Zigzag (or diagonal) traversal of Matrix
Given a 2D matrix, print all elements of the given matrix in diagonal order. For example, consider the following 5 X 4 input matrix.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Diagonal printing of the above matrix is
1 5 2 9 6 3 13 10 7 4 17 14 11 8 18 15 12 19 16 20
We strongly recommend that you click here and practice it, before moving on to the solution.
Following is the code for diagonal printing.
The diagonal printing of a given matrix “matrix[ROW][COL]” always has “ROW + COL – 1” lines in output.
C++
#include <stdio.h> #include <stdlib.h> #define ROW 5 #define COL 4 // A utility function to find min of two integers int minu( int a, int b) { return (a < b)? a: b; } // A utility function to find min of three integers int min( int a, int b, int c) { return minu(minu(a, b), c);} // A utility function to find max of two integers int max( int a, int b) { return (a > b)? a: b; } // The main function that prints given matrix in diagonal order void diagonalOrder( int matrix[][COL]) { // There will be ROW+COL-1 lines in the output for ( int line=1; line<=(ROW + COL -1); line++) { /* Get column index of the first element in this line of output. The index is 0 for first ROW lines and line - ROW for remaining lines */ int start_col = max(0, line-ROW); /* Get count of elements in this line. The count of elements is equal to minimum of line number, COL-start_col and ROW */ int count = min(line, (COL-start_col), ROW); /* Print elements of this line */ for ( int j=0; j<count; j++) printf ( "%5d " , matrix[minu(ROW, line)-j-1][start_col+j]); /* Ptint elements of next diagonal on next line */ printf ( "\n" ); } } // Utility function to print a matrix void printMatrix( int matrix[ROW][COL]) { for ( int i=0; i< ROW; i++) { for ( int j=0; j<COL; j++) printf ( "%5d " , matrix[i][j]); printf ( "\n" ); } } // Driver program to test above functions int main() { int M[ROW][COL] = {{1, 2, 3, 4}, {5, 6, 7, 8}, {9, 10, 11, 12}, {13, 14, 15, 16}, {17, 18, 19, 20}, }; printf ( "Given matrix is \n" ); printMatrix(M); printf ( "\nDiagonal printing of matrix is \n" ); diagonalOrder(M); return 0; } |
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Java
class GFG { static final int ROW = 5 ; static final int COL = 4 ; // A utility function to find min // of two integers static int min( int a, int b) { return (a < b) ? a : b; } // A utility function to find min // of three integers static int min( int a, int b, int c) { return min(min(a, b), c); } // A utility function to find max // of two integers static int max( int a, int b) { return (a > b) ? a : b; } // The main function that prints given // matrix in diagonal order static void diagonalOrder( int matrix[][]) { // There will be ROW+COL-1 lines in the output for ( int line = 1 ; line <= (ROW + COL - 1 ); line++) { // Get column index of the first element in this // line of output.The index is 0 for first ROW // lines and line - ROW for remaining lines int start_col = max( 0 , line - ROW); // Get count of elements in this line. The count // of elements is equal to minimum of line number, // COL-start_col and ROW int count = min(line, (COL - start_col), ROW); // Print elements of this line for ( int j = 0 ; j < count; j++) System.out.print(matrix[min(ROW, line) - j - 1 ] [start_col + j] + " " ); // Print elements of next diagonal on next line System.out.println(); } } // Utility function to print a matrix static void printMatrix( int matrix[][]) { for ( int i = 0 ; i < ROW; i++) { for ( int j = 0 ; j < COL; j++) System.out.print(matrix[i][j] + " " ); System.out.print( "\n" ); } } // Driver code public static void main(String[] args) { int M[][] = { { 1 , 2 , 3 , 4 }, { 5 , 6 , 7 , 8 }, { 9 , 10 , 11 , 12 }, { 13 , 14 , 15 , 16 }, { 17 , 18 , 19 , 20 }, }; System.out.print( "Given matrix is \n" ); printMatrix(M); System.out.print( "\nDiagonal printing of matrix is \n" ); diagonalOrder(M); } } // This code is contributed by Anant Agarwal. |
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Python3
