Calculate Factorial of an Integer (N!)

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Problem Statement

Given a non-negative integer N, compute its factorial N! = 1 * 2 * 3 * ... * N, with appropriate validation for 0! = 1 and error handling for negative inputs.

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Variable Dictionary / Table

Variable Name	Data Type	Role & Purpose
N	Integer	Input number (0 <= N <= 20)
fact	Unsigned Long Long	Product accumulator, initialized to 1
i	Integer	Loop counter running from 1 to N

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Step-by-Step Formal Algorithm

Step 1: Start.
Step 2: Read integer N.
Step 3: If N < 0:
         Print 'Error: Factorial undefined for negative numbers' and Stop.
Step 4: Initialize fact = 1, i = 1.
Step 5: While (i <= N):
         fact = fact * i
         i = i + 1
Step 6: Print N, '! = ', fact.
Step 7: Stop.

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Flowchart (Interactive Graphical Diagram)

flowchart TD Start([Start]) --> In[/"Read N"/] In --> Valid{"Is N < 0 ?"} Valid -- Yes --> Err[/"Print 'Factorial Undefined for Negative'"/] Err --> Stop([Stop]) Valid -- No --> Init["fact = 1, i = 1"] Init --> Cond{"Is i <= N ?"} Cond -- Yes --> Calc["fact = fact * i
i = i + 1"] Calc --> Cond Cond -- No --> Out[/"Print fact"/] Out --> Stop

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Flowchart (ANSI Terminal ASCII Chart)

         +-----------------+
         |     [ START ]   |
         +-----------------+
                  |
                  v
         +-----------------+
         |     Read N      |
         +-----------------+
                  |
                  v
               /     \
             /  N < 0? \ ---YES--> [Print Undefined] --> [STOP]
             \         /
                  | NO
                  v
         +-----------------+
         | fact = 1, i = 1 |
         +-----------------+
                  |
                  v
               /     \
             /  i <= N? \ ---NO---> [Print fact] ------> [STOP]
             \         /
                  | YES
                  v
         +-----------------+
         | fact = fact * i |
         | i = i + 1       |
         +-----------------+
                  |
                  +------> (Loop back to i <= N?)

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Dry-Run Execution Trace Table

Execution Step / Case	Variables State 1	Variables State 2	Condition Evaluation	Output / Result
N=0	fact=1, i=1	Loop cond 1 <= 0 is False	Loop skipped immediately	0! = 1
N=5, Step 1-5	i=1..5	fact: 1->2->6->24->120	12345	5! = 120

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Interactive C++ Compiler & Runner

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Edit the code directly with the Edit Code button, provide custom inputs, and press Run Code to compile and execute in the live terminal console below!

📄 problem_3.cpp

GCC 13.2 • C++20

#include <iostream>
using namespace std;

int main() {
    int n;
    cout << "Enter a non-negative integer (0 to 20): ";
    if (!(cin >> n)) {
        cout << "Invalid input! Please enter an integer.\n";
        return 1;
    }

    if (n < 0) {
        cout << "Error: Factorial is undefined for negative integers!\n";
        return 1;
    }

    unsigned long long fact = 1;
    for (int i = 1; i <= n; ++i) {
        fact *= i;
    }

    cout << n << "! = " << fact << "\n";
    return 0;
}

⌨️ Standard Input (cin):

Presets:

💻 Terminal Output • Ready to run

Input:
6

Output:
6! = 720

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Developer & Exam Key Takeaway

Factorial grows super-exponentially. In standard C++, unsigned long long tops out at 20! (2,432,902,008,176,640,000). Beyond N=20, big integer libraries or arrays are mandatory.