What is the time complexity of Map Sum Pairs?

The optimal solution has a time complexity of O(K).

What data structures are used to solve Map Sum Pairs?

This problem uses Hash Table, String, Design, Trie. Understanding these concepts is essential for solving this Medium problem efficiently.

What are the key insights for solving Map Sum Pairs?

Insight 1: Using a Trie data structure to efficiently store and search prefixes. Insight 2: Maintaining a separate map to store key-value pairs to handle value updates correctly.

Which companies ask LeetCode 677. Map Sum Pairs in interviews?

This problem is frequently asked at Akuna Capital.

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Map Sum Pairs - LeetCode 677 Solution

Map Sum Pairs - Complete Solution Guide

Map Sum Pairs is LeetCode problem 677, a Medium level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

Design a map that allows you to do the following: Maps a string key to a given value. Returns the sum of the values that have a key with a prefix equal to a given string. Implement the MapSum class: MapSum() Initializes the MapSum object. void insert(String key, int val) Inserts the key-val pair into the map. If the key already existed, the original key-value pair will be overridden to the new one. int sum(string prefix) Returns the sum of all the pairs' value whose key starts with the prefix .

Detailed Explanation

The problem requires designing a data structure, `MapSum`, that supports two main operations: `insert(key, val)` and `sum(prefix)`. The `insert` operation adds a key-value pair to the map, overwriting the value if the key already exists. The `sum` operation calculates the sum of all values in the map whose keys start with the given `prefix`. The constraints include the key and prefix lengths, value range, and the maximum number of calls to `insert` and `sum`.

Solution Approach

The solution uses a Trie to store the keys. Each node in the Trie represents a character in the key. Crucially, each node also stores the sum of all values associated with keys that pass through that node (i.e., have that node as a prefix). A separate hash map is maintained to keep track of the most recent value inserted for each key. This allows for calculating the 'delta' needed to update the prefix sums in the Trie when a key's value is updated.

Step-by-Step Algorithm

Step 1: Initialize the Trie root node and the hash map.
Step 2: In the `insert` function, calculate the difference (delta) between the new value and the old value (if any) for the given key.
Step 3: Update the hash map with the new key-value pair.
Step 4: Traverse the Trie, starting from the root, following the characters of the key.
Step 5: For each node visited, update its `prefix_sum` by adding the delta. If a node doesn't exist for a character, create it.
Step 6: In the `sum` function, traverse the Trie, starting from the root, following the characters of the prefix.
Step 7: If a node is not found for a character in the prefix, return 0 (no keys with that prefix exist).
Step 8: If the entire prefix is found in the Trie, return the `prefix_sum` of the last node visited.

Key Insights

Insight 1: Using a Trie data structure to efficiently store and search prefixes.
Insight 2: Maintaining a separate map to store key-value pairs to handle value updates correctly.
Insight 3: Caching the prefix sum within each Trie node to optimize the `sum` operation.

Complexity Analysis

Time Complexity: O(K)

Space Complexity: O(K)

Topics

This problem involves: Hash Table, String, Design, Trie.

Companies

Asked at: Akuna Capital.

Map Sum Pairs | LeetCode 677

Medium

Hash Table String Design Trie

Time: O(K)Space: O(K)

Solution Code

Available in:

import java.util.HashMap;
import java.util.Map;

class MapSum {

    class TrieNode {
        Map<Character, TrieNode> children;
        int prefixSum;

        public TrieNode() {
            this.children = new HashMap<>();
            this.prefixSum = 0;
        }
    }

    TrieNode root;
    Map<String, Integer> map;

    public MapSum() {
        this.root = new TrieNode();
        this.map = new HashMap<>();
    }

    public void insert(String key, int val) {
        int delta = val - this.map.getOrDefault(key, 0);
        this.map.put(key, val);