# Python3 program to print all elements # of given matrix in diagonal order ROW = 5 COL = 4 # Main function that prints given # matrix in diagonal order def diagonalOrder(matrix) : # There will be ROW+COL-1 lines in the output for line in range ( 1 , (ROW + COL)) : # Get column index of the first element # in this line of output. The index is 0 # for first ROW lines and line - ROW for # remaining lines start_col = max ( 0 , line - ROW) # Get count of elements in this line. # The count of elements is equal to # minimum of line number, COL-start_col and ROW count = min (line, (COL - start_col), ROW) # Print elements of this line for j in range ( 0 , count) : print (matrix[ min (ROW, line) - j - 1 ] [start_col + j], end = "\t" ) print () # Utility function to print a matrix def printMatrix(matrix) : for i in range ( 0 , ROW) : for j in range ( 0 , COL) : print (matrix[i][j], end = "\t" ) print () # Driver COde M = [ [ 1 , 2 , 3 , 4 ], [ 5 , 6 , 7 , 8 ], [ 9 , 10 , 11 , 12 ], [ 13 , 14 , 15 , 16 ], [ 17 , 18 , 19 , 20 ] ] print ( "Given matrix is " ) printMatrix(M) print ( "\nDiagonal printing of matrix is " ) diagonalOrder(M) # This code is contributed by Nikita Tiwari. |
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C#
// C# program to print all elements // of given matrix in diagonal order using System; class GFG { static int ROW = 5; static int COL = 4; // The main function that prints given // matrix in diagonal order static void diagonalOrder( int [,]matrix) { // There will be ROW+COL-1 lines in the output for ( int line = 1; line <= (ROW + COL - 1); line++) { // Get column index of the first element // in this line of output.The index is 0 // for first ROW lines and line - ROW for // remaining lines int start_col = Math.Max(0, line - ROW); // Get count of elements in this line. The // count of elements is equal to minimum of // line number, COL-start_col and ROW int count = Math.Min(line, Math.Min( (COL - start_col), ROW)); // Print elements of this line for ( int j = 0; j < count; j++) Console.Write(matrix[ Math.Min(ROW, line) - j - 1, start_col + j] + " " ); // Print elements of next diagonal on next line Console.WriteLine(); } } // Utility function to print a matrix static void printMatrix( int [,]matrix) { for ( int i = 0; i < ROW; i++) { for ( int j = 0; j < COL; j++) Console.Write(matrix[i,j] + " " ); Console.WriteLine( "\n" ); } } // Driver code public static void Main() { int [,]M = {{1, 2, 3, 4}, {5, 6, 7, 8}, {9, 10, 11, 12}, {13, 14, 15, 16}, {17, 18, 19, 20}}; Console.Write( "Given matrix is \n" ); printMatrix(M); Console.Write( "\nDiagonal printing" + " of matrix is \n" ); diagonalOrder(M); } } // This code is contributed by Sam007. |
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PHP
<?php // PHP Code for Zigzag (or diagonal) // traversal of Matrix $ROW = 5; $COL = 4; // The main function that prints // given matrix in diagonal order function diagonalOrder(& $matrix ) { global $ROW , $COL ; // There will be ROW+COL-1 // lines in the output for ( $line = 1; $line <= ( $ROW + $COL - 1); $line ++) { /* Get column index of the first element in this line of output. The index is 0 for first ROW lines and line - ROW for remaining lines */ $start_col = max(0, $line - $ROW ); /* Get count of elements in this line. The count of elements is equal to minimum of line number, COL-start_col and ROW */ $count = min( $line , ( $COL - $start_col ), $ROW ); /* Print elements of this line */ for ( $j = 0; $j < $count ; $j ++) { echo $matrix [min( $ROW , $line ) - $j - 1][ $start_col + $j ]; echo "\t" ; } /* Print elements of next diagonal on next line */ print ( "\n" ); } } // Utility function // to print a matrix function printMatrix(& $matrix ) { global $ROW , $COL ; for ( $i = 0; $i < $ROW ; $i ++) { for ( $j = 0; $j < $COL ; $j ++) { echo $matrix [ $i ][ $j ] ; echo "\t" ; } print ( "\n" ); } } // Driver Code $M = array ( array (1, 2, 3, 4), array (5, 6, 7, 8), array (9, 10, 11, 12), array (13, 14, 15, 16), array (17, 18, 19, 20)); echo "Given matrix is \n" ; printMatrix( $M ); printf ( "\nDiagonal printing " . "of matrix is \n" ); diagonalOrder( $M ); // This code is contributed // by ChitraNayal ?> |
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Output:
Given matrix is 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Diagonal printing of matrix is 1 5 2 9 6 3 13 10 7 4 17 14 11 8 18 15 12 19 16 20
Below is an Alternate Method to solve the above problem.
