📘 Day 16 – Teacher's Day Challenge | Beautiful Matrix

🗓️ Date: August 09, 2025
🧩 Platform: Codeforces
🔢 Problems Solved Today: 1
🎯 Focus Topic: 2D Arrays, Manhattan Distance

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🔗 Table of Contents

• Problem 1 – Beautiful Matrix

• Daily Summary

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🧩 Problem 1 – Beautiful Matrix

📚 Difficulty: Easy-Medium
🧠 Concepts: 2D Arrays, Absolute Difference, Manhattan Distance

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📄 Problem Statement (Summary):
You are given a 5×5 matrix with exactly one cell containing 1 and all other cells containing 0. You can swap adjacent rows or adjacent columns in one move.
The goal is to move the 1 to the center cell (3, 3) (1-indexed). Find the minimum number of moves needed.

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🔢 Input Format:
Five lines, each containing five integers (0 or 1). Exactly one integer is 1.

🧾 Output Format:
A single integer — the minimum moves to place 1 in the center.

🔍 Example 1:
Input:

0 0 0 0 0  
0 0 0 0 1  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0

Output:

3

🔍 Example 2:
Input:

0 0 0 0 0  
0 0 0 0 0  
0 1 0 0 0  
0 0 0 0 0  
0 0 0 0 0

Output:

1

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💡 Approach:

• Identify the position (row, col) of the 1 in the matrix.

• The target position is (2, 2) in 0-indexed terms (center).

• Minimum moves = |row - 2| + |col - 2| (Manhattan Distance).

• Print the result.

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🧪 Code (C++):

#include <iostream>
#include <cmath>
using namespace std;

int main() {
    int mat[5][5];
    int row = -1, col = -1;

    for (int i = 0; i < 5; i++) {
        for (int j = 0; j < 5; j++) {
            cin >> mat[i][j];
            if (mat[i][j] == 1) {
                row = i;
                col = j;
            }
        }
    }

    int count = abs(row - 2) + abs(col - 2);
    cout << count << endl;

    return 0;
}

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📸 Submission Screenshot:

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✅ Key Takeaways:

• 2D array scanning is straightforward with nested loops.

• Manhattan distance formula is perfect for grid movement problems.

• Breaking down positions into row & column differences simplifies logic.

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📈 Daily Summary

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🏷️ Tags:
#codeforces #arrays #cpp #beginner #dsa #43DaysChallenge