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:
- Count number of trailing zeros in product of array
- Count number of trailing zeros in Binary representation of a number using Bitset
- Count unique numbers that can be generated from N by adding one and removing trailing zeros
- Find the smallest number X such that X! contains at least Y trailing zeros.
- Smallest number divisible by n and has at-least k trailing zeros
- Count trailing zeroes in factorial of a number
- Count numbers having N 0's and and M 1's with no leading zeros
- Count of N-bit binary numbers without leading zeros
- Trailing number of 0s in product of two factorials
- Number of trailing zeroes in base B representation of N!
- Smallest number with at least n trailing zeroes in factorial
- Largest number with maximum trailing nines which is less than N and greater than N-D
- Check if the given array can be reduced to zeros with the given operation performed given number of times
- Count number of triplets with product equal to given number with duplicates allowed
- Find count of digits in a number that divide the number
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