Matrix => 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Observe the sequence 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11 / 12 / 13 / 14 / 15 / 16 / 17 / 18 / 19 / 20
C++
#include<bits/stdc++.h> #define R 5 #define C 4 using namespace std; bool isValid( int i, int j) { if (i < 0 || i >= R || j >= C || j < 0) return false ; return true ; } void diagonalOrder( int arr[][C]) { /* through this for loop we choose each element of first column as starting point and print diagonal starting at it. arr[0][0], arr[1][0]....arr[R-1][0] are all starting points */ for ( int k = 0; k < R; k++) { cout << arr[k][0] << " " ; int i = k-1; // set row index for next point in diagonal int j = 1; // set column index for next point in diagonal /* Print Diagonally upward */ while (isValid(i,j)) { cout << arr[i][j] << " " ; i--; j++; // move in upright direction } cout << endl; } /* through this for loop we choose each element of last row as starting point (except the [0][c-1] it has already been processed in previous for loop) and print diagonal starting at it. arr[R-1][0], arr[R-1][1]....arr[R-1][c-1] are all starting points */ //Note : we start from k = 1 to C-1; for ( int k = 1; k < C; k++) { cout << arr[R-1][k] << " " ; int i = R-2; // set row index for next point in diagonal int j = k+1; // set column index for next point in diagonal /* Print Diagonally upward */ while (isValid(i,j)) { cout << arr[i][j] << " " ; i--; j++; // move in upright direction } cout << endl; } } // Driver program to test above int main() { int arr[][C] = {{1, 2, 3, 4}, {5, 6, 7, 8}, {9, 10, 11, 12}, {13, 14, 15, 16}, {17, 18, 19, 20}, }; diagonalOrder(arr); return 0; } |
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Java
// JAVA Code for Zigzag (or diagonal) // traversal of Matrix class GFG{ public static int R,C; private static void diagonalOrder( int [][] arr) { /* through this for loop we choose each element of first column as starting point and print diagonal starting at it. arr[0][0], arr[1][0] ....arr[R-1][0] are all starting points */ for ( int k = 0 ; k < R; k++) { System.out.print(arr[k][ 0 ] + " " ); int i = k - 1 ; // set row index for next // point in diagonal int j = 1 ; // set column index for // next point in diagonal /* Print Diagonally upward */ while (isValid(i, j)) { System.out.print(arr[i][j] + " " ); i--; j++; // move in upright direction } System.out.println( "" ); } /* through this for loop we choose each element of last row as starting point (except the [0][c-1] it has already been processed in previous for loop) and print diagonal starting at it. arr[R-1][0], arr[R-1][1].... arr[R-1][c-1] are all starting points */ // Note : we start from k = 1 to C-1; for ( int k = 1 ; k < C; k++) { System.out.print(arr[R- 1 ][k] + " " ); int i = R - 2 ; // set row index for next // point in diagonal int j = k + 1 ; // set column index for // next point in diagonal /* Print Diagonally upward */ while (isValid(i, j)) { System.out.print(arr[i][j] + " " ); i--; j++; // move in upright direction } System.out.println( "" ); } } public static boolean isValid( int i, int j) { if (i < 0 || i >= R || j >= C || j < 0 ) return false ; return true ; } // driver program to test above function public static void main(String[] args) { int arr[][] = { { 1 , 2 , 3 , 4 }, { 5 , 6 , 7 , 8 }, { 9 , 10 , 11 , 12 }, { 13 , 14 , 15 , 16 }, { 17 , 18 , 19 , 20 }, }; R=arr.length; C=arr[ 0 ].length; diagonalOrder(arr); } } // This code is contributed by Arnav Kr. Mandal. |
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Python3
# Python3 program to print all elements # of given matrix in diagonal order R = 5 C = 4 def isValid( i, j) : if (i < 0 or i > = R or j > = C or j < 0 ) : return False return True def diagonalOrder(arr) : # through this for loop we choose each element # of first column as starting point and print # diagonal starting at it. # arr[0][0], arr[1][0]....arr[R-1][0] # are all starting points for k in range ( 0 , R) : print (arr[k][ 0 ], end = " " ) # set row index for next point in diagonal i = k - 1 # set column index for next point in diagonal j = 1 # Print Diagonally upward while (isValid(i, j)) : print (arr[i][j], end = " " ) i - = 1 j + = 1 # move in upright direction print () # Through this for loop we choose each # element of last row as starting point # (except the [0][c-1] it has already been # processed in previous