# Row-wise vs column-wise traversal of matrix

• Difficulty Level : Easy
• Last Updated : 15 Nov, 2022

Two common ways of traversing a matrix are row-major-order and column-major-order.
Row Major Order: When matrix is accessed row by row.
Column Major Order: When matrix is accessed column by column.
Examples:

Input : mat[][] = {{1, 2, 3},
{4, 5, 6},
{7, 8, 9}}

Output : Row-wise: 1 2 3 4 5 6 7 8 9
Col-wise : 1 4 7 2 5 8 3 6 9

Difference: If we see according to time complexity, both lead to O(n2), but when it comes to cache level one of the orders access will be faster as compare to other one. It depends on the language we are using. Like in C, store matrix in row major form so while accessing the i+1th element after ith, most probably it will lead to a hit, which will further reduce the time of program.

The following codes are showing the time difference in row major and column major access.

## C++

 // C++ program showing time difference// in row major and column major access#include #include  // taking MAX 10000 so that time difference// can be shown#define MAX 10000 int arr[MAX][MAX] = { 0 }; void rowMajor(){     int i, j;     // accessing element row wise    for (i = 0; i < MAX; i++) {        for (j = 0; j < MAX; j++) {            arr[i][j]++;        }    }} void colMajor(){     int i, j;     // accessing element column wise    for (i = 0; i < MAX; i++) {        for (j = 0; j < MAX; j++) {            arr[j][i]++;        }    }} // driver codeint main(){    int i, j;     // Time taken by row major order    clock_t t = clock();    rowMajor();    t = clock() - t;    printf("Row major access time :%f s\n",           t / (float)CLOCKS_PER_SEC);     // Time taken by column major order    t = clock();    colMajor();    t = clock() - t;    printf("Column major access time :%f s\n",           t / (float)CLOCKS_PER_SEC);    return 0;}

## Java

 // Java program showing time difference// in row major and column major accessimport java.time.Duration;import java.time.Instant;import java.util.*; class GFG {     // taking MAX 10000 so that time difference    // can be shown    static int MAX = 10000;     static int[][] arr = new int[MAX][MAX];     static void rowMajor()    {         int i, j;         // accessing element row wise        for (i = 0; i < MAX; i++) {            for (j = 0; j < MAX; j++) {                arr[i][j]++;            }        }    }     static void colMajor()    {         int i, j;         // accessing element column wise        for (i = 0; i < MAX; i++) {            for (j = 0; j < MAX; j++) {                arr[j][i]++;            }        }    }     // Driver code    public static void main(String[] args)    {         // Time taken by row major order        Instant start = Instant.now();        rowMajor();        Instant end = Instant.now();        System.out.println("Row major access time : "                           + Duration.between(start, end));         // Time taken by column major order        start = Instant.now();        colMajor();        end = Instant.now();        System.out.printf("Column major access time : "                          + Duration.between(start, end));    }} // This code is contributed by 29AjayKumar

## Python3

 # Python3 program showing time difference# in row major and column major access # taking MAX 10000 so that time difference# can be shownfrom time import clockMAX = 1000 arr = [[0 for i in range(MAX)] for i in range(MAX)]  def rowMajor():    global arr     # accessing element row wise    for i in range(MAX):        for j in range(MAX):            arr[i][j] += 1  def colMajor():    global arr     # accessing element column wise    for i in range(MAX):        for j in range(MAX):            arr[j][i] += 1  # Driver codeif __name__ == '__main__':     # Time taken by row major order    t = clock()    rowMajor()    t = clock() - t    print("Row major access time :{:.2f} s".format(t))     # Time taken by column major order    t = clock()    colMajor()    t = clock() - t    print("Column major access time :{:.2f} s".format(t)) # This code is contributed by mohit kumar 29

## C#

 // C# program showing time difference// in row major and column major accessusing System;using static System.DateTime;public class GFG {     // taking MAX 10000 so that time difference    // can be shown    public static int MAX = 1000;    public static int[, ] arr = new int[GFG.MAX, GFG.MAX];    public static void rowMajor()    {        int i;        int j;        // accessing element row wise        for (i = 0; i < GFG.MAX; i++) {            for (j = 0; j < GFG.MAX; j++) {                GFG.arr[i, j]++;            }        }    }    public static void colMajor()    {        int i;        int j;        // accessing element column wise        for (i = 0; i < GFG.MAX; i++) {            for (j = 0; j < GFG.MAX; j++) {                GFG.arr[j, i]++;            }        }    }    // Driver code    public static void Main(String[] args)    {        // Time taken by row major order        var start = DateTime.UtcNow;        GFG.rowMajor();        var end = DateTime.UtcNow;        TimeSpan spanR = end.Subtract(start);        Console.WriteLine("Row major access time : "                          + spanR.TotalMinutes + " min");         // Time taken by column major order        start = DateTime.UtcNow;        GFG.colMajor();        end = DateTime.UtcNow;        TimeSpan spanC = end.Subtract(start);        Console.WriteLine("Column major access time : "                          + spanC.TotalMinutes + " min");    }} // This code is contributed by yoursthek2002

## Javascript

 // JavaScript program showing time difference// in row major and column major access // taking MAX 10000 so that time difference can be shownlet MAX = 1000 function rowMajor() {    let i, j;         // accessing element row wise    for (i = 0; i < MAX; i++) {        for (j = 0; j < MAX; j++) {            arr[i][j]++;        }    }} function colMajor() {    let i, j;    // accessing element column wise    for (i = 0; i < MAX; i++) {        for (j = 0; j < MAX; j++) {            arr[j][i]++;        }    }} // Driver code var arr = new Array(MAX);for (let i = 0; i < MAX; i++)    arr[i] = new Array(MAX); // Time taken by row major orderlet start, end;start = Date.now();rowMajor();end = Date.now();console.log(`Row major access time: \${end - start} ms`); // Time taken by column major orderstart = Date.now();colMajor();end = Date.now();console.log(`Col major access time: \${end - start} ms`); // This code is contributed by ajaymakavana.

Output:

Row major access time :0.492000 s
Column major access time :1.621000 s

Time Complexity: O(MAX*MAX)
Auxiliary Space: O(MAX*MAX)

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