Sum of Digits & Armstrong (Narcissistic) Number Check

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Problem Statement

Given a positive integer N, compute the sum of its decimal digits and simultaneously check if N is a 3-digit Armstrong number (where the sum of the cubes of its digits equals the number itself, e.g., 153 = 1^3 + 5^3 + 3^3 = 1 + 125 + 27 = 153).

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Variable Dictionary / Table

Variable Name	Data Type	Role & Purpose
N	Integer	Input integer
Orig	Integer	Preserves original number
SumDigits	Integer	Sum of decimal digits
ArmstrongSum	Integer	Sum of cubes of decimal digits
Rem	Integer	Extracted digit (temp % 10)

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Step-by-Step Formal Algorithm

Step 1: Start.
Step 2: Read positive integer N.
Step 3: Set Orig = N, SumDigits = 0, ArmstrongSum = 0.
Step 4: While (N > 0):
         Rem = N % 10
         SumDigits = SumDigits + Rem
         ArmstrongSum = ArmstrongSum + (Rem * Rem * Rem)
         N = N / 10
Step 5: Print 'Sum of Digits:', SumDigits.
Step 6: If (ArmstrongSum == Orig):
         Print Orig, 'is an Armstrong Number.'
Step 7: Else:
         Print Orig, 'is NOT an Armstrong Number.'
Step 8: Stop.

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Flowchart (Interactive Graphical Diagram)

flowchart TD Start([Start]) --> In[/"Read N"/] In --> Init["Orig = N
SumDigits = 0
ArmstrongSum = 0"] Init --> Cond{"Is N > 0 ?"} Cond -- Yes --> Calc["Rem = N % 10
SumDigits += Rem
ArmstrongSum += Rem^3
N = N / 10"] Calc --> Cond Cond -- No --> OutSum[/"Print SumDigits"/] OutSum --> ChkArm{"Does ArmstrongSum == Orig ?"} ChkArm -- Yes --> OutYes[/"Print 'Armstrong Number'"/] OutYes --> Stop([Stop]) ChkArm -- No --> OutNo[/"Print 'Not Armstrong'"/] OutNo --> Stop

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Flowchart (ANSI Terminal ASCII Chart)

         +-----------------+
         |     [ START ]   |
         +-----------------+
                  |
                  v
         +-----------------+
         |     Read N      |
         +-----------------+
                  |
                  v
         +----------------------------+
         | Orig = N                   |
         | SumDigits = 0              |
         | ArmstrongSum = 0           |
         +----------------------------+
                  |
                  v
               /     \
             /  N > 0 ? \ ---NO---> [Print SumDigits]
             \         /                    |
                  | YES                     v
                  v                      /     \
         +----------------------------+/ArmstrongSum\
         | Rem = N % 10               |\ == Orig ?  /
         | SumDigits += Rem           / YES/     \NO
         | ArmstrongSum += Rem^3     /    v       v
         | N = N / 10               /  [Arm]   [Not Arm]
         +-------------------------+      |       |
                  |                       +---+---+
                  +------>                    |
                                              v
                                           [STOP]

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Dry-Run Execution Trace Table

Execution Step / Case	Variables State 1	Variables State 2	Condition Evaluation	Output / Result
N = 153	Orig = 153	Digits: 3, 5, 1	Sum = 3+5+1=9; Cubes = 27+125+1 = 153 == Orig	ARMSTRONG NUMBER
N = 370	Orig = 370	Digits: 0, 7, 3	Sum = 10; Cubes = 0+343+27 = 370 == Orig	ARMSTRONG NUMBER
N = 120	Orig = 120	Digits: 0, 2, 1	Sum = 3; Cubes = 0+8+1 = 9 != 120	NOT ARMSTRONG

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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_9.cpp

GCC 13.2 • C++20

#include <iostream>
using namespace std;

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

    int original = n;
    int sumOfDigits = 0;
    int armstrongSum = 0; // Sum of cubes of digits

    int temp = n;
    while (temp > 0) {
        int digit = temp % 10;
        sumOfDigits += digit;
        armstrongSum += (digit * digit * digit);
        temp /= 10;
    }

    cout << "\n========================================\n";
    cout << "Original Number     : " << original << "\n";
    cout << "Sum of Digits       : " << sumOfDigits << "\n";
    cout << "Sum of Cubed Digits : " << armstrongSum << "\n";
    cout << "----------------------------------------\n";

    if (armstrongSum == original) {
        cout << "Result: " << original << " is a 3-DIGIT ARMSTRONG (Narcissistic) NUMBER!\n";
    } else {
        cout << "Result: " << original << " is NOT an Armstrong number.\n";
    }
    cout << "========================================\n";
    return 0;
}

#include <iostream>
using namespace std;

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

int original = n;
    int sumOfDigits = 0;
    int armstrongSum = 0; // Sum of cubes of digits

int temp = n;
    while (temp > 0) {
        int digit = temp % 10;
        sumOfDigits += digit;
        armstrongSum += (digit * digit * digit);
        temp /= 10;
    }

cout << "\n========================================\n";
    cout << "Original Number     : " << original << "\n";
    cout << "Sum of Digits       : " << sumOfDigits << "\n";
    cout << "Sum of Cubed Digits : " << armstrongSum << "\n";
    cout << "----------------------------------------\n";

if (armstrongSum == original) {
        cout << "Result: " << original << " is a 3-DIGIT ARMSTRONG (Narcissistic) NUMBER!\n";
    } else {
        cout << "Result: " << original << " is NOT an Armstrong number.\n";
    }
    cout << "========================================\n";
    return 0;
}

⌨️ Standard Input (cin):

Presets:

💻 Terminal Output • Ready to run

Input:
153

Output:
========================================
Original Number     : 153
Sum of Digits       : 9
Sum of Cubed Digits : 153
----------------------------------------
Result: 153 is a 3-DIGIT ARMSTRONG (Narcissistic) NUMBER!
========================================

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Developer & Exam Key Takeaway

Famous 3-digit Armstrong numbers are 153, 370, 371, and 407. Preserving the original number in a temporary variable before mutating it inside the loop is a crucial exam programming pattern.