# Check if a Matrix is Reverse Bitonic or Not

Given a matrix m[][], the task is to check if the given matrix is Reverse Bitonic or not. If the given matrix is Reverse Bitonic, then print Yes. Otherwise, print No.

If all the rows and the columns of the given matrix have elements in one of the following orders:

• Strictly increasing
• Strictly decreasing
• Strictly decreasing followed by strictly increasing

Then the given matrix is said to be a Reverse Bitonic Matrix

Examples:

Input: m[][] = {{2, 3, 4}, {1, 2, 3}, {4, 5, 6} }
Output: Yes
Explanation:
All the rows of the given matrix forms an increasing sequence.
All the columns of the given matrix {2, 1, 4}, {3, 2, 5}, {4, 3, 6} forms a decreasing followed by increasing sequence.
Therefore, the matrix is Reverse Bitonic.
Input: m[][] = {{1, 2, 3}, {4, 5, 6}, {2, 5, 4}}
Output: No
Explanation:
Since the column {1, 4, 2} does not satisfy any of the three conditions, the given matrix is not Reverse Bitonic.

Approach
Follow the steps below to solve the problem:

• Check the elements of each row of the matrix one by one, if it forms a Reverse Bitonic sequence or not. If any row is found to be not Reverse Bitonic, print No.
• Similarly, check the elements of each column one by one, if it forms a Reverse Bitonic sequence or not. If any row is found to be not Reverse Bitonic, print No.
• If all the rows and columns are found to be Reverse Bitonic, then print Yes.

Below is the implementation of the above approach:

## C++

 // C++ Program to check if a // matrix is Reverse Bitonic or not #include using namespace std;   const int N = 3, M = 3;   // Function to check if an // array is Reverse Bitonic or not bool checkReverseBitonic(int arr[], int n) {     int i, j, f = 0;       // Check for decreasing sequence     for (i = 1; i < n; i++) {         if (arr[i] < arr[i - 1])             continue;           if (arr[i] == arr[i - 1])             return false;           else {             f = 1;             break;         }     }       if (i == n)         return true;       // Check for increasing sequence     for (j = i + 1; j < n; j++) {         if (arr[j] > arr[j - 1])             continue;           if (arr[i] == arr[i - 1])             return false;           else {             if (f == 1)                 return false;         }     }       return true; }   // Function to check whether given // matrix is bitonic or not void check(int arr[N][M]) {     int f = 0;       // Check row-wise     for (int i = 0; i < N; i++) {         if (!checkReverseBitonic(arr[i], M)) {             cout << "No" << endl;             return;         }     }       // Check column wise     for (int i = 0; i < N; i++) {         // Generate an array         // consisting of elements         // of the current column         int temp[N];           for (int j = 0; j < N; j++) {             temp[j] = arr[j][i];         }           if (!checkReverseBitonic(temp, N)) {             cout << "No" << endl;             return;         }     }       cout << "Yes"; }   // Driver Code int main() {     int m[N][M] = { { 2, 3, 4 },                     { 1, 2, 3 },                     { 4, 5, 6 } };       check(m);       return 0; }

## Java

 // Java Program to check if a // matrix is Reverse Bitonic or not import java.util.*; class GFG{   static int N = 3, M = 3;   // Function to check if an // array is Reverse Bitonic or not static boolean checkReverseBitonic(int arr[], int n) {     int i, j, f = 0;       // Check for decreasing sequence     for (i = 1; i < n; i++)     {         if (arr[i] < arr[i - 1])             continue;           if (arr[i] == arr[i - 1])             return false;           else         {             f = 1;             break;         }     }       if (i == n)         return true;       // Check for increasing sequence     for (j = i + 1; j < n; j++)     {         if (arr[j] > arr[j - 1])             continue;           if (arr[i] == arr[i - 1])             return false;           else         {             if (f == 1)                 return false;         }     }       return true; }   // Function to check whether given // matrix is bitonic or not static void check(int arr[][]) {     int f = 0;       // Check row-wise     for (int i = 0; i < N; i++)     {         if (!checkReverseBitonic(arr[i], M))         {             System.out.print("No" + "\n");             return;         }     }       // Check column wise     for (int i = 0; i < N; i++)     {         // Generate an array         // consisting of elements         // of the current column         int temp[] = new int[N];           for (int j = 0; j < N; j++)         {             temp[j] = arr[j][i];         }           if (!checkReverseBitonic(temp, N))         {             System.out.print("No" + "\n");             return;         }     }     System.out.print("Yes"); }   // Driver Code public static void main(String[] args) {     int m[][] = { { 2, 3, 4 },                   { 1, 2, 3 },                   { 4, 5, 6 } };       check(m); } }   // This code is contributed by Rajput-Ji

