Learning C++ Programming from Scratch, Day 416: Problem 1196 – Corner I; Question Bank Answers; Third Method

1196 – Corner I

1. Problem Understanding Phase (Minimum Number Matrix Problem)

We need to print a special N×N matrix characterized by:

1. The value of each element in the matrix equals the smaller of its row index i and column index j

2. Using nested loops to traverse the matrix

3. Each number output occupies a width of 3 characters

2. Core Algorithm Idea

The program adopts the method of double loops:

1. The outer loop controls the row index i from 1 to N

2. The inner loop controls the column index j from 1 to N

3. Using min(i,j) to calculate the value at each position

4. Using setw(3) to control the output format

3. Detailed Execution Process (Example with N=3)

Output Matrix:
  1  1  1
  1  2  2
  1  2  3

Reference Code

#include<bits/stdc++.h> // Include all standard library headers
using namespace std;   // Use standard namespace
int main() {    int n; // Define matrix size variable
    cin >> n; // Read user input for matrix size
    // Outer loop: control row index i from 1 to n    for(int i = 1; i <= n; i++) {        // Inner loop: control column index j from 1 to n        for(int j = 1; j <= n; j++) {            // Output the smaller value of i and j, width set to 3 characters            cout << setw(3) << min(i, j);        }        // New line after each row output        cout << endl;    }
    return 0; // Program ends normally
}

Super Detailed Program Documentation (For Beginners)

1. Program Function Description

This program implements the following functions:

• Input: A positive integer N (matrix size)

• Output: An N×N matrix where each element’s value is the smaller of the row and column indices

• Output format: Each number occupies a width of 3 characters, right-aligned

• Example: When input is 3, the output is the matrix shown above

2. Core Algorithm Analysis

Double Loop Structure:

1. Outer Loop:

• Control variable i (row index) increments from 1 to N

• Each loop iteration processes one row of the matrix

Inner Loop:

• Control variable j (column index) increments from 1 to N

• Calculate and output min(i,j)

Key Functions:

• min(i,j): Returns the smaller of the two numbers

• setw(3): Sets the output field width to 3

3. Variable Role Description

• <span>n</span>: Stores the user input for matrix size

• <span>i</span>: Outer loop variable, representing the current row index

• <span>j</span>: Inner loop variable, representing the current column index

4. Execution Process Example (N=3)

1. i=1:

• j=1: Output 1

• j=2: Output 1

• j=3: Output 1

• New line

i=2:

• j=1: Output 1

• j=2: Output 2

• j=3: Output 2

• New line

i=3:

• j=1: Output 1

• j=2: Output 2

• j=3: Output 3

• New line

5. Loop Execution Diagram

Outer loop i=1→3
│
├── Inner loop j=1→3
│   ├── Output min(1,1)=1
│   ├── Output min(1,2)=1
│   └── Output min(1,3)=1
│
├── Inner loop j=1→3
│   ├── Output min(2,1)=1
│   ├── Output min(2,2)=2
│   └── Output min(2,3)=2
│
└── Inner loop j=1→3
    ├── Output min(3,1)=1
    ├── Output min(3,2)=2
    └── Output min(3,3)=3

6. Important Notes

1. Format Control:

• setw(3) ensures each number occupies 3 characters

• Default right alignment

Boundary Handling:

• Loop variables start from 1

• Includes boundary value n

Input Limitations:

• The program does not check the range of input

• In practical use, n should not be too large

7. Reference Test Cases

Input N	Output Matrix
1	1
2	1 11 2
3	1 1 11 2 21 2 3
4	1 1 1 11 2 2 21 2 3 31 2 3 4

This explanation is entirely based on the original code, providing a detailed analysis of the execution process and visualizing the call relationships to help beginners deeply understand the implementation principles of double loops printing matrices.