for loop) and print # diagonal starting at it. # arr[R-1][0], arr[R-1][1]....arr[R-1][c-1] # are all starting points # Note : we start from k = 1 to C-1; for k in range ( 1 , C) : print (arr[R - 1 ][k], end = " " ) # set row index for next point in diagonal i = R - 2 # set column index for next point in diagonal j = k + 1 # Print Diagonally upward while (isValid(i, j)) : print ( arr[i][j], end = " " ) i - = 1 j + = 1 # move in upright direction print () # Driver Code arr = [ [ 1 , 2 , 3 , 4 ], [ 5 , 6 , 7 , 8 ], [ 9 , 10 , 11 , 12 ], [ 13 , 14 , 15 , 16 ], [ 17 , 18 , 19 , 20 ] ] diagonalOrder(arr) # This code is contributed by Nikita Tiwari. |
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C#
// C# Code for Zigzag (or diagonal) // traversal of Matrix using System; class GFG { public static int R, C; private static void diagonalOrder( int [,] arr) { /* through this for loop we choose each element of first column as starting point and print diagonal starting at it. arr[0,0], arr[1,0]....arr[R-1,0] are all starting points */ for ( int k = 0; k < R; k++) { Console.Write(arr[k, 0] + " " ); int i = k - 1; // set row index for next // point in diagonal int j = 1; // set column index for // next point in diagonal /* Print Diagonally upward */ while (isValid(i, j)) { Console.Write(arr[i, j] + " " ); i--; j++; // move in upright direction } Console.Write( "\n" ); } /* through this for loop we choose each element of last row as starting point (except the [0][c-1] it has already been processed in previous for loop) and print diagonal starting at it. arr[R-1,0], arr[R-1,1].... arr[R-1,c-1] are all starting points */ // Note : we start from k = 1 to C-1; for ( int k = 1; k < C; k++) { Console.Write(arr[R - 1, k] + " " ); int i = R - 2; // set row index for next // point in diagonal int j = k + 1; // set column index for // next point in diagonal /* Print Diagonally upward */ while (isValid(i, j)) { Console.Write(arr[i, j] + " " ); i--; j++; // move in upright direction } Console.Write( "\n" ); } } public static bool isValid( int i, int j) { if (i < 0 || i >= R || j >= C || j < 0) return false ; return true ; } // Driver code public static void Main() { int [,]arr = {{1, 2, 3, 4}, {5, 6, 7, 8}, {9, 10, 11, 12}, {13, 14, 15, 16}, {17, 18, 19, 20}}; R = arr.GetLength(0); C = arr.GetLength(1); diagonalOrder(arr); } } // This code is contributed // by ChitraNayal |
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PHP
<?php // PHP code for Zigzag (or diagonal) // traversal of Matrix define( "R" , 5); define( "C" , 4); function isValid( $i , $j ) { if ( $i < 0 || $i >= R || $j >= C || $j < 0) return false; return true; } function diagonalOrder(& $arr ) { /* through this for loop we choose each element of first column as starting point and print diagonal starting at it. arr[0][0], arr[1][0]....arr[R-1][0] are all starting points */ for ( $k = 0; $k < R; $k ++) { echo $arr [ $k ][0] . " " ; $i = $k - 1; // set row index for next // point in diagonal $j = 1; // set column index for next // point in diagonal /* Print Diagonally upward */ while (isValid( $i , $j )) { echo $arr [ $i ][ $j ] . " " ; $i --; $j ++; // move in upright direction } echo "\n" ; } /* through this for loop we choose each element of last row as starting point (except the [0][c-1] it has already been processed in previous for loop) and print diagonal starting at it. arr[R-1][0], arr[R-1][1]....arr[R-1][c-1] are all starting points */ //Note : we start from k = 1 to C-1; for ( $k = 1; $k < C; $k ++) { echo $arr [R - 1][ $k ] . " " ; $i = R - 2; // set row index for next // point in diagonal $j = $k + 1; // set column index for next // point in diagonal /* Print Diagonally upward */ while (isValid( $i , $j )) { echo $arr [ $i ][ $j ] . " " ; $i --; $j ++; // move in upright direction } echo "\n" ; } } // Driver Code $arr = array ( array (1, 2, 3, 4), array (5, 6, 7, 8), array (9, 10, 11, 12), array (13, 14, 15, 16), array (17, 18, 19, 20)); diagonalOrder( $arr ); // This code is contributed // by rathbhupendra ?> |
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Output:
1 5 2 9 6 3 13 10 7 4 17 14 11 8 18 15 12 19 16 20
Thanks to Gaurav Ahirwar for suggesting this method.
This article is compiled by Ashish Anand and reviewed by GeeksforGeeks team. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
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