I have this math assignment that I should make into code.
I've tried all I thought of but I couldn't find a solution.
All this should be done without using php functions, only math operations.
You can use while, for, and such...
So I have number for example 9
Now I should create number of the length 9 which would be 999999999
If I had, for example, number 3, then the result should be 333.
Any ideas?
$gen = -1;
while($highest > 0) {
$gen = $highest + ($highest * 10);
$highest = $highest - 1;
}
echo $gen;
Here is a method that does not build a string; it uses pure math. (There will be many, many ways to do this task)
$x=9;
$result=0;
for($i=$x; $i; --$i){ // this looping expression can be structured however you wish potato-potatoe
$result+=$x*(10**($i-1)); // x times (10 to the power of (i-1))
}
echo $result;
// 999999999
*note: ** acts like pow() if you want to look it up.
Late edit: here is a clever, little loopless method (quietly proud). I am only calling range() and foreach() to demo; it is not an integral component of my method.
Demo: https://3v4l.org/GIjfG
foreach(range(0,9) as $n){
// echo "$n -> ",(integer)(1/9*$n*(10**$n)-($n/10)),"\n";
// echo "$n -> ",(1/9*$n*(10**$n)-(1/9*$n)),"\n";
// echo "$n -> ",(int)(1/9*10**$n)*$n,"\n";
// echo "$n -> ",(int)(10**$n/9)*$n,"\n";
echo "$n -> ",(10**$n-1)/9*$n,"\n";
}
Output:
0 -> 0
1 -> 1
2 -> 22
3 -> 333
4 -> 4444
5 -> 55555
6 -> 666666
7 -> 7777777
8 -> 88888888
9 -> 999999999
1/9 is the hero of this method because it generates .111111111(repeating). From this float number, I am using 10**$n to "shift" just enough 1s to the left side of the decimal point, then multiplying this float number by $n, then the float must be converted to an integer to complete.
Per #axiac's comment, the new hero is 10**$n-1 which generates a series of nines to the desired length (no float numbers). Next divide the nines by nine to generate a series of ones which becomes the perfect multiplier. Finally, multiply the series of ones and the input number to arrive at the desired output.
There are two operations you need to accomplish:
given a number $number, append the digit $n to it;
repeat operation #1 some number of times ($n times).
Operation #1 is easy:
$number = $number * 10 + $n;
Operation #2 is even easier:
for ($i = 0; $i < $n; $i ++)
What else do you need?
Initialization of the variable used to store the computed number:
$number = 0;
Put them in order and you get:
// The input digit
// It gives the length of the computed number
// and also its digits
$n = 8;
// The number we compute
$number = 0;
// Put the digit $n at the end of $number, $n times
for ($i = 0; $i < $n; $i ++) {
$number = $number * 10 + $n;
}
// That's all
If intval() is accepted:
$result = '';
$input = 9;
for($i=0; $i < $input; $i++){
$result .= $input;
}
$result = intval($result);
else:
$result = 0;
$input = 9;
for($i=0; $i < $input; $i++){
$factor = 1;
for($j = 0; $j < $i; $j++){
$factor *= 10;
}
$result += $input * $factor;
}
=>
9 + 90 + 900 + 9000 + 90000...
Related
For an endless number such as Pi, how would one go about finding the first occurrence of an exact sum of digits for a given number n.
For example. If n=20
Pi=3.14159265358979323846264338327950288419716939...
then the first occurrence is from digit 1 to digit 5 since:
1+4+1+5+9=20
if n=30, then the first occurrence is from digit 5 to digit 11
since 9+2+6+5+3+5=30
answer should have a working php demo
The answer to this is using sliding window that will maintain the sum. so maintain two pointers say i and j. Keep increasing j and adding the elements inside. when it crosses the desired sum increase i and decrease the element at i. Then keep increasing j until the sum is reached or the sum overflows so you repeat the above process.
Example sum = 30
141592653589793238 >> i=j=0 current_sum = 1
141592653589793238 >> i=0 j=6 current_sum=28
in the next iteration adding 5 will result in current_sum>30 so hence you increment i
141592653589793238 >> i=1 j=6 current_sum=27
141592653589793238 >> i=2 j=6 current_sum=23
141592653589793238 >> i=2 j=7 current_sum=28
Keep going in this manner and it will finally reach the window that is equal to the sum =30 . That should break you out of the loop and help you find the answer.
