest is PhP.
The maths are based of the "Series definition" of Sine on Wikipedia :
--> http://en.wikipedia.org/wiki/Sine#Series_definition
Here's my code :
<?php
function factorial($int) {
if($int<2)return 1;
for($f=2;$int-1>1;$f*=$int--);
return $f;
};
if(isset($_POST["x"]) && isset($_POST["iterations"])) {
$x = $_POST["x"];
$iterations = $_POST["iterations"];
}
else {
$error = "You forgot to enter the 'x' or the number of iterations you want.";
global $error;
}
if(isset($x) && is_numeric($x) && isset($iterations) && is_numeric($iterations)) {
$x = floatval($x);
$iterations = floatval($iterations);
for($i = 0; $i <= ($iterations-1); $i++) {
if($i%2 == 0) {
$operator = 1;
global $operator;
}
else {
$operator = -1;
global $operator;
}
}
for($k = 1; $k <= (($iterations-(1/2))*2); $k+2) {
$k = $k;
global $k;
}
function sinus($x, $iterations) {
if($x == 0 OR ($x%180) == 0) {
return 0;
}
else {
while($iterations != 0) {
$result = $result+(((pow($x, $k))/(factorial($k)))*$operator);
$iterations = $iterations-1;
return $result;
}
}
}
$result = sinus($x, $iterations);
global $result;
}
else if(!isset($x) OR !isset($iterations)) {
$error = "You forgot to enter the 'x' or the number of iterations you want.";
global $error;
}
else if(isset($x) && !is_numeric($x)&& isset($iterations) && is_numeric($iterations)) {
$error = "Not a valid number.";
global $error;
}
?>
My mistake probably comes from an infinite loop at this line :
$result = $result+(((pow($x, $k))/(factorial($k)))*$operator);
but I don't know how to solve the problem.
What I'm tring to do at this line is to calculate :
((pow($x, $k)) / (factorial($k)) + (((pow($x, $k))/(factorial($k)) * ($operator)
iterating :
+ (((pow($x, $k))/(factorial($k)) * $operator)
an "$iterations" amount of times with "$i"'s and "$k"'s values changing accordingly.
I'm really stuck here ! A bit of help would be needed. Thank you in advance !
Btw : The factorial function is not mine. I found it in a PhP.net comment and apparently it's the optimal factorial function.
Why are you computing the 'operator' and power 'k' out side the sinus function.
sin expansion looks like = x - x^2/2! + x^3/3! ....
something like this.
Also remember iteration is integer so apply intval on it and not floatval.
Also study in net how to use global. Anyway you do not need global because your 'operator' and power 'k' computation will be within sinus function.
Best of luck.
That factorial function is hardly optimal—for speed, though it is not bad. At least it does not recurse. It is simple and correct though. The major aspect of the timeout is that you are calling it a lot. One technique for improving its performance is to remember, in a local array, the values for factorial previously computed. Or just compute them all once.
There are many bits of your code which could endure improvement:
This statement:
while($iterations != 0)
What if $iterations is entered as 0.1? Or negative. That would cause an infinite loop. You can make the program more resistant to bad input with
while ($iterations > 0)
The formula for computing a sine uses the odd numbers: 1, 3, 5, 7; not every integer
There are easier ways to compute the alternating sign.
Excess complication of arithmetic expressions.
return $result is within the loop, terminating it early.
Here is a tested, working program which has adjustments for all these issues:
<?php
// precompute the factorial values
global $factorials;
$factorials = array();
foreach (range (0, 170) as $j)
if ($j < 2)
$factorials [$j] = 1;
else $factorials [$j] = $factorials [$j-1] * $j;
function sinus($x, $iterations)
{
global $factorials;
$sign = 1;
for ($j = 1, $result = 0; $j < $iterations * 2; $j += 2)
{
$result += pow($x, $j) / $factorials[$j] * $sign;
$sign = - $sign;
}
return $result;
}
// test program to prove functionality
$pi = 3.14159265358979323846264338327950288419716939937510582097494459230781640628620;
$x_vals = array (0, $pi/4, $pi/2, $pi, $pi * 3/2, 2 * $pi);
foreach ($x_vals as $x)
{
$y = sinus ($x, 20);
echo "sinus($x) = $y\n";
}
?>
Output:
sinus(0) = 0
sinus(0.78539816339745) = 0.70710678118655
sinus(1.5707963267949) = 1
sinus(3.1415926535898) = 3.4586691443274E-16
sinus(4.7123889803847) = -1
sinus(6.2831853071796) = 8.9457384260403E-15
By the way, this executes very quickly: 32 milliseconds for this output.