        TrieNode node = this.root;
        node.prefixSum += delta;
        for (char c : key.toCharArray()) {
            if (!node.children.containsKey(c)) {
                node.children.put(c, new TrieNode());
            }
            node = node.children.get(c);
            node.prefixSum += delta;
        }
    }

    public int sum(String prefix) {
        TrieNode node = this.root;
        for (char c : prefix.toCharArray()) {
            if (!node.children.containsKey(c)) {
                return 0;
            }
            node = node.children.get(c);
        }
        return node.prefixSum;
    }
}

/**
 * Your MapSum object will be instantiated and called as such:
 * MapSum obj = new MapSum();
 * obj.insert(key,val);
 * int param_2 = obj.sum(prefix);
 */

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Problem Info

Description

Problem 677: Map Sum Pairs - Detailed explanation and solution approaches.

Topics

Hash Table String Design Trie

Companies

Akuna Capital

Stats

Difficulty:Medium

Languages:4

Companies:1

Problem #:677

Problem Explanation

💡

Think Before You Code

🤔 Ask Yourself

→What is the input? What output do I need?
→Can I solve a smaller version of this problem first?
→What patterns have I seen in similar problems?

✏️ Try This First

Before looking at the solution, try to solve it on paper with a simple example!

🚀 Try on LeetCode

Solution Approach

📋

Step-by-Step Solution

8 steps

1
Step 1: Initialize the Trie root node and the hash map.
2
Step 2: In the `insert` function, calculate the difference (delta) between the new value and the old value (if any) for the given key.
3
Step 3: Update the hash map with the new key-value pair.
4
Step 4: Traverse the Trie, starting from the root, following the characters of the key.
5
Step 5: For each node visited, update its `prefix_sum` by adding the delta. If a node doesn't exist for a character, create it.
6
Step 6: In the `sum` function, traverse the Trie, starting from the root, following the characters of the prefix.
7
Step 7: If a node is not found for a character in the prefix, return 0 (no keys with that prefix exist).
8
Step 8: If the entire prefix is found in the Trie, return the `prefix_sum` of the last node visited.

💡

Pro Tip for Students

Try tracing through each step with a small example on paper before coding. Understanding "why" each step happens is more important than memorizing the code!

⚡

Complexity Analysis

⏱️

Time Complexity

O(K)

💾

Space Complexity

O(K)

📝

Why?

The time complexity is O(K) because both `insert` and `sum` iterate through the characters of the input string (key or prefix), where K is its length. The hash map operations (get and put) have an average time complexity of O(1). The space complexity is O(K) because, in the worst-case scenario, the Trie will store all the characters from the inserted keys, and the hash map will store all the keys.

📖New to Big O? Click to learn more

Big O Notation - Quick Guide

O(1)Best - Instant

O(log n)Excellent - Binary Search

O(n)Good - One loop

O(n log n)OK - Sorting

O(n²)Slow - Nested loops

O(2ⁿ)Very Slow - Recursion

Alternative Approaches

Brute-force approach

Store all keys in a list. For the `sum` operation, iterate through the list and check if each key starts with the given prefix. If it does, add its value to the sum.

Time: O(N*K) for `sum`, where N is the number of keys and K is the average length of the keys. O(1) for insert.Space: O(N*K), where N is the number of keys and K is the average length of the keys.

Trade-offs: This approach is simpler to implement but less efficient for the `sum` operation, especially when there are many keys. It's suitable for a small number of keys or when the `sum` operation is not frequently called. Trie-based is generally faster for many sum calls.

✨

Key Insights

1Insight 1: Using a Trie data structure to efficiently store and search prefixes.
2Insight 2: Maintaining a separate map to store key-value pairs to handle value updates correctly.
3Insight 3: Caching the prefix sum within each Trie node to optimize the `sum` operation.

📚

Key Terms Explained

For Students

Hash Table

A data structure that maps keys to values for quick lookup. Like a dictionary!

String

A sequence of characters. Like a word or sentence in programming!

