Given an integer n, the task is to find the number of trailing zeros in the function i.e. f(n) = 11 * 22 * 33 * … * nn.
Input: n = 5
f(5) = 11 * 22 * 33 * 44 * 55 = 1 * 4 * 27 * 256 * 3125 = 86400000
Input: n = 12
Approach: We know that 5 * 2 = 10 i.e. 1 trailing zero is the result of the multiplication of a single 5 and a single 2. So, if we have x number of 5 and y number of 2 then the number of trailing zeros will be min(x, y).
Now, for every number i in the series, we need to count the number of 2 and 5 in its factors say x and y but the number of 2s and 5s will be x * i and y * i respectively because in the series i is raised to the power itself i.e. ii. Count the number of 2s and 5s in the complete series and print the minimum of them which is the required answer.
Below is the implementation of the above approach:
$val /= 2;
// If we get a factor 2 then we
// have i number of 2s because
// the power of the number is
// raised to i
$count_of_two += $i;
while ($val % 5 == 0 && $val > 0)
$val /= 5;
// If we get a factor 5 then
// we have i number of 5s
// because the power of the
// number is raised to i
$count_of_five += $i;
// Take the minimum of them
$ans = min($count_of_two, $count_of_five);
// Driver code
$N = 12;
// This code is contributed by ita_c
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