1347. Minimum Number of Steps to Make Two Strings Anagram

MediumHash TableStringCounting
Leetcode Link

Problem Description

In this problem, you have two strings s and t of equal length. You're tasked with converting string t into an anagram of string s. An anagram is defined as a different arrangement of letters that are exactly the same in both strings. The way to do this is by choosing any character from t and replacing it with another character. The goal is to achieve this in the minimum number of steps. A step is defined as one instance of changing a character in t. The main question is to find out the least amount of steps necessary to turn t into an anagram of s.


The intuitive approach to solving this problem is based on tracking the frequency of each character in both strings, and then determining how many characters in t do not match the frequency needed to make an anagram of s. Here's how we arrive at the solution:

  1. We first create a count (frequency) of all the characters in s using something like a Counter or a dictionary.
  2. We then iterate through each character in t, checking against our previously made frequency count.
  3. If the character in t is found in the frequency count, and the count for that character is greater than 0, it means we already have this character in s, so we decrement the count for that character.
  4. If the character is not found or its count is already 0, it means this character is extra or not needed, so this is a character that needs to be replaced. Hence, we increment our answer which represents the number of changes needed.
  5. After iterating through all characters in t, the value of our answer will represent the minimum number of steps required to make t an anagram of s.

Solution Approach

The implementation of the solution can be explained with the following steps:

  1. Import the Counter class from the collections module. Counter is a subclass of dictionary used for counting hashable objects, subtly simplifying the process of frequency computation for us.

  2. Define the minSteps function which accepts two strings s and t, representing the initial and target strings, where we want to convert string t into an anagram of string s.

  3. Instantiate a Counter for the string s to get the frequency of each character in s. The resulting cnt is a dictionary-like object where cnt[c] is the count of occurrences of character c in string s.

  4. Initialize a variable ans to zero, which will be used to keep track of the number of changes we need to make in t to turn it into an anagram of s.

  5. Iterate over each character c in t:

    • If cnt[c] is greater than zero, it implies that character c is present in s and we haven't matched all occurrences of c in s yet, so we decrease cnt[c] by one, indicating that we've matched this instance of c in t with an instance in s.

    • If cnt[c] is zero or c is not present, it implies that s does not require this character or we already have enough of this character to match s (i.e., excess characters in t), and therefore, we increment ans by one since this character needs to be replaced.

  6. After the for-loop terminates, ans stores the total number of replacements needed for t to become an anagram of s, and this value is returned.

Using these steps, the solution efficiently computes the minimum number of steps to make t an anagram of s, taking advantage of hash maps (in this case, the Counter object) for fast access and update of character frequencies.

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What's the output of running the following function using input [30, 20, 10, 100, 33, 12]?

