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In this approach, we perform the following steps:
Time Complexity: O((n + m) log n) where n = number of items and m = number of queries.
Space Complexity: O(n) for storing the processed items data.
1function maxBeautyForQueries(items, queries) {
2 items.sort((a, b) => a[0] - b[0]);
3 const maxBeauty = new Array(items.length);
4 let maxB = 0;
5
6 for (let i = 0; i < items.length; i++) {
7 maxB = Math.max(maxB, items[i][1]);
8 maxBeauty[i] = maxB;
9 }
10
11 function findBest(query) {
12 let left = 0, right = items.length - 1;
13 while (left <= right) {
14 const mid = Math.floor((left + right) / 2);
15 if (items[mid][0] <= query) {
16 left = mid + 1;
17 } else {
18 right = mid - 1;
19 }
20 }
21 return right >= 0 ? maxBeauty[right] : 0;
22 }
23
24 return queries.map(findBest);
25}
26
27// Example usage:
28const items = [[1,2],[3,2],[2,4],[5,6],[3,5]];
29const queries = [1,2,3,4,5,6];
30console.log(maxBeautyForQueries(items, queries));This JavaScript implementation sorts items and maintains a cumulative maximum beauty list. Each query uses a binary search to quickly locate the applicable maximum beauty at the time of querying.
Coordinate compression can be used to reduce problem complexity when dealing with large range values like prices. In this approach:
Time Complexity: O((n + m) log(n + m)) due to sorting during compression.
Space Complexity: O(n + m) for storing all price points and decision arrays.
This solution first compresses the range of prices into indexes, reducing the search space. A dynamic programming approach then determines the maximum beauty at each possible price point index, allowing quick lookup when answering queries. This methodology deals efficiently with large query ranges.