703452. Large Factorials
Medium
Large Factorials
Slug: large-factorials2539
Difficulty: Medium
Id: 703452
Topic Tags: Arrays, factorial, Data Structures
Company Tags: None
Summary
The problem Large Factorials is about calculating the factorials of a given range of numbers efficiently. The key concepts involved are arrays and basic arithmetic operations.
Detailed Explanation
To solve this problem, we can use an array to store the factorials up to a certain limit. We can then calculate the factorial for any number within that range by looking it up in the array. This approach reduces the time complexity of calculating large factorials from exponential to constant.
Here's a step-by-step breakdown of the solution:
- Create an array
factorialsof sizen+1, wherenis the maximum value for which we want to calculate the factorial. - Initialize the first element of the array as 1, since the factorial of 0 and 1 is 1.
- Calculate the factorial for each subsequent number in the range by multiplying the current number with the previous factorial and storing it in the
factorialsarray. - To calculate the factorial of a given number within the range, simply look up its value in the
factorialsarray.
The time complexity of this approach is O(1), since we only need to access the factorials array once to get the desired result. The space complexity is O(n), where n is the maximum value for which we want to calculate the factorial.
Optimized Solutions
Java
public class LargeFactorials {
public static void main(String[] args) {
int n = 20; // adjust this value as needed
long[] factorials = new long[n+1];
factorials[0] = 1;
for (int i = 1; i <= n; i++) {
factorials[i] = (long) Math.pow(i, i);
}
System.out.println("Factorial of 10: " + factorials[10]);
}
}