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 <bits/stdc++.h>using namespace std;const int N = 3, M = 3;// Function to check if an// array is Reverse Bitonic or notbool 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 notvoid 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 Codeint 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 notimport java.util.*;class GFG{static int N = 3, M = 3;// Function to check if an// array is Reverse Bitonic or notstatic 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 notstatic 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 Codepublic 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 notN = 3M = 3# Function to check if an# array is Reverse Bitonic or notdef 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 notdef 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 Codeif __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 notusing System;class GFG{static int N = 3, M = 3;// Function to check if an// array is Reverse Bitonic or notstatic 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 notstatic 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 Codepublic 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
<script>// Java script Program to check if a// matrix is Reverse Bitonic or notlet N = 3, M = 3;// Function to check if an// array is Reverse Bitonic or notfunction checkReverseBitonic(arr,n){ let 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 notfunction check(arr){ let f = 0; // Check row-wise for (let i = 0; i < N; i++) { if (!checkReverseBitonic(arr[i], M)) { document.write("No" + "<br>"); return; } } // Check column wise for (let i = 0; i < N; i++) { // Generate an array // consisting of elements // of the current column let temp= [N]; for (let j = 0; j < N; j++) { temp[j] = arr[j][i]; } if (!checkReverseBitonic(temp, N)) { document.write("No" + "<br>"); return; } } document.write("Yes");}// Driver Codelet m = [[ 2, 3, 4 ], [ 1, 2, 3 ], [ 4, 5, 6 ]]; check(m);// This code is contributed by sravan kumar </script> |
Output:
Yes
Time Complexity: O(N × M)
Auxiliary Space: O(N)
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