Edge Cases

Edge case 1: Empty prefix in `sum`. The solution correctly returns the `prefix_sum` of the root node, which represents the sum of all values.
Edge case 2: Key already exists in `insert`. The solution correctly updates the old value in the hash map and adjusts the prefix sums in the Trie by the delta.
Edge case 3: Prefix not found in `sum`. The solution returns 0, indicating no keys start with the given prefix.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Not handling the case where the key already exists in `insert`. This can lead to incorrect prefix sums in the Trie.

✗Common mistake 2: Incorrectly updating the `prefix_sum` in the Trie during `insert`. It's crucial to calculate the delta and apply it correctly to each node along the path.

✗Common mistake 3: Not handling the case where the prefix is not found in the Trie during `sum`. This can lead to unexpected results or errors.

✅

Learning Tip

Every mistake is a learning opportunity! When you make an error, understand why it happened before moving on.

🌍

Where is This Used in Real Life?

💼Real-world scenario 1: Autocompletion systems. Predicting the next word based on the prefix the user has typed.

🏦Real-world scenario 2: IP routing. Finding the longest prefix match in a routing table to determine the next hop for a packet. The prefix sum could be thought of as the cost or bandwidth associated with that route.

💡Understanding real-world applications helps you see the "why" behind algorithms. It's not just about passing interviews—these concepts power the apps and websites you use every day!

Author's Notes

💡 Key Insight

Hash tables trade space for time. Before using one, consider if the problem constraints allow the extra memory. In interviews, always mention this trade-off.

🎯 Interview Tip

Consider multiple approaches before coding. Mentioning alternatives shows breadth of knowledge.

⚠️ Watch Out

Don't forget to handle key collisions and null/undefined keys. Consider what happens with duplicate values.

Written by Saswata Mondal

Software Engineer • Algorithms Enthusiast • Interview Coach

👨‍💻

About the Author

👨‍💻

Saswata MondalAuthor400+ LC Problems

B.Tech CSE, IEM Kolkata | LeetCode Rating: 1672 (Top 15%)

Certified: IBM Java Developer, NPTEL Programming in Java

Last updated: October 16, 2024LeetCode Profile GitHub

This solution has been crafted based on my experience solving 400+ LeetCode problems. Each explanation is designed to help you understand the underlying concepts, not just memorize the code.

Community Tips & Insights

I was asked this exact problem at my Google interview. The interviewer wanted me to optimize space complexity.

@InterviewProJul 14

Try solving this without using extra space first. It's a great exercise for understanding the underlying pattern.

@CodeNinjaJul 7

In a real interview, always clarify constraints first. Ask about input size and value ranges.

@TechLeadJun 30

❓

Frequently Asked Questions

How do I choose between a hash map and a hash set?

Use a hash set when you only need to track presence/absence of elements (like detecting duplicates). Use a hash map when you need to associate values with keys (like counting frequencies or storing indices). Hash sets use less memory since they only store keys.

What is the sliding window technique for string problems?

Sliding window maintains a "window" of characters with two pointers. Expand the right pointer to include characters, shrink from left when window violates constraints. Useful for substring problems, anagrams, and longest/shortest substring with properties.

How much time should I spend on a medium problem in interviews?

In a 45-minute interview, aim for: 5-10 minutes understanding and clarifying, 5-10 minutes discussing approach, 20-25 minutes coding, and 5-10 minutes testing. If stuck after 15 minutes of thinking, verbalize your thought process and ask for hints.

What is the importance of time and space complexity analysis?

Complexity analysis is crucial because: 1) Interviewers always ask about it, 2) It helps you choose between approaches, 3) It demonstrates CS fundamentals. Always state both time and space complexity, and be prepared to explain how you derived them.

What is the optimal approach for "Map Sum Pairs"?

For this medium-level Hash Table problem, the key is to identify the core pattern. Analyze the input constraints to determine acceptable time complexity. Consider whether string techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

🤖 Need help with this problem?