1def fun(arr: List[int]) -> List[int]:
2    import heapq
3    heapq.heapify(arr)
4    res = []
5    for i in range(3):
6        res.append(heapq.heappop(arr))
7    return res
1public static int[] fun(int[] arr) {
2    int[] res = new int[3];
3    PriorityQueue<Integer> heap = new PriorityQueue<>();
4    for (int i = 0; i < arr.length; i++) {
5        heap.add(arr[i]);
6    }
7    for (int i = 0; i < 3; i++) {
8        res[i] = heap.poll();
9    }
10    return res;
1class HeapItem {
2    constructor(item, priority = item) {
3        this.item = item;
4        this.priority = priority;
5    }
8class MinHeap {
9    constructor() {
10        this.heap = [];
11    }
13    push(node) {
14        // insert the new node at the end of the heap array
15        this.heap.push(node);
16        // find the correct position for the new node
17        this.bubble_up();
18    }
20    bubble_up() {
21        let index = this.heap.length - 1;
23        while (index > 0) {
24            const element = this.heap[index];
25            const parentIndex = Math.floor((index - 1) / 2);
26            const parent = this.heap[parentIndex];
28            if (parent.priority <= element.priority) break;
29            // if the parent is bigger than the child then swap the parent and child
30            this.heap[index] = parent;
31            this.heap[parentIndex] = element;
32            index = parentIndex;
33        }
34    }
36    pop() {
37        const min = this.heap[0];
38        this.heap[0] = this.heap[this.size() - 1];
39        this.heap.pop();
40        this.bubble_down();
41        return min;
42    }
44    bubble_down() {
45        let index = 0;
46        let min = index;
47        const n = this.heap.length;
49        while (index < n) {
50            const left = 2 * index + 1;
51            const right = left + 1;
53            if (left < n && this.heap[left].priority < this.heap[min].priority) {
54                min = left;
55            }
56            if (right < n && this.heap[right].priority < this.heap[min].priority) {
57                min = right;
58            }
59            if (min === index) break;
60            [this.heap[min], this.heap[index]] = [this.heap[index], this.heap[min]];
61            index = min;
62        }
63    }
65    peek() {
66        return this.heap[0];
67    }
69    size() {
70        return this.heap.length;
71    }
74function fun(arr) {
75    const heap = new MinHeap();
76    for (const x of arr) {
77        heap.push(new HeapItem(x));
78    }
79    const res = [];
80    for (let i = 0; i < 3; i++) {
81        res.push(heap.pop().item);
82    }
83    return res;

Example Walkthrough

Let's consider a small example where s = "anagram" and t = "mangaar". Our goal is to determine the minimum number of steps needed to transform t into an anagram of s.

  1. First, using the Counter class to count the frequency of characters in s, we would get:

    1Counter('anagram') = {'a': 3, 'n': 1, 'g': 1, 'r': 1, 'm': 1}
  2. We start with ans = 0. This ans keeps track of the required changes.

  3. We examine each character in t:

    • For the first character 'm', Counter for s has {'m': 1}. We match 'm' in t to one in s, so we decrement by 1: now Counter is {'m': 0}.
    • The next character is 'a', Counter has {'a': 3}. After decrementing, it becomes {'a': 2}.
    • The following two characters are 'n' and 'g', Counter for 'n' is {'n': 0} and for 'g' is {'g': 0} after decrementing since both are present once in s.
    • Next, we have two 'a's, but Counter shows {'a': 2}. After matching both, Counter updates to {'a': 0}. So far, no steps required as all characters matched.
    • The final letter in t is 'r', which is already matched in s (Counter for 'r' {'r': 0}). Since it's extra, we need to replace it, incrementing ans to 1.
  4. After examining all characters in t, our ans equals 1. This means that we only need to replace one character in t to make it an anagram of s.

So, in this example, we only need a single step: replace the extra 'r' in t with a missing 'm' to make t an anagram of s.

