Sponsored
Sponsored
Using HashMap
This approach uses two hash maps. The first map stores the keys and their respective values, while the second map, usually called the prefix map, is used to cache the sums of prefixes. Every time a key-value pair is inserted, we iteratively update the sums of all prefixes for that key. In this approach, every insert operation might take time proportional to the length of the key, and the sum operation is almost constant time thanks to the prefix sums map.
Time Complexity: O(k) for insert, where k is the length of the key. O(1) for sum.
Space Complexity: O(n), where n is the number of keys stored.
1class MapSum {
2 constructor() {
3 this.map = new Map();
4 this.prefixMap = new Map();
5 }
6
7 insert(key, val) {
8 const delta = val - (this.map.get(key) || 0);
9 this.map.set(key, val);
10
11 for (let i = 1; i <= key.length; i++) {
12 const prefix = key.slice(0, i);
13 this.prefixMap.set(prefix, (this.prefixMap.get(prefix) || 0) + delta);
14 }
15 }
16
17 sum(prefix) {
18 return this.prefixMap.get(prefix) || 0;
19 }
20}The JavaScript solution uses the Map object to store key-value pairs and prefix sums. The insert method adjusts each prefix's sum by the delta value, while the sum method simply retrieves the value from the prefix map.
Using Trie
This approach involves using a Trie (Prefix Tree) for storing keys. Along with each node of the Trie, maintain a map that stores prefix sum. Every time a key is inserted, traverse each node and update the corresponding prefix sum. When retrieving a sum for a given prefix, traverse the Trie up to the end of the prefix and return the stored prefix sum.
Time Complexity: O(k) for insert and O(p) for sum, where k is the length of the key and p is the length of the prefix.
Space Complexity: O(n), where n is the number of keys stored in the Trie.
1
This Java solution utilizes a TrieNode and constructs a Trie structure to manage the prefixes and their sums. Each Trie node maintains a value that represents sums of keys using that prefix. Similar to the Python solution, adjustments to the prefix sums are applied during insertion, and the sum of a prefix is retrieved via traversal of the Trie nodes.