矩阵的逐行与逐列遍历

遍历矩阵的两种常见方式是行优先和列优先。
行主要顺序：当矩阵被逐行访问时。
列主要顺序：当矩阵被逐列访问时。
例子：

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

区别：如果我们根据时间复杂度来看，两者都会导致O(n ² ) ，但是当涉及到缓存级别时，其中一个命令的访问速度会比其他命令更快。这取决于我们使用的语言。像在C中一样，以行主要形式存储矩阵，因此在访问 i ^th之后的第 i+1^个元素时，很可能会导致命中，这将进一步减少程序时间。
以下代码显示了行主要和列主要访问的时间差异。

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 code
int 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 access
import 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 shown
MAX = 1000
from time import clock
 
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 code
if __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 access
using 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

输出：

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