Find the factorial of suffixes in a given array and the suffix sum array in C++

Discovering suffix factorials and respective suffix sum arrays from an array is quite feasible when you know C++ programming language tools and techniques. That's precisely what we'll discuss in this write-up covering method syntax, algorithm intricacies as well as Plural meansuresto unraveling them efficiently. Moreover,two concrete code examples based on those methods are showcased further in this article. Ultimately, we'll summarize our insights into essential takeaway points.

Syntax

To ensure clear understanding of the forthcoming code examples. Let us first acquaint ourselves with the syntax of the method being used prior to delving into its algorithm. −

// Method syntax
<return_type> methodName(<parameters>) {
   // Method implementation
}

Algorithm

Now, let's outline the step-by-step algorithm to find the suffix factorials and the suffix sum array −

• Initialize an empty array to store the suffix factorials.

• To successfully fulfill this task. It is recommended to iterate over the provided array in reverse order. During each iteration a factorials calculation must be performed for the current element and the result stored in an additional suffix factorials array.

• Initialize the suffix sum array with the last element of the given array.

• Iterate over the suffix factorials array in reverse order.

• For each element in the suffix factorials array, calculate the corresponding suffix sum by adding it to the previous sum and store it in the suffix sum array.

Approach 1: Iterative Approach

In this approach, we will use Iterative Approach to find the suffix factorials and the suffix sum array..

Example

#include <iostream>

// Function to calculate the factorial of a given number
int factorial(int n) {
   int fact = 1;
   for (int i = 2; i <= n; i++) {
      fact *= i;
   }
   return fact;
}

int main() {
   // Initialize the given array
   int arr[] = {1, 2, 3, 4, 5};
   int n = sizeof(arr) / sizeof(arr[0]);

   // Create an array to store the suffix factorials
   int suffixFactorials[n];

   // Calculate the suffix factorials
   for (int i = n - 1; i >= 0; i--) {
      suffixFactorials[i] = factorial(arr[i]);
   }
   
   // Create an array to store the suffix sum
   int suffixSum[n];
   
   // Calculate the suffix sum
   suffixSum[n - 1] = arr[n - 1];
   for (int i = n - 2; i >= 0; i--) {
      suffixSum[i] = suffixSum[i + 1] + suffixFactorials[i];
   }
   
   // Output the suffix factorials and the suffix sum
   for (int i = 0; i < n; i++) {
      std::cout << "Suffix Factorial[" << i << "]: " << suffixFactorials[i] << std::endl;
      std::cout << "Suffix Sum[" << i << "]: " << suffixSum[i] << std::endl;
   }
   return 0;
}

Output

Suffix Factorial[0]: 1
Suffix Sum[0]: 38
Suffix Factorial[1]: 2
Suffix Sum[1]: 37
Suffix Factorial[2]: 6
Suffix Sum[2]: 35
Suffix Factorial[3]: 24
Suffix Sum[3]: 29
Suffix Factorial[4]: 120
Suffix Sum[4]: 5

Explanation

The iterative approach for finding the suffix factorials and the suffix sum array involves iterating over the given array in reverse order. For each element in the array, the factorial is calculated using an iterative method and stored in the suffix factorials array. The suffix sum array is also created and initialized with the last element of the given array. Implementing a simple yet effective strategy can help solve this problem with ease and efficiency simultaneously. The first step entails performing an iteration on the suffix factorials array while keeping its order reversed rather than forward . Using this means of traversal enables us to compute each post-fix total effortlessly as we can merely add it together with its precedent calculation before encoding it into our intended output variable .

Approach 2: Recursive Approach

Our strategy entails utilizing the Hamming distance concept to tackle the problem that has been presented.

Example

#include <iostream>

// Function to calculate the factorial of a given number recursively
int factorial(int n) {
   if (n == 0 || n == 1) {
      return 1;
   }
   return n * factorial(n - 1);
}

int main() {
   // Initialize the given array
   int arr[] = {1, 2, 3, 4, 5};
   int n = sizeof(arr) / sizeof(arr[0]);

   // Create an array to store the suffix factorials
   int suffixFactorials[n];

   // Calculate the suffix factorials
   for (int i = n - 1; i >= 0; i--) {
      suffixFactorials[i] = factorial(arr[i]);
   }

   // Create an array to store the suffix sum
   int suffixSum[n];

   // Calculate the suffix sum
   suffixSum[n - 1] = arr[n - 1];
   for (int i = n - 2; i >= 0; i--) {
      suffixSum[i] = suffixSum[i + 1] + suffixFactorials[i];
   }

   // Output the suffix factorials and the suffix sum
   for (int i = 0; i < n; i++) {
      std::cout << "Suffix Factorial[" << i << "]: " << suffixFactorials[i] << std::endl;
      std::cout << "Suffix Sum[" << i << "]: " << suffixSum[i] << std::endl;
   }
   return 0;
}

Output

Suffix Factorial[0]: 1
Suffix Sum[0]: 38
Suffix Factorial[1]: 2
Suffix Sum[1]: 37
Suffix Factorial[2]: 6
Suffix Sum[2]: 35
Suffix Factorial[3]: 24
Suffix Sum[3]: 29
Suffix Factorial[4]: 120
Suffix Sum[4]: 5

Explanation

To derive the suffix factorial and sum arrays, a recursive strategy is utilized. Beginning by reversely iterating through the given array, a recursive function calculates its factorial. These values are then stored within an associated suffix factorial array. The following step involves initializing a new suffix sum array by assigning it with the last element from our input set. Continuing our iterations over prior calculations from our previously constructed factorials collection in a backward sequence permits summation computation to be tabulated into this newly generated array as well; Hereby producing our sought after resultants via an effective use of recursive iteration.

Conclusion

In summary, we have examined the concept of identifying suffix factorials and their matching suffix sum arrays in an inputted array with C++ programming language. Our analysis yielded two different methods: an iterative one as well as a recursive one. Additionally, accurate code examples effectively demonstrating each method's functionality were included. By understanding and implementing these approaches, you can efficiently solve similar problems that involve the calculation of suffix factorials and the suffix sum array. Keep exploring and experimenting with different algorithms to enhance your programming skills.