Multi-dimensional arrays — Hinglish notes

5.1.11 · Coding › C Programming

Multi-dimensional array KIYA hota hai?

Definition

C mein ek multi-dimensional array memory ka ek contiguous block hota hai jisme same type ke elements hote hain, jo ek se zyada subscripts se index hote hain. Sabse common hai 2D array:

int a[3][4];   // 3 rows, 4 columns -> 12 ints total

a ka type hai "3 elements ki array, jahan har element 4 ints ki array hai". a[i] ka type hai "4 ints ki array". a[i][j] ka type hai int.

C ise "array of arrays" KYU kehta hai? Kyunki C mein sirf 1D arrays sach mein hote hain. int a[3][4] ko int (a[3])[4] ki tarah padha jaata hai — 3 cheezein ki array, jahan har cheez int[4] hai. Yeh ek fact hi sab kuch explain karta hai jo neeche likha hai.

Ise store KAISE kiya jaata hai? (Row-major order)

C elements ko row by row rakhta hai. Ise row-major order kehte hain.

int a[3][4] ke liye, memory order kuch aisi hai:

a[0][0] a[0][1] a[0][2] a[0][3] a[1][0] a[1][1] ... a[2][3]

Formula

a[i][j] ka Address — scratch se derive karke KIYA chahiye: T a[R][C] mein element a[i][j] ka byte address.

Step 1 — Row-major kyun matter karta hai. Row $i$ tak pahunchne ke liye, humein saari pehle wali complete rows skip karni padti hain. Har row mein $C$ elements hote hain, toh hum $i \times C$ elements skip karte hain. Kyun? Kyunki rows back-to-back store hoti hain.

Step 2 — Row ke andar, hum $j$ elements aage jaate hain. Kyun? Kyunki ek row ke andar columns consecutive hote hain.

Step 3 — Elements count karo, bytes mein convert karo. Total elements skipped $= i C + j$ . Har element $s = sizeof (T)$ bytes ka hota hai.

$addr (a [i] [j]) = base + (i \cdot C + j) \cdot s$

Notice karo ki $R$ (rows ki number) appear hi nahi karta! Address compute karne ke liye sirf column count $C$ chahiye — isi wajah se C ko majbooran array pass karte waqt pehle dimension ke alawa baaki sab dimensions deni padti hain.

Pointer wala view (KYU `a[i][j]` kaam karta hai)

C mein, a[i] exactly *(a + i) hai aur a[i][j] exactly *(*(a+i)+j) hai.

Declare karna aur initialize karna

int m[2][3] = { {1, 2, 3},
                {4, 5, 6} };          // explicit, sabse clear
 
int n[2][3] = {1, 2, 3, 4, 5, 6};     // same data, flat list (row-major fill)
 
int z[2][3] = {0};                    // sab zero
 
int p[][3] = {{1,2,3},{4,5,6}};       // pehla dim infer hoga = 2; andar wala dim DENA HI PADEGA

Functions mein pass karna

void print(int rows, int cols, int a[][cols]);   // C99 VLA param, ya:
void print2(int a[][4], int rows);               // fixed inner dimension

KYU inner dimension(s) specify karni padti hain: function sirf ek pointer receive karta hai (a decay hokar int(*)[4] banta hai). Andar a[i][j] compute karne ke liye, compiler ko phir bhi $C$ chahiye taaki iC+j ho sake.

Worked example Trace: 2×3 matrix fill aur sum karna

int a[2][3], sum = 0;
for (int i = 0; i < 2; i++)
    for (int j = 0; j < 3; j++) {
        a[i][j] = i*3 + j;   // 0,1,2,3,4,5
        sum += a[i][j];
    }
// sum = 0+1+2+3+4+5 = 15

i*3 + j kyun? Yeh literally row-major element index hai — storage layout confirm karta hai.

Recall Feynman: ek 12-saal ke bacche ko samjhao

Socho ek lambi shelf hai jisme ek line mein 12 boxes hain. Tum pretend karte ho ki yeh 3 shelves hain, har ek mein 4 boxes, taaki "row 2, box 1" bolna aasaan ho. Lekin asli mein yeh ek seedhi line hai! "Row 2, box 1" dhundhne ke liye tum count karte ho: 2 poori shelves skip karo (woh $2 \times 4 = 8$ boxes hain) phir 1 aur aage jao — box number 9. Computer yahi counting trick karta hai jab bhi tum a[2][1] likhte ho. Isi liye use pata hona chahiye ki har shelf par kitne boxes hain (columns), lekin use parwah nahi kitni shelves hain.

Flashcards

C ek 2D array ko memory mein kaise store karta hai?

Ek contiguous block ke roop mein row-major order mein — pehle row 0 sab, phir row 1 sab, aur aage bhi aisa hi.

int a[][C] declare karte waqt ya parameter mein column size kyun specify karni padti hai (lekin row size nahi)?

Address = base + (i*C + j)*size; ise compute karne ke liye C chahiye lekin R kabhi nahi, isliye R chhoda ja sakta hai.

T a[R][C] mein a[i][j] ka address formula kya hai, base B ke saath?

B + (i \cdot C + j) \cdot sizeof (T)

a[i][j] ko sirf pointers use karke likhो.

*(*(a + i) + j).

int a[3][4] ke liye, a kis type mein decay hota hai?

int (*)[4] — 4 ints ki array ka pointer.

C mein a[1,2] ka kya matlab hai aur kyun?

Yeh comma operator hai: 1,2 evaluate hokar 2 banta hai, toh matlab hai a[2] (ek puri row), element (1,2) NAHI.

3D address: T a[X][Y][Z] mein a[i][j][k] ke liye index i ko kisse multiply kiya jaata hai?

Y \cdot Z

(uske right wale saare dimensions ka product).

int m[2][3]={1,2,3,4,5,6}; mein m[1][0] kya hai?

4 (flat list row-major fill karta hai: row1 = {4,5,6}).

Connections

C Arrays (1D) — multi-D bas ek "array of arrays" hai.
Pointers in C — subscripting hi pointer arithmetic hai.
Array Decay — kyun a pass hote waqt int(*)[C] ban jaata hai.
Pointer to Array vs Array of Pointers — int (*p)[4] vs int *p[4].
sizeof Operator — element aur poori array ka size.
Row-major vs Column-major — C vs Fortran/MATLAB storage.
Variable Length Arrays (C99) — int a[][cols] parameters.