Find the Largest of Three Numbers

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Problem Statement

Given three distinct numbers A, B, and C, formulate a step-by-step algorithm and draw a flowchart to determine and print the largest number among them using minimal nested comparison branches.

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Variable Dictionary / Table

Variable Name	Data Type	Role & Purpose
A, B, C	Float / Double	Three input numerical values to compare
largest	Float / Double	Stores the maximum identified value

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Step-by-Step Formal Algorithm

Step 1: Start.
Step 2: Read values of A, B, and C.
Step 3: If A >= B:
         If A >= C:
             largest = A
         Else:
             largest = C
Step 4: Else (B > A):
         If B >= C:
             largest = B
         Else:
             largest = C
Step 5: Print 'The largest number is:', largest.
Step 6: Stop.

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Flowchart (Interactive Graphical Diagram)

flowchart TD Start([Start]) --> Input[/Read A, B, C/] Input --> Dec1{"Is A >= B ?"} Dec1 -- Yes --> Dec2{"Is A >= C ?"} Dec1 -- No --> Dec3{"Is B >= C ?"} Dec2 -- Yes --> OutA[/"Print 'A is Largest'"/] Dec2 -- No --> OutC1[/"Print 'C is Largest'"/] Dec3 -- Yes --> OutB[/"Print 'B is Largest'"/] Dec3 -- No --> OutC2[/"Print 'C is Largest'"/] OutA --> Stop([Stop]) OutC1 --> Stop OutB --> Stop OutC2 --> Stop

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Flowchart (ANSI Terminal ASCII Chart)

         +-----------------+
         |     [ START ]   |
         +-----------------+
                  |
                  v
         +-----------------+
         |  Read A, B, C   |
         +-----------------+
                  |
                  v
               /     \
             / A >= B ? \
             \         /
            YES/     \NO
             v         v
          /     \   /     \
        / A >= C?\ / B >= C?\
        \       /  \       /
        Y|     |N   Y|     |N
         v     v     v     v
       [A]    [C]   [B]   [C]
        |      |     |     |
        +------+-----+-----+
                  |
                  v
         +-----------------+
         |     [ STOP ]    |
         +-----------------+

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Dry-Run Execution Trace Table

Execution Step / Case	Variables State 1	Variables State 2	Condition Evaluation	Output / Result
Test Case 1	A=25, B=14, C=9	A >= B (True), A >= C (True)	Branch Dec1 -> Dec2	Largest = 25 (A)
Test Case 2	A=10, B=80, C=45	A >= B (False), B >= C (True)	Branch Dec1 -> Dec3	Largest = 80 (B)
Test Case 3	A=5, B=12, C=99	A >= B (False), B >= C (False)	Branch Dec1 -> Dec3 -> C	Largest = 99 (C)

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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_1.cpp

GCC 13.2 • C++20

#include <iostream>
using namespace std;

int main() {
    double a, b, c;
    cout << "Enter three numbers (A B C): ";
    if (!(cin >> a >> b >> c)) {
        cout << "Invalid input! Please enter valid numeric values.\n";
        return 1;
    }

    double largest;
    // Step-by-step nested branching
    if (a >= b) {
        if (a >= c) {
            largest = a;
        } else {
            largest = c;
        }
    } else {
        if (b >= c) {
            largest = b;
        } else {
            largest = c;
        }
    }

    cout << "\n========================================\n";
    cout << "Input values: A = " << a << ", B = " << b << ", C = " << c << "\n";
    cout << "Result      : Largest Number is " << largest << "\n";
    cout << "========================================\n";
    return 0;
}

⌨️ Standard Input (cin):

Presets:

💻 Terminal Output • Ready to run

Input:
25.5 89.2 44.0

Output:
========================================
Input values: A = 25.5, B = 89.2, C = 44
Result      : Largest Number is 89.2
========================================

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Developer & Exam Key Takeaway

Nested conditional logic guarantees finding the maximum in exactly 2 comparisons, which is optimal for 3 elements (log2(3!) ≈ 2.58).