The number of substrings that can be formed from string given by “a d e f b g h n m p” is

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This question was previously asked in

UGC NET Computer Science (Paper 2) Dec 2018 Paper

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Answer 1

Concepts:

A substring is a contiguous sequence of characters within a string.

Example:

String: “GATE”

Substring: G, A, T, E, GA, AT, TE, GAT, ATE, GATE and Λ (empty string or null string)

Therefore, number of substrings = 11

Formula:

If character is not repeated, then

\({\rm{number\;of\;substring}} = \frac{{{\rm{n}} \times \left( {{\rm{n}} + 1} \right)}}{2} + 1\)

Calculation:

String: “a d e f b g h n m p”

∴ number of characters = n = 10

Repetition is not present in a string

\({\rm{number\;of\;substring}} = \frac{{10 \times \left( {10 + 1} \right)}}{2} + 1 = 56\;\)