Check whether the given Matrix is balanced or not
Last Updated :
30 Aug, 2021
Given a matrix mat[][] of dimensions NxM, the task is to check whether the given matrix is balanced or not. Print “Balanced” if it is a balanced matrix else print “Unbalanced”.
A matrix is balanced if all cells in the matrix are balanced and a cell of the matrix is balanced if the number of cells in that matrix that are adjacent to that cell is strictly greater than the value written in this cell.
Adjacent cell means cells in the top, down, left, and right cell of each cell if it exists.
Examples:
Input: N = 3, M = 3
mat[][] = {{1, 2, 3},
{4, 5, 6},
{7, 8, 9}}
Output: Unbalanced
Explanation: Each cell of the given grid is not stable, so the overall grid is unbalanced.
Input: N = 3, M = 3
mat[][] = {{1, 2, 1},
{2, 3, 2},
{1, 2, 1}}
Output: Balanced
Explanation: Each cell of the given grid is stable, so the overall grid is Balanced.
Approach:
- Traverse the given matrix mat[][].
- For each cell of the matrix check if all the adjacent cells i.e., mat[i+1][j], mat[i][j+1], mat[i-1][j], mat[i][j-1] are strictly smaller than the current cell.
- For the corner cells of the matrix, there are only two adjacent cells i.e., mat[i+1][j] and mat[i][j+1] check if all these adjacent cells are strictly smaller than the corner cell.
- For border cell of the matrix, there are 3 adjacent cells i.e., mat[i-1][j], mat[i+1][j], and mat[i][j+1] check if all these adjacent cells are strictly smaller than the border cell.
- If all the above conditions are true for all the cells of the matrix then print “Balanced” else print “Unbalanced”.
Below is the implementation of the above approach:
C++
// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
// Define size of matrix
#define N 4
#define M 4
// Function to check given matrix
// balanced or unbalanced
string balancedMatrix(int mat[][M])
{
// Flag for check matrix is balanced
// or unbalanced
bool is_balanced = true;
// Iterate row until condition is true
for (int i = 0; i < N && is_balanced; i++) {
// Iterate cols until condition is true
for (int j = 0; j < M && is_balanced; j++) {
// Check for corner edge elements
if ((i == 0 || i == N - 1)
&& (j == 0 || j == M - 1)) {
if (mat[i][j] >= 2)
is_balanced = false;
}
// Check for border elements
else if (i == 0 || i == N - 1
|| j == 0 || j == M - 1) {
if (mat[i][j] >= 3)
is_balanced = false;
}
else {
// Check for the middle ones
if (mat[i][j] >= 4)
is_balanced = false;
}
}
}
// Return balanced or not
if (is_balanced)
return "Balanced";
else
return "Unbalanced";
}
// Driver Code
int main()
{
// Given Matrix mat[][]
int mat[N][M] = { { 1, 2, 3, 4 },
{ 3, 5, 2, 6 },
{ 5, 3, 6, 1 },
{ 9, 5, 6, 0 } };
// Function Call
cout << balancedMatrix(mat);
return 0;
}
// Java program for the above approach
import java.util.*;
class GFG{
// Define size of matrix
static final int N = 4;
static final int M = 4;
// Function to check given matrix
// balanced or unbalanced
static String balancedMatrix(int mat[][])
{
// Flag for check matrix is balanced
// or unbalanced
boolean is_balanced = true;
// Iterate row until condition is true
for (int i = 0; i < N && is_balanced; i++)
{
// Iterate cols until condition is true
for (int j = 0; j < M && is_balanced; j++)
{
// Check for corner edge elements
if ((i == 0 || i == N - 1) &&
(j == 0 || j == M - 1))
{
if (mat[i][j] >= 2)
is_balanced = false;
}
// Check for border elements
else if (i == 0 || i == N - 1 ||
j == 0 || j == M - 1)
{
if (mat[i][j] >= 3)
is_balanced = false;
}
else
{
// Check for the middle ones
if (mat[i][j] >= 4)
is_balanced = false;
}
}
}
// Return balanced or not
if (is_balanced)
