Symmetric Matrix Check
Problem
A square matrix is symmetric when m[i][j] == m[j][i] for all i and j. Read a matrix and print true if it is symmetric. A matrix that is not square is never symmetric.
Constraints
- 1 <= r, c <= 500
Examples
Input
2 2 1 2 2 1
Output
true
Solutions
Only the half above the diagonal needs to be checked, because the other half is the mirror. That halves the work.
/*
* Problem : Process a matrix.
* Input : r and c, then r rows of c integers.
* Output : true or false.
* Approach: Compare mirrored elements.
* Time : O(n^2)
* Space : O(1)
* Java : 8 or newer.
*/
import java.util.Scanner;
public class Main {
// This method solves the task. It receives the input and returns the answer.
static boolean solve(int[][] m) {
// Step 1: A matrix that is not square cannot be symmetric.
if (m.length != m[0].length) {
return false;
}
// Step 2: Compare each element above the diagonal with its mirror below the diagonal.
for (int i = 0; i < m.length; i++) {
for (int j = i + 1; j < m.length; j++) {
if (m[i][j] != m[j][i]) {
return false;
}
}
}
return true;
}
public static void main(String[] args) {
Scanner scanner = new Scanner(System.in);
int rows = scanner.nextInt();
int cols = scanner.nextInt();
int[][] m = new int[rows][cols];
for (int i = 0; i < rows; i++) {
for (int j = 0; j < cols; j++) {
m[i][j] = scanner.nextInt();
}
}
System.out.println(solve(m));
}
}
Hints (1)
- Which elements need to be compared?