Method 1 (suggested by Ashwin Bhat)
This implementation uses two pivots. The sum of digits between $pivot_a and $pivot_b is computed. Depending on the value of the sum, we increment $pivot_b (if the sum is less) or $pivot_a (if the sum is greater). If the sum is equal to $n, break. The values of the pivots give the appropriate digit indices.
$pi = "314159265358979323846264338327950288419716939";
$n = 30;
$pivot_a = $pivot_b = 0;
$sum = 0;
for( ; $pivot_b < strlen($pi); ) {
if($sum < $n) {
$sum += $pi[$pivot_b++];
} elseif ($sum > $n) {
$sum -= $pi[$pivot_a++];
} else {
print('Solution found from digit '.$pivot_a.' to '.$pivot_b.'.');
exit;
}
}
print('No match was found.');
Method 2
This implementation uses one pivot only, from which it starts summing up the digits. If the sum happens to be greater than the desired value, it resets the sum to zero, shifts the pivot one position and starts the summing again.
$pi = "314159265358979323846264338327950288419716939";
$n = 30;
// Let's sum up all the elements from $pivot until we get the exact sum or a
// number greater than that. In the latter case, shift the $pivot one place.
$pivot = 0;
$sum = 0;
for($k=0 ; $sum != $n && $k < strlen($pi) ; $k++) {
$sum += $pi[$k];
print($pi[$k]);
if($sum > $n) {
print(' = '.$sum.' fail, k='.($pivot+1).PHP_EOL);
$sum = 0;
$k = $pivot++;
} elseif($sum < $n) {
print("+");
}
}
print(' = '.$n.' found from digit '.$pivot.' to '.$k.'.');
The implementation is not very effective but tries to explain the steps. It prints
3+1+4+1+5+9+2+6 = 31 fail, k=1
1+4+1+5+9+2+6+5 = 33 fail, k=2
4+1+5+9+2+6+5 = 32 fail, k=3
1+5+9+2+6+5+3 = 31 fail, k=4
5+9+2+6+5+3 = 30 found from digit 4 to 10.
Here's another approach. It builds an array of sums along the way and, on every iteration, attempts to add the current digit to the previous sums, and so on, while always only keeping the sums that are still relevant (< target).
The function either returns:
an array of 2 values representing the 0-based index interval within the digits,
or null if it couldn't find the target sum
Code:
function findFirstSumOccurrenceIndexes(string $digits, int $targetSum): ?array
{
$sums = [];
for ($pos = 0, $length = strlen($digits); $pos < $length; $pos++) {
$digit = (int)$digits[$pos];
if ($digit === $targetSum) {
return [$pos, $pos];
}
foreach ($sums as $startPos => $sum) {
if ($sum + $digit === $targetSum) {
return [$startPos, $pos];
}
if ($sum + $digit < $targetSum) {
$sums[$startPos] += $digit;
}
else {
unset($sums[$startPos]);
}
}
$sums[] = $digit;
}
return null;
}
Demo: https://3v4l.org/9t3vf
My task, using php, is to create a random number, then make that number multiply itself. However i cannot use the multiply operator (*) and have been told to create a for loop instead however I'm having some troubles.
$startNum = rand(1,10);
for ($i = $startNum; $i <= 10; $i++)
{
echo $i;
}
This is what i have so far, however this is completely wrong and will only get a random number and count to 10 from it.
Any help would be very appreciated, thanks.
When squaring you are just multiplying a number by itself, another way to do this is through addition, add a number to itself x amount of times. So, with 4 squared, that is 4 * 4 or, 4 + 4 + 4 + 4.
Doing this in a for loop should be as simple as
$startNum = rand(1,10);
$endNum = 0;
for ($i = 0; $i < $startNum; $i++)
{
$endNum += $startNum;
}
echo $endNum;
Caveat: I don't program Php so forgive syntax errors.
$startNum*$startNum means that the loop should loop $startNum times and in each iteration add $startNum, i.e., the number itself
$s = 0;
for($i=1;$i<=$startNum;$i++){
$s += $startNum;
}
echo $s;
Still not using the multiplication operator :p
$n = mt_rand(1, 10);
echo array_sum(array_fill(0, $n, $n));
you can do this by simple addition(+) operator
square means add that number into same number for same time.
example : square of 2 means : 2+2;
square of 4 means : addition of 4 with 4 for 4 times : 4+4+4+4
so you can do like that
$startNum = rand(1,10);
$ans=0;
for ($i = 0 ;$i < $startNum; $i++)
{
echo $ans+=$startNum;
}
I've searched through a number of similar questions, but unfortunately I haven't been able to find an answer to this problem. I hope someone can point me in the right direction.