return "Balanced";
else
return "Unbalanced";
}
// Driver Code
public static void main(String[] args)
{
// Given Matrix mat[][]
int mat[][] = {{1, 2, 3, 4},
{3, 5, 2, 6},
{5, 3, 6, 1},
{9, 5, 6, 0}};
// Function Call
System.out.print(balancedMatrix(mat));
}
}
// This code is contributed by shikhasingrajput
# Python3 program for the above approach
# Define the size of the matrix
N = 4
M = 4
# Function to check given matrix
# balanced or unbalanced
def balancedMatrix(mat):
# Flag for check matrix is balanced
# or unbalanced
is_balanced = True
# Iterate row until condition is true
i = 0
while i < N and is_balanced:
# Iterate cols until condition is true
j = 0
while j < N and is_balanced:
# Check for corner edge elements
if ((i == 0 or i == N - 1) and
(j == 0 or j == M - 1)):
if mat[i][j] >= 2:
isbalanced = False
# Check for border elements
elif (i == 0 or i == N - 1 or
j == 0 or j == M - 1):
if mat[i][j] >= 3:
is_balanced = False
# Check for the middle ones
else:
if mat[i][j] >= 4:
is_balanced = False
j += 1
i += 1
# Return balanced or not
if is_balanced:
return "Balanced"
else:
return "Unbalanced"
# Driver code
# Given matrix mat[][]
mat = [ [ 1, 2, 3, 4 ],
[ 3, 5, 2, 6 ],
[ 5, 3, 6, 1 ],
[ 9, 5, 6, 0 ] ]
# Function call
print(balancedMatrix(mat))
# This code is contributed by Stuti Pathak
// C# program for the above approach
using System;
class GFG{
// Define size of matrix
static readonly int N = 4;
static readonly int M = 4;
// Function to check given matrix
// balanced or unbalanced
static String balancedMatrix(int [, ]mat)
{
// Flag for check matrix is balanced
// or unbalanced
bool is_balanced = true;
// Iterate row until condition is true
for (int i = 0; i < N && is_balanced; i++)
{
// Iterate cols until condition is true
for (int j = 0; j < M && is_balanced; j++)
{
// Check for corner edge elements
if ((i == 0 || i == N - 1) &&
(j == 0 || j == M - 1))
{
if (mat[i, j] >= 2)
is_balanced = false;
}
// Check for border elements
else if (i == 0 || i == N - 1 ||
j == 0 || j == M - 1)
{
if (mat[i, j] >= 3)
is_balanced = false;
}
else
{
// Check for the middle ones
if (mat[i, j] >= 4)
is_balanced = false;
}
}
}
// Return balanced or not
if (is_balanced)
return "Balanced";
else
return "Unbalanced";
}
// Driver Code
public static void Main(String[] args)
{
// Given Matrix [,]mat
int [, ]mat = {{1, 2, 3, 4},
{3, 5, 2, 6},
{5, 3, 6, 1},
{9, 5, 6, 0}};
// Function Call
Console.Write(balancedMatrix(mat));
}
}
// This code is contributed by 29AjayKumar
<script>
// Javascript Script program to implement
// the above approach
// Define size of matrix
let N = 4;
let M = 4;
// Function to check given matrix
// balanced or unbalanced
function balancedMatrix(mat)
{
// Flag for check matrix is balanced
// or unbalanced
let is_balanced = true;
// Iterate row until condition is true
for (let i = 0; i < N && is_balanced; i++)
{
// Iterate cols until condition is true
for (let j = 0; j < M && is_balanced; j++)
{
// Check for corner edge elements
if ((i == 0 || i == N - 1) &&
(j == 0 || j == M - 1))
{
if (mat[i][j] >= 2)
is_balanced = false;
}
// Check for border elements
else if (i == 0 || i == N - 1 ||
j == 0 || j == M - 1)
{
if (mat[i][j] >= 3)
is_balanced = false;
}
else
{
// Check for the middle ones
if (mat[i][j] >= 4)
is_balanced = false;
}
}
}
// Return balanced or not
if (is_balanced)
return "Balanced";
else
return "Unbalanced";
}
// Driver Code
// Given Matrix mat[][]
let mat = [[1, 2, 3, 4],
[3, 5, 2, 6],
[5, 3, 6, 1],
[9, 5, 6, 0]];
// Function Call
document.write(balancedMatrix(mat));
</script>
Time Complexity: O(N*M)
Auxiliary Space: O(1)
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