## Python3

 # Python3 program to check if a # matrix is Reverse Bitonic or not N = 3 M = 3   # Function to check if an # array is Reverse Bitonic or not def checkReverseBitonic(arr, n):       f = 0       # Check for decreasing sequence     for i in range(1, n):         if (arr[i] < arr[i - 1]):             continue           if (arr[i] == arr[i - 1]):             return False           else:             f = 1             break       if (i == n):         return True       # Check for increasing sequence     for j in range(i + 1, n):         if (arr[j] > arr[j - 1]):             continue           if (arr[i] == arr[i - 1]):             return False           else:             if (f == 1):                 return False           return True   # Function to check whether given # matrix is bitonic or not def check(arr):       f = 0       # Check row-wise     for i in range (N):         if (not checkReverseBitonic(arr[i], M)):             print("No")             return       # Check column wise     for i in range(N):                   # Generate an array         # consisting of elements         # of the current column         temp = [0] * N           for j in range(N):             temp[j] = arr[j][i]           if (not checkReverseBitonic(temp, N)):             print("No")             return       print("Yes")   # Driver Code if __name__ == "__main__":       m = [ [ 2, 3, 4 ],           [ 1, 2, 3 ],           [ 4, 5, 6 ] ]       check(m)   # This code is contributed by chitranayal

## C#

 // C# Program to check if a // matrix is Reverse Bitonic or not using System; class GFG{   static int N = 3, M = 3;   // Function to check if an // array is Reverse Bitonic or not static bool checkReverseBitonic(int []arr, int n) {     int i, j, f = 0;       // Check for decreasing sequence     for (i = 1; i < n; i++)     {         if (arr[i] < arr[i - 1])             continue;           if (arr[i] == arr[i - 1])             return false;           else         {             f = 1;             break;         }     }       if (i == n)         return true;       // Check for increasing sequence     for (j = i + 1; j < n; j++)     {         if (arr[j] > arr[j - 1])             continue;           if (arr[i] == arr[i - 1])             return false;           else         {             if (f == 1)                 return false;         }     }       return true; }   // Function to check whether given // matrix is bitonic or not static void check(int [,]arr) {     // Check row-wise     for (int i = 0; i < N; i++)     {         if (!checkReverseBitonic(GetRow(arr, i), M))         {             Console.Write("No" + "\n");             return;         }     }       // Check column wise     for (int i = 0; i < N; i++)     {         // Generate an array         // consisting of elements         // of the current column         int []temp = new int[N];           for (int j = 0; j < N; j++)         {             temp[j] = arr[j,i];         }           if (!checkReverseBitonic(temp, N))         {             Console.Write("No" + "\n");             return;         }     }     Console.Write("Yes"); }     public static int[] GetRow(int[,] matrix, int row) {     var rowLength = matrix.GetLength(1);     var rowVector = new int[rowLength];       for (var i = 0; i < rowLength; i++)       rowVector[i] = matrix[row, i];       return rowVector; }     // Driver Code public static void Main(String[] args) {     int [,]m = {{ 2, 3, 4 },                 { 1, 2, 3 },                 { 4, 5, 6 }};       check(m); } }   // This code is contributed by Rajput-Ji

## Javascript



Output:

Yes

Time Complexity: O(N Ã— M)
Auxiliary Space: O(N)

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