Anagram Check Techniques in DSA Typescript - Time & Space Complexity

Time Complexity: Anagram Check Techniques

O(n)

Understanding Time Complexity

We want to know how the time needed to check if two words are anagrams changes as the words get longer.

How does the method we use affect the time it takes?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

function areAnagrams(s1: string, s2: string): boolean {
  if (s1.length !== s2.length) return false;
  const count: Record = {};
  for (const char of s1) {
    count[char] = (count[char] || 0) + 1;
  }
  for (const char of s2) {
    if (!count[char]) return false;
    count[char]--;
  }
  return true;
}
    

This code checks if two strings are anagrams by counting characters in the first and matching counts with the second.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Two loops each going through all characters of the strings.
• How many times: Each loop runs once for every character, so twice the length of the strings.

How Execution Grows With Input

As the strings get longer, the number of steps grows roughly twice as much because we check each character twice.

Input Size (n)	Approx. Operations
10	About 20 steps
100	About 200 steps
1000	About 2000 steps

Pattern observation: The time grows linearly with the length of the strings.

Final Time Complexity

Time Complexity: O(n)

This means the time to check anagrams grows in direct proportion to the length of the strings.

Common Mistake

[X] Wrong: "Sorting both strings is always faster than counting characters."

[OK] Correct: Sorting takes more time (O(n log n)) than counting characters (O(n)) for long strings, so counting is usually faster.

Interview Connect

Understanding how different ways to check anagrams affect time helps you choose the best method in real problems.

Self-Check

"What if we used sorting both strings instead of counting characters? How would the time complexity change?"

Practice

1. What does it mean if two strings are anagrams of each other?

easy

A. They contain the same characters in any order

B. They have the same length but different characters

C. They start with the same character

D. They end with the same character

Solution

1. Step 1: Understand the definition of anagrams

   Anagrams are words or phrases made by rearranging the letters of another, so they must have the same characters.

2. Step 2: Compare the character sets

   If two strings have exactly the same characters, just in different orders, they are anagrams.

3. Final Answer:

   They contain the same characters in any order -> Option A

4. Quick Check:

   Anagrams = same characters [OK]

Hint: Check if sorted strings match to confirm anagrams [OK]

Common Mistakes:

• Thinking same length means anagrams
• Only comparing first or last characters
• Ignoring character counts

2. Which TypeScript code snippet correctly checks if two strings are anagrams by sorting?

easy

A. const isAnagram = (a: string, b: string) => a.split('').sort().join('') === b.split('').sort().join('');

B. const isAnagram = (a: string, b: string) => a.split('').sort() === b.split('').sort();

C. const isAnagram = (a: string, b: string) => a.sort() === b.sort();

D. const isAnagram = (a: string, b: string) => a === b;

Solution

1. Step 1: Understand string sorting in TypeScript

   Strings must be split into arrays, sorted, then joined back to strings for comparison.

2. Step 2: Identify correct syntax

   const isAnagram = (a: string, b: string) => a.split('').sort().join('') === b.split('').sort().join(''); correctly splits, sorts, and joins both strings before comparing.

3. Final Answer:

   const isAnagram = (a: string, b: string) => a.split('').sort().join('') === b.split('').sort().join(''); -> Option A

4. Quick Check:

   Sort and join strings before compare [OK]

Hint: Always join after sorting arrays to compare strings [OK]

Common Mistakes:

• Comparing arrays directly without join
• Trying to sort strings directly
• Comparing strings without sorting

3. What is the output of this TypeScript code?

function areAnagrams(s1: string, s2: string): boolean {
  const normalize = (str: string) => str.toLowerCase().replace(/\s+/g, '').split('').sort().join('');
  return normalize(s1) === normalize(s2);
}

console.log(areAnagrams('Listen', 'Silent'));
console.log(areAnagrams('Hello', 'Olelh'));
console.log(areAnagrams('Test', 'Taste'));

medium

A. true false false

B. true true false

C. false true true

D. false false true

Solution

1. Step 1: Normalize strings by lowercasing, removing spaces, sorting

   'Listen' and 'Silent' normalize to 'eilnst', 'Hello' and 'Olelh' normalize to 'ehllo', 'Test' and 'Taste' normalize to 'estt' and 'aestt' respectively.

