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# Emulating a 2-d array using 1-d array in C++

In this problem, we will understand the conversion of 2-D array to 1-D array. We will see how to store the elements of a 2-D array to a 1-D array.

Here, the size of 1-D array is same as the total number of elements in 2-D array which is n*m.

In programming there are two ways to store a 2-D array to 1-D array. They are−

- Row Major
- Column Major

**Row Major: **In row major, All the elements of a row are stored together then it moves to the next row.

If an element of 2-D array of size nXm has an index (i, j) is stored in 1-D array, its index in 1-D array is

*(j) + (i)*m*

**Column Major: **In column major, all elements of a column are stored together then the next column is traversed.

If an element of 2-D array of size nXm has an index (i, j) is stored in 1-D array, its index in 1-D array is

*(i) + (j)*n*

## Lets see an example to understand the problem,

**Input: **n = 3, m = 5, (i,j) = (0, 2)

**Output: **row-major =

column-major =

**Explanation: **

Row-major = 2 + 0*3 = 3

Col-major = 0 + 2*5 = 10

## Program to illustrate the conversion of 2-D to 1-D,

## Example

#include<iostream> using namespace std; int main() { int n = 3; int m = 5; int grid[n][m] = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}, {10, 11, 12}, {13, 14, 15}}; int i = 0; int j = 2; int rowMajorIndex = i*n + j; cout<<"Index of element at index (0, 2) in 1-D array using row-major is "<<rowMajorIndex<<endl; int colMajorIndex = i + j*m; cout<<"Index of element at index (0, 2) in 1-D array using column-major is "<<colMajorIndex<<endl; return 0; }

## Output −

Index of element at index (0, 2) in 1-D array using row-major is 2 Index of element at index (0, 2) in 1-D array using column-major is 10

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