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**Two Dimensional Arrays Rohit Khokher**

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**Two dimensional Arrays**

A vector can be represented as an one dimensional array A matrix can be represented as a two dimensional array A[8][10] Columns Rows A[5][6] Array element

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**The value of sales of three items by four sales person**

1 2 3 A[0][0] A[0][1] A[0][2] A[1][0] A[1][1] A[1][2] A[2][0] A[2][1] A[2][2] 4 A[3][0] A[3][1] A[3][2] Sales Persons

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**2-D array 2-Day Array Declaration #define ROWS 2 #define COLS 3**

1 float A[ROWS ][COLS]; Compile time Initialization int A[ROWS ][COLS]= {0,0,0,1,1,1}; or int A[ROWS ][COLS]= ({0,0,0},{1,1,1});

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**Compile time initialization**

1 int A[ROWS ][COLS]= {{0,0,0}, {1,1,1}}; int A[ ][COLS]= { {0,0,0}, {1,1,1} }; 1 2 int A[ROWS][COLS]= { {0,0}, {2} }; The missing values are initialized to zero automatically

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**Runtime Initialization for (i=0; i<ROWS; i++) **

for (j=0; i<COLS; j++) a[i][j]=0; Reading the elements of 2-D array Read data row-wise for (i=0; i<ROWS; i++) for (j=0; j<COLS; j++) scanf (“%d”, &a[i][j]); Priniting the elements of 2-D array for (i=0; i<ROWS; i++) { Print a row for (j=0; j<COLS; j++) printf (“%d”, &a[i][j]); Change line printf (“\n”); }

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**Matrix manipulation Read a matrix A (4,4) of real numbers and compute:**

sum of each row entries sum of each column entries sum of the main diagonal entries sum of the secondary diagonal entries

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**Compute row sum for (i=0; i<ROWS; i++) { R[i]=0; Initialize R[i]**

for (j=0; j<COLS; j++) R[i]=R[i]+A[i][j]; }

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**Compute Column sum for (j=0; j<COLS; j++) { C[j]=0;**

A[0][0] A[0][1] A[0][2] A[0][3] A[1][0] A[1][1] A[1][2] A[1][3] A[2][0] A[2][1] A[2][2] A[2][3] A[3][0] A[3][1] A[3][2] A[3][3] for (j=0; j<COLS; j++) { C[j]=0; for (i=0; i<ROWS; i++) C[j]=C[j]+A[i][j]; } Initialize C[j] C[0]= A[0][0] + A[1][0] + A[2][0] + A[3][0] C[1]= A[0][1] + A[1][1] + A[2][1] + A[3][1] C[2]= A[0][2] + A[1][2] + A[2][2] + A[3][2] C[3]= A[0][3] + A[1][3] + A[2][3] + A[3][3]

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**Compute diagonal sum D =0; for (j=0; j<COLS; j++) D= D+ A[j][j]; OR**

for (i=0; i<ROWS; i++) D=D+A[i][i]; D= A[0][0] + A[1][1] + A[2][2] + A[3][3]

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**Compute second diagonal sum**

for (i=0; i<ROWS; i++) D= D+ A[i][COLS-i]; D= A[0][3] + A[1][2] + A[2][1] + A[3][0]

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Practice question Write a C program to find the largest element of each row of a 2D array. Write a C program to find the row and column numbers of the smallest element of a 2D array and count the sum of its neighbors. In a 2D array an element A[i][j] may have up to eight neighbors defined as: i-1,j-1 i-1,j i-1, j+1 I,j-1 i,j i,j+1 i+1,j-1 i+1,j i+1,j+1

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**Add two matrices for (i=0; i<ROWS; i++) for (j=0; j<COLS; j++)**

C[i][j]=A[i][j]+B[i][j];

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**Multiplication of two matrices**

c11=a11 x b11 + a12 x b21 c12=a11 x b12 + a12 x b22 c13=a11 x b13 + a12 x b23 for (i=0; i<ROWSA; i++) c21=a21 x b11 + a22 x b21 for (j=0; j<COLSB; j++) c22=a21 x b12 + a22 x b22 c23=a21 x b13 + a22 x b23 { C[i][j]=0; c31=a31 x b11 + a32 x b21 for (k=0; j<COLSA; j++) C[i][j]= C[i][j]+A[i][k]+B[k][j]; } c22=a31 x b12 + a32 x b22 c33=a31 x b13 + a32 x b23

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Practice problem To verify the correctness the matrix multiplication algorithm described before compute:

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Practice problem A square 2D array is called a magic square if sums of each row, each column, and both the diagonals of the array are equal. A 3 x 3 magic square is shown below. Read more about magic square at Write a program that reads a 2D array and determines whether the array is a magic square or not.

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Project Read about the tic-tac-toe game at . Find the simplest algorithm that can be implemented in C using 1D and 2D arrays.

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10.4 Matrix Algebra 1.Matrix Notation 2.Sum/Difference of 2 matrices 3.Scalar multiple 4.Product of 2 matrices 5.Identity Matrix 6.Inverse of a matrix.

10.4 Matrix Algebra 1.Matrix Notation 2.Sum/Difference of 2 matrices 3.Scalar multiple 4.Product of 2 matrices 5.Identity Matrix 6.Inverse of a matrix.

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