Given an integer, n, find each x such that:
- 0<=x <=n
- n+x = n^ x
where ^ denotes the bitwise XOR operator. Then print an integer denoting the total number of x‘s satisfying the criteria above.
Input Format
A single integer, n.
Constraints
- 0<=n <=10**15
Subtasks
- 0<=n <=100 for 60% of the maximum score.
Output Format
Print the total number of integer x ‘s satisfying both of the conditions specified above.
Sample Input 0
5
Sample Output 0
2
Explanation 0
For n=5 , the x values 0 and 2 satisfy the conditions:
- 5 + 0 = 5 ^ 0 = 5
- 5 + 2 = 5 ^ 2 = 5
Thus, we print 2 as our answer.
Sample Input 1
10
Sample Output 1
4
Solution in PHP
problem link Click Here
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This solution is totally a mathematical trick.
just count total numbers of ZERO present in binary number of given n, and answer will be the 2 to the power of (total num of zero).
<?php
$handle = fopen ("php://stdin","r");
fscanf($handle,"%s",$n);
echo ($n>0)?pow(2,substr_count(decbin($n),'0')):1;
<?php
$handle = fopen ("php://stdin","r");
fscanf($handle,"%d",$n);
$count=0;
while($n>0){
$count += fmod($n,2) ? 0 : 1;
$n /=2;
$n=floor($n);
}
echo pow(2,$count);
$handle = fopen ("php://stdin","r");
fscanf($handle,"%s",$n);
$count=0;
while($n>0){
$count += bcmod($n,2) ? 0 : 1;
$n /=2;
$n=floor($n);
}
echo bcpow(2,$count);
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