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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.
Utilizing Java's TreeSet for compression of prices, this implementation transforms original indices into a reduced form that provides rapid resolution using dynamic programming to maintain maximum beauty confirmation at each point.