PHP Program for Count ways to reach the n\’th stair
Last Updated :
16 Jun, 2022
There are n stairs, a person standing at the bottom wants to reach the top. The person can climb either 1 stair or 2 stairs at a time. Count the number of ways, the person can reach the top.
Consider the example shown in diagram. The value of n is 3. There are 3 ways to reach the top. The diagram is taken from Easier Fibonacci puzzles
PHP
<?php
function fib( $n )
{
if ( $n <= 1)
return $n ;
return fib( $n - 1) +
fib( $n - 2);
}
function countWays( $s )
{
return fib( $s + 1);
}
$s = 4;
echo "Number of ways = " ,
countWays( $s );
?>
|
Output:
Number of ways = 5
The time complexity of the above implementation is exponential (golden ratio raised to power n). It can be optimized to work in O(Logn) time using the previously discussed Fibonacci function optimizations.
PHP
<?php
function countWaysUtil( $n , $m )
{
if ( $n <= 1)
return $n ;
$res = 0;
for ( $i = 1; $i <= $m &&
$i <= $n ; $i ++)
$res += countWaysUtil( $n - $i , $m );
return $res ;
}
function countWays( $s , $m )
{
return countWaysUtil( $s + 1, $m );
}
$s = 4; $m = 2;
echo "Number of ways = " ,
countWays( $s , $m );
?>
|
Output
Number of ways = 5
Time complexity: O(2n)
Auxiliary Space: O(n)
PHP
<?php
function countWaysUtil( $n , $m )
{
$res [0] = 1; $res [1] = 1;
for ( $i = 2; $i < $n ; $i ++)
{
$res [ $i ] = 0;
for ( $j = 1; $j <= $m && $j <= $i ; $j ++)
$res [ $i ] += $res [ $i - $j ];
}
return $res [ $n - 1];
}
function countWays( $s , $m )
{
return countWaysUtil( $s + 1, $m );
}
$s = 4;
$m = 2;
echo "Number of ways = " , countWays( $s , $m );
?>
|
Time Complexity: O(m*n)
Auxiliary Space: O(n)
Please refer complete article on Count ways to reach the n’th stair for more details!
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