Data Structures and Algorithms Practice Problems
Q1. Array Address Calculation (Row & Column Major)
Problem: An array ARR[-5...15, 10...20] stores elements in Row Major with each element requiring 2 bytes. Base address is 2500. Find the address of ARR[10][15].
Answer:
- Row range: -5 to 15, so Lr = -5, Ur = 15
- Column range: 10 to 20, so Lc = 10, Uc = 20
- Element size (w) = 2 bytes
- Base Address (BA) = 2500
Step 1: Calculate dimensions
- Number of rows (M) = Ur - Lr + 1 = 15 - (-5) + 1 = 21
- Number of columns (N) = Uc - Lc + 1 = 20 - 10 + 1 = 11
Step 2: Row Major Order Formula
Address(A[i][j]) = BA + [(i - Lr) × N + (j - Lc)] × w
Address(ARR[10][15]) = 2500 + [(10 - (-5)) × 11 + (15 - 10)] × 2
= 2500 + [15 × 11 + 5] × 2
= 2500 + [165 + 5] × 2
= 2500 + 170 × 2 = 2840
Step 3: Column Major Order Formula
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