2. Step 2: Compare normalized strings

   'Listen' vs 'Silent' match (true), 'Hello' vs 'Olelh' match (true), 'Test' vs 'Taste' do not match (false).

3. Final Answer:

   true true false -> Option B

4. Quick Check:

   Normalized strings equal means true [OK]

Hint: Normalize strings before comparing for anagram check [OK]

Common Mistakes:

• Ignoring case differences
• Not removing spaces
• Not sorting characters

4. Identify the bug in this TypeScript function that checks anagrams:

function isAnagram(a: string, b: string): boolean {
  return a.split('').sort() === b.split('').sort();
}

medium

A. Not removing spaces before comparison

B. Missing toLowerCase() for case-insensitive check

C. Comparing arrays directly instead of strings

D. Using split() without arguments

Solution

1. Step 1: Understand array comparison in TypeScript

   Arrays compared with === check reference, not content, so two sorted arrays won't be equal even if same elements.

2. Step 2: Fix by joining arrays to strings before comparing

   Joining sorted arrays to strings allows content comparison, fixing the bug.

3. Final Answer:

   Comparing arrays directly instead of strings -> Option C

4. Quick Check:

   Arrays need join() before compare [OK]

Hint: Join sorted arrays before comparing for equality [OK]

Common Mistakes:

• Comparing arrays with ===
• Ignoring case sensitivity
• Not trimming spaces

5. Given two strings, how can you efficiently check if they are anagrams using a character count map in TypeScript? Which code snippet correctly implements this?

hard

A. function isAnagram(a: string, b: string): boolean {
if (a.length !== b.length) return false;
const count: Record = {};
for (const char of a) count[char] = (count[char] || 0) + 1;
for (const char of b) {
if (!count[char]) return false;
count[char]--;
}
return true;
}

B. function isAnagram(a: string, b: string): boolean {
return a.split('').sort().join('') === b.split('').sort().join('');
}

C. function isAnagram(a: string, b: string): boolean {
return a.length === b.length;
}

D. function isAnagram(a: string, b: string): boolean {
const mapA = new Map();
for (const c of a) mapA.set(c, (mapA.get(c) || 0) + 1);
for (const c of b) mapA.set(c, (mapA.get(c) || 0) - 1);
return [...mapA.values()].every(v => v === 0);
}

Solution

1. Step 1: Understand character count map approach

   Count characters in first string, subtract counts using second string, then check all counts zero.

2. Step 2: Analyze each option

   function isAnagram(a: string, b: string): boolean { if (a.length !== b.length) return false; const count: Record = {}; for (const char of a) count[char] = (count[char] || 0) + 1; for (const char of b) { if (!count[char]) return false; count[char]--; } return true; } misses checking if count goes negative; function isAnagram(a: string, b: string): boolean { return a.split('').sort().join('') === b.split('').sort().join(''); } uses sorting (correct but not map); function isAnagram(a: string, b: string): boolean { return a.length === b.length; } only checks length; function isAnagram(a: string, b: string): boolean { const mapA = new Map(); for (const c of a) mapA.set(c, (mapA.get(c) || 0) + 1); for (const c of b) mapA.set(c, (mapA.get(c) || 0) - 1); return [...mapA.values()].every(v => v === 0); } correctly uses Map to count and verify zero counts.

3. Final Answer:

   Option D correctly implements character count map with Map and zero check -> Option D

4. Quick Check:

   Map counts increment/decrement, all zero means anagram [OK]

Hint: Use map to count chars, decrement, then check all zero [OK]

Common Mistakes:

• Not checking for negative counts
• Only comparing lengths
• Using sorting instead of counting