I need to come up with a PHP function which will produce a random number within a set range and mean. The range, in my case, will always be 1 to 100. The mean could be anything within the range.
For example...
r = f(x)
where...
r = the resulting random number
x = the mean
...running this function in a loop should produce random values where the average of the resulting values should be very close to x. (The more times we loop the closer we get to x)
Running the function in a loop, assuming x = 10, should produce a curve similar to this:
+
+ +
+ +
+ +
+ +
Where the curve starts at 1, peeks at 10, and ends at 100.
Unfortunately, I'm not well versed in statistics. Perhaps someone can help me word this problem correctly to find a solution?
interesting question. I'll sum it up:
We need a funcion f(x)
f returns an integer
if we run f a million times the average of the integer is x(or very close at least)
I am sure there are several approaches, but this uses the binomial distribution: http://en.wikipedia.org/wiki/Binomial_distribution
Here is the code:
function f($x){
$min = 0;
$max = 100;
$curve = 1.1;
$mean = $x;
$precision = 5; //higher is more precise but slower
$dist = array();
$lastval = $precision;
$belowsize = $mean-$min;
$abovesize = $max-$mean;
$belowfactor = pow(pow($curve,50),1/$belowsize);
$left = 0;
for($i = $min; $i< $mean; $i++){
$dist[$i] = round($lastval*$belowfactor);
$lastval = $lastval*$belowfactor;
$left += $dist[$i];
}
$dist[$mean] = round($lastval*$belowfactor);
$abovefactor = pow($left,1/$abovesize);
for($i = $mean+1; $i <= $max; $i++){
$dist[$i] = round($left-$left/$abovefactor);
$left = $left/$abovefactor;
}
$map = array();
foreach ($dist as $int => $quantity) {
for ($x = 0; $x < $quantity; $x++) {
$map[] = $int;
}
}
shuffle($map);
return current($map);
}
You can test it out like this(worked for me):
$results = array();
for($i = 0;$i<100;$i++){
$results[] = f(20);
}
$average = array_sum($results) / count($results);
echo $average;
It gives a distribution curve that looks like this:
I'm not sure if I got what you mean, even if I didn't this is still a pretty neat snippet:
<?php
function array_avg($array) { // Returns the average (mean) of the numbers in an array
return array_sum($array)/count($array);
}
function randomFromMean($x, $min = 1, $max = 100, $leniency = 3) {
/*
$x The number that you want to get close to
$min The minimum number in the range
$max Self-explanatory
$leniency How far off of $x can the result be
*/
$res = [mt_rand($min,$max)];
while (true) {
$res_avg = array_avg($res);
if ($res_avg >= ($x - $leniency) && $res_avg <= ($x + $leniency)) {
return $res;
break;
}
else if ($res_avg > $x && $res_avg < $max) {
array_push($res,mt_rand($min, $x));
}
else if ($res_avg > $min && $res_avg < $x) {
array_push($res, mt_rand($x,$max));
}
}
}
$res = randomFromMean(22); // This function returns an array of random numbers that have a mean close to the first param.
?>
If you then var_dump($res), You get something like this:
array (size=4)
0 => int 18
1 => int 54
2 => int 22
3 => int 4
EDIT: Using a low value for $leniency (like 1 or 2) will result in huge arrays, since testing, I recommend a leniency of around 3.
I want to get 3 int values in a for loop connected with each other. What I basically want is this:
000
001
002
003
010
011
...
323
330
331
I want to have each of the 3 numbers in a variable starting from 0 and max 3 when it gets higher than 3 it increases the number left to it by 1
For example
for($i = 0; $i <= $array; $i++){
echo $a . $b . $c . "<br />"; //Output would be the example I showed above
}
You can use base_convert to convert between arbitrary bases, in your case base 4.
for($i=0, $max = base_convert(333, 4, 10); $i < $max; ++$i) {
echo base_convert($i, 10 , 4);
}
To get 0-padded output, use printf with a format specifier:
printf('%03d', base_convert($i, 10 , 4));
for($i = 0; $i <= 63; $i++){
$c = $i % 4;
$b = ($i - $c)/4 % 4;
$a = (($i - $c)/4 - $b)/4;
echo $a . $b . $c . "<br />"; //Output would be the example I showed above
}
It's really just an explicit version of knittl's answer. The for loop has us step through every number from 0 thru 63, which happens to correspond with 0 through 333 in base 4. We then take $i, which is in base 10, and convert it to base 4 step by step. The % is the modulo operator - it returns the remainder after division. The least significant char is simply the remainder of $i/4, so we save that as $c. The next char is the 4 place (like the 10 place in base 10). So we subtract $c, which is already accounted for and divide by 4 and do the same thing.