Solution Implementation

1from collections import Counter
3class Solution:
4    def minSteps(self, s: str, t: str) -> int:
5        # Create a Counter (multiset) for all characters in string 's'
6        char_count = Counter(s)
8        # Initialize a variable to count the number of steps
9        steps = 0
11        # Iterate over each character in string 't'
12        for char in t:
13            # If the character is in the counter and count is greater than 0
14            if char_count[char] > 0:
15                # Decrease the count for that character since it can be transformed
16                char_count[char] -= 1
17            else:
18                # If the character is not present or count is 0,
19                # increase the steps needed, as this requires an additional operation
20                steps += 1
22        # Return the total number of steps required to make 't' equal to 's'
23        return steps
1class Solution {
2    public int minSteps(String s, String t) {
3        // Initialize an array to count the frequency of each character in the string s
4        int[] charFrequency = new int[26];
6        // Populate the character frequency array with the count of each character in s
7        for (int i = 0; i < s.length(); ++i) {
8            charFrequency[s.charAt(i) - 'a']++;
9        }
11        // This variable will keep track of the minimum number of steps (character changes)
12        int minSteps = 0;
14        // Iterate over the string t and decrease the frequency of each character in the charFrequency array
15        for (int i = 0; i < t.length(); ++i) {
16            // If the character's frequency after decrementing is negative,
17            // it means that t has an extra occurrence of this character
18            // that is not matched by a character in s.
19            if (--charFrequency[t.charAt(i) - 'a'] < 0) {
20                // Since this character is extra and unneeded, increase the minSteps
21                minSteps++;
22            }
23        }
24        // Return the total minimum number of steps to make t an anagram of s
25        return minSteps;
26    }
1class Solution {
3    // Function to find the minimum number of steps required to make the strings 's' and 't' anagrams
4    int minSteps(string s, string t) {
5        // Array to count the frequency of each character in the string 's'
6        int charCounts[26] = {0};
8        // Increment the frequency of each character found in the string 's'
9        for (char& ch : s) {
10            charCounts[ch - 'a']++;
11        }
13        // This will count the number of extra characters in the string 't' that aren't in string 's' or are in abundance
14        int extraChars = 0;
16        // Loop over the string 't'
17        for (char& ch : t) {
18            // If decrementing leads to a negative count, it means 't' has an extra character that 's' doesn't have or that it's in abundance
19            extraChars += --charCounts[ch - 'a'] < 0;
20        }
22        // The answer is the number of extra characters which need to be changed in 't' to make it an anagram of 's'
23        return extraChars;
24    }
1// Function definition using TypeScript with explicit input and output types
3 * Determines the minimum number of steps to make two strings anagrams by replacing letters.
4 * @param {string} stringOne - The first string to be compared.
5 * @param {string} stringTwo - The second string to be compared.
6 * @returns {number} The minimum number of steps required to make the strings anagrams.
7 */
8const minSteps = (stringOne: string, stringTwo: string): number => {
9    // Initialize an array to count character frequencies for stringOne
10    const charCount = new Array(26).fill(0);
12    // Populate the character frequency array for stringOne
13    for (const char of stringOne) {
14        const index = char.charCodeAt(0) - 'a'.charCodeAt(0);
15        charCount[index]++;
16    }
18    // Initialize a counter for the number of steps needed
19    let steps = 0;
21    // Iterate through stringTwo and decrement the corresponding character count from stringOne
22    for (const char of stringTwo) {
23        const index = char.charCodeAt(0) - 'a'.charCodeAt(0);
24        // Increment steps if character count falls below zero, which indicates a character in stringTwo not present in stringOne
25        steps += --charCount[index] < 0 ? 1 : 0;
26    }
28    // Return the total number of steps required to make the two strings anagrams
29    return steps;

Time and Space Complexity

Time Complexity

The time complexity of the code is determined by two main operations: the construction of the counter from string s and the iteration over string t.

  1. Constructing cnt using Counter(s) involves iterating over all characters in s, which has a complexity of O(N) where N is the length of s.
  2. The iteration over t also has a complexity of O(M) where M is the length of t.

Combining these, the total time complexity of the code is O(N + M) since the operations are sequential, not nested.

Space Complexity

The space complexity is primarily dictated by the space required to store the counter cnt, which at most contains as many entries as there are unique characters in s. If the character set is fixed (like ASCII or Unicode), this can be considered a constant O(1). However, if we consider the size of the character set U (which could grow with the input size in some theoretical cases), the space complexity could also be considered O(U).

In practical programming scenarios where s and t consist of Unicode characters and the upper bound for U is the size of the Unicode character set, which is a constant O(1) as it doesn't change with the input size.

Combining the consideration for unique characters in the counter with any overhead for the storage structure, the overall space complexity is O(U) which, in the context of Unicode, simplifies to O(1) constant space complexity.

Learn more about how to find time and space complexity quickly using problem constraints.

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1void search(Node root) {
2  if (!root) return;
3  visit(root);
4  root.visited = true;
5  for (Node node in root.adjacent) {
6    if (!node.visited) {
7      search(node);
8    }
9  }

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