Consider the following two C code segments. $Y$ and $X$ are one and two dimensional arrays of size $n$ and $n \times n$ respectively, where $2 \le n \le 10$. Assume that in both code segments, elements of $Y$ are initialized to 0 and each element $X[i][j]$ of array $X$ is initialized to $i+j$. Further assume that when stored in main memory all elements of $X$ are in same main memory page frame. Code segment 1://initialize elements of Y to 0 //initialize elements X[i][j] of X to i+j for(i = 0; i < n; i++) Y[i] += X[0][i];Code Segment 2://initialize elements of Y to 0 //initialize elements X[i][j] of X to i+j for(i = 0; i < n; i++) Y[i] += X[i][0];Which of the following statements is/are correct? S1: Final contents of array $Y$ will be same in both code segments S2: Elements of array $X$ accessed inside the for loop shown in code segment 1 are contiguous in main memory S3: Elements of array $X$ accessed inside the for loop shown in code segment 2 are contiguous in main memory

Let us analyze each statement:

1. Statement S1:

   • In Code segment 1, for each index $i$ from $0$ to $n-1$:

     $$Y[i] = X[0][i] = 0 + i = i$$

   • In Code segment 2, for each index $i$ from $0$ to $n-1$:

     $$Y[i] = X[i][0] = i + 0 = i$$

   Since both code segments assign $Y[i] = i$ for all $0 \le i < n$, the final contents of array $Y$ will be identical in both cases. Therefore, S1 is correct.

2. Statement S2:

   • In C, two-dimensional arrays are stored in row-major order.

   • In Code segment 1, the loop accesses elements of the first row: $X[0][0], X[0][1], \dots, X[0][n-1]$. In row-major layout, all elements of a single row are stored contiguously in memory. Therefore, S2 is correct.

3. Statement S3:

   • In Code segment 2, the loop accesses elements of the first column: $X[0][0], X[1][0], \dots, X[n-1][0]$. Consecutive elements in a column are separated by $n$ elements in row-major layout and are not contiguous. Therefore, S3 is incorrect.

Thus, only S1 and S2 are correct (Option C).