for($a = 0; $a <= 3; $a++){
for($b = 0; $b <= 3; $b++){
for($c = 0; $c <= 3; $c++){
echo $a . $b . $c . "<br />";
}
}
}
Try this:
$count = 20; //how many numbers do you want
for($i =0; $i<$count; $i++) {
echo str_pad(base_convert($i, 10, 4),3,'0' , STR_PAD_LEFT) . '<br/>';
}
base_convert() converts every $i value from 10 base to 4.
str_pad() fill it with '0' to given length (3 here).
STR_PAD_LEFT means that zeros should be added on left side.
i had applied for a job recently and the requirement was to complete a test and then interview
2 questions were given for test which was very simple and i did it successfully but still i was told that i have failed the test because the script took more than 18 seconds to complete execution. here is the program i dont understand what else i could do to make it fast. although i have failed the test but still wants to know else i could do?
Program language is PHP and i had to do it using command line input
here is the question:
K Difference
Given N numbers , [N<=10^5] we need to count the total pairs of numbers that have a difference of K. [K>0 and K<1e9]
Input Format:
1st line contains N & K (integers).
2nd line contains N numbers of the set. All the N numbers are assured to be distinct.
Output Format:
One integer saying the no of pairs of numbers that have a diff K.
Sample Input #00:
5 2
1 5 3 4 2
Sample Output #00:3
Sample Input #01:
10 1
363374326 364147530 61825163 1073065718 1281246024 1399469912 428047635 491595254 879792181 1069262793
Sample Output #01:
0
Note: Java/C# code should be in a class named "Solution"
Read input from STDIN and write output to STDOUT.
and this is the solution
$fr = fopen("php://stdin", "r");
$fw = fopen("php://stdout", "w");
fscanf($fr, "%d", $total_nums);
fscanf($fr, "%d", $diff);
$ary_nums = array();
for ($i = 0; $i < $total_nums; $i++) {
fscanf($fr, "%d", $ary_nums[$i]);
}
$count = 0;
sort($ary_nums);
for ($i = $total_nums - 1; $i > 0; $i--) {
for ($j = $i - 1; $j >= 0; $j--) {
if ($ary_nums[$i] - $ary_nums[$j] == $diff) {
$count++;
$j = 0;
}
}
}
fprintf($fw, "%d", $count);
Your algorithm's runtime is O(N^2) that is approximately 10^5 * 10^5 = 10^10. With some basic observation it can be reduced to O(NlgN) which is approximately 10^5*16 = 1.6*10^6 only.
Algorithm:
Sort the array ary_nums.
for every i'th integer of the array, make a binary search to find if ary_nums[i]-K, is present in the array or not. If present increase result, skip i'th integer otherwise.
sort($ary_nums);
for ($i = $total_nums - 1; $i > 0; $i--) {
$hi = $i-1;
$low = 0;
while($hi>=$low){
$mid = ($hi+$low)/2;
if($ary_nums[$mid]==$ary_nums[$i]-$diff){
$count++;
break;
}
if($ary_nums[$mid]<$ary_nums[$i]-$diff){
$low = $mid+1;
}
else{
$hi = $mid-1;
}
}
}
}
I got the same question for my technical interview. I wonder if we are interviewing for the same company. :)
Anyway, here is my answer I came up with (after the interview):
// Insert code to get the input here
$count = 0;
sort ($arr);
for ($i = 0, $max = $N - 1; $i < $max; $i++)
{
$lower_limit = $i + 1;
$upper_limit = $max;
while ($lower_limit <= $upper_limit)
{
$midpoint = ceil (($lower_limit + $upper_limit) / 2);
$diff = $arr[$midpoint] - $arr[$i];
if ($diff == $K)
{
// Found it. Increment the count and break the inner loop.
$count++;
$lower_limit = $upper_limit + 1;
}
elseif ($diff < $K)
{
// Search to the right of midpoint
$lower_limit = $midpoint + 1;
}
else
{
// Search to the left of midpoint
$upper_limit = $midpoint - 1;
}
}
}
#Fallen: Your code failed for the following inputs:
Enter the numbers N and K: 10 3
Enter numbers for the set: 1 2 3 4 5 6 7 8 9 10
Result: 6
I think it has to do with your calculation of $mid (not accounting for odd number)