Substring Search Patterns in DSA Rust - Time & Space Complexity

Time Complexity: Substring Search Patterns

O(n * m)

Understanding Time Complexity

We want to understand how long it takes to find a smaller string inside a bigger one.

How does the search time change when the strings get longer?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

fn contains_substring(text: &str, pattern: &str) -> bool {
    let n = text.len();
    let m = pattern.len();
    if m > n {
        return false;
    }
    for i in 0..=n - m {
        if &text[i..i + m] == pattern {
            return true;
        }
    }
    false
}
    

This code checks if the pattern appears anywhere inside the text by comparing slices one by one.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Comparing the pattern with a slice of the text.
• How many times: Up to (n - m + 1) times, where n is text length and m is pattern length.

How Execution Grows With Input

Each position in the text is checked by comparing up to m characters.

Input Size (n)	Approx. Operations
10 (text), 3 (pattern)	~8 * 3 = 24 comparisons
100 (text), 5 (pattern)	~96 * 5 = 480 comparisons
1000 (text), 10 (pattern)	~991 * 10 = 9,910 comparisons

Pattern observation: The work grows roughly by multiplying text length by pattern length.

Final Time Complexity

Time Complexity: O(n * m)

This means the time to search grows proportionally to the product of text and pattern lengths.

Common Mistake

[X] Wrong: "The search always takes time proportional to the text length only."

[OK] Correct: Because each position requires checking the whole pattern, so pattern length matters too.

Interview Connect

Understanding this helps you explain why simple substring search can be slow and why smarter methods exist.

Self-Check

"What if we used a smarter algorithm like KMP? How would the time complexity change?"

Practice

1. What is the main purpose of substring search algorithms in strings?

easy

A. To find if a smaller string exists inside a larger string

B. To sort characters in a string alphabetically

C. To reverse the order of characters in a string

D. To count the total number of characters in a string

Solution

1. Step 1: Understand substring search goal

   Substring search algorithms check if a smaller string (pattern) appears inside a bigger string (text).

2. Step 2: Compare with other string operations

   Sorting, reversing, and counting characters are different operations unrelated to searching for a substring.

3. Final Answer:

   To find if a smaller string exists inside a larger string -> Option A

4. Quick Check:

   Substring search = find smaller string inside bigger string [OK]

Hint: Substring search means finding a smaller string inside a bigger one [OK]

Common Mistakes:

• Confusing substring search with sorting or reversing strings
• Thinking substring search counts characters
• Mixing substring search with string length calculation

2. Which Rust code snippet correctly checks if the string needle is a substring of haystack?

easy

A. if haystack.index_of(needle) { println!("Found"); }

B. if haystack.find(needle) { println!("Found"); }

C. if needle.in(haystack) { println!("Found"); }

D. if haystack.contains(needle) { println!("Found"); }

Solution

1. Step 1: Identify correct Rust substring method

   Rust's standard library provides contains method on strings to check substring presence, returning a boolean.

2. Step 2: Check other options for syntax errors

   find returns an Option, not a boolean; in is not a Rust keyword; index_of does not exist in Rust standard strings.

3. Final Answer:

   if haystack.contains(needle) { println!("Found"); } -> Option D

4. Quick Check:

   Rust substring check uses contains() [OK]

Hint: Use .contains() to check substring presence in Rust strings [OK]

Common Mistakes:

• Using .find() as a boolean without checking Option
• Trying Python or other language syntax like 'in'
• Using non-existent methods like index_of

3. What will be the output of this Rust code?

let text = "hello world";
let pattern = "wor";
if text.contains(pattern) {
    println!("Pattern found");
} else {
    println!("Pattern not found");
}

medium

A. Compilation error

B. Pattern found

C. Pattern not found

D. Runtime panic

Solution

1. Step 1: Check if pattern is substring of text

   The string "hello world" contains "wor" starting at index 6.

2. Step 2: Evaluate the if condition

   Since text.contains(pattern) returns true, the code prints "Pattern found".

3. Final Answer:

   Pattern found -> Option B

4. Quick Check:

   "hello world" contains "wor" = true [OK]

Hint: Check if substring exists literally inside the main string [OK]

Common Mistakes:

• Assuming contains() checks for whole words only
• Confusing contains() with starts_with() or ends_with()
• Expecting compilation or runtime errors without syntax issues

4. Identify the error in this Rust code snippet for substring search:

let text = "rustacean";
let pattern = "ace";
if text.find(pattern) {
    println!("Found");
} else {
    println!("Not found");
}

medium

A. Missing semicolon after let statements

B. Using contains() instead of find()

C. Using find() without handling Option result

D. Pattern string is empty

Solution

1. Step 1: Understand return type of find()

   In Rust, find() returns an Option<usize>, not a boolean.

2. Step 2: Check if condition usage

   The if condition expects a boolean, but text.find(pattern) returns Option, causing a type mismatch error.

3. Final Answer:

   Using find() without handling Option result -> Option C

4. Quick Check:

   find() returns Option, not bool [OK]

Hint: Remember find() returns Option, not boolean; unwrap or check Some [OK]

Common Mistakes:

• Treating find() as boolean directly in if
• Ignoring Option type returned by find()
• Confusing contains() and find() return types

5. Given a large text and multiple patterns, which substring search approach is best to efficiently find all patterns in the text?

hard

A. Using a Trie or Aho-Corasick algorithm to search all patterns simultaneously

B. Naive search checking each pattern separately in the text

C. Sorting all patterns and text then binary searching each pattern

D. Reversing the text and patterns before searching

Solution

1. Step 1: Analyze naive approach inefficiency

   Checking each pattern separately in a large text is slow because it repeats scanning multiple times.

2. Step 2: Understand advanced multi-pattern search

   Trie-based algorithms like Aho-Corasick build a structure to search all patterns at once efficiently.

3. Step 3: Evaluate other options

   Sorting and binary searching patterns is not suitable for substring search; reversing strings does not help search efficiency.

4. Final Answer:

   Using a Trie or Aho-Corasick algorithm to search all patterns simultaneously -> Option A

5. Quick Check:

   Multi-pattern search uses Trie/Aho-Corasick [OK]

Hint: Use Trie or Aho-Corasick for multiple substring searches efficiently [OK]

Common Mistakes:

• Using naive repeated searches for many patterns
• Trying sorting-based methods for substring search
• Thinking reversing strings improves search speed