Arrange numbers 1 to N^2 in a Zig-Zag Matrix in ascending order

Given a positive integer N, the task is to print an N × N zig-zag matrix consisting of numbers from 1 to N2, such that the ZigZag traversal of the matrix yields the number in ascending order.

Examples:

Input: N = 3
Output:
1 2 4
3 5 7
6 8 9
Explanation:

Input: N = 4
Output:
1 2 4 7
3 5 8 11
6 9 12 14
10 13 15 16

Approach:
The required matrix can be broken down into two right angle triangles.



  • An upside down right angled triangle(considered as upper triangle).
  • A normal right angled triangle(considered as lower triangle).

The idea is to iterate two nested loop to fill the upper triangle with respective values. Then iterate two nested loop again to fill the lower triangle with respective values. After the above two operations print the desired matrix.

Below is the implementation of the above approach:

C++

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// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
  
// Function to print the pattern
void printPattern(int n)
{
    // N * N matrix to store the
    // values
    int arr[n][n];
  
    arr[0][0] = 1;
  
    // Fill the values of
    // upper triangle
    for (int i = 0; i < n; i++) {
  
        if (i > 0) {
            arr[i][0] = arr[i - 1][0] + i + 1;
        }
        for (int j = 1;
             j < n - i; j++) {
  
            arr[i][j] = arr[i][j - 1] + i + j;
        }
    }
  
    // Fill the values of
    // lower triangle
    arr[1][n - 1] = arr[n - 1][0] + 1;
    int div = 0;
  
    for (int i = 2; i < n; i++) {
  
        div = n - 2;
        for (int j = n - i;
             j < n; j++) {
  
            if (j == n - i) {
                arr[i][j] = arr[i - 1][j + 1]
                            + 1;
            }
            else {
                arr[i][j] = arr[i][j - 1]
                            + div;
                div--;
            }
        }
    }
  
    // Print the array
    for (int i = 0; i < n; i++) {
  
        for (int j = 0; j < n; j++) {
  
            cout << arr[i][j] << " ";
        }
        cout << "\n";
    }
}
  
// Driver Code
int main()
{
    // Given size of matrix
    int N = 4;
  
    // Function Call
    printPattern(N);
    return 0;
}

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Output:

1 2 4 7 
3 5 8 11 
6 9 12 14 
10 13 15 16

Time Complexity: O(N2)
Auxillary Space: O(N2)

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