index-to-character-conversion

Index-to-character conversion is the inverse of character-to-index mapping. Given an integer index i (0–25 for lowercase English), adding the base character’s ASCII value produces the corresponding character: ch = i + 'a'.

$\text{char}(i) = \text{ASCII}^{-1}(\text{ASCII}('a') + i)$

After building a frequency array, the stored data is indexed numerically (0–25). To produce human-readable output (printing “a = 3” not “0 = 3”), you must convert each index back to its character. This is the reverse of the ch - 'a' mapping and uses i + 'a'.

1. During traversal of the frequency array, you have an index i (0 to 25)
2. Compute char ch = i + 'a'
3. Use ch for output or further processing
4. For i=0 → ‘a’, i=1 → ‘b’, …, i=25 → ‘z’

$\text{char}(i) = i + 97 = i + \text{ASCII}('a')$

$\text{char}(0) = 'a', \quad \text{char}(1) = 'b', \quad \dots, \quad \text{char}(25) = 'z'$

• O(1) computation — simple integer addition
• Must match the base used in the forward mapping ('a' for ch - 'a')
• Produces only lowercase letters when used with 0–25 indices
• No bounds checking — caller must ensure index is in valid range

• Built from: Character-to-Index Mapping — index-to-character is the mathematical inverse of character-to-index
• Builds into: Most Frequent Character — after finding the max index, convert back to character
• Builds into: Frequency Array — used during the traversal phase to produce output
• Contrasts with: Hash Map Traversal Method — maps store key-value pairs directly, no conversion needed

• Using 'A' as base when the mapping used 'a' produces wrong letters
• Indices outside 0–25 produce non-alphabetic characters (e.g., i=26 → ’{’)
• Forgetting this step and printing raw indices is a common beginner mistake
• When using uppercase mapping (ch - 'A'), the reverse must use i + 'A'