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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.
1using System;
2using System.Collections.Generic;
3
4public class Solution {
5 public int[] MaxBeautyForQueries(int[][] items, int[] queries) {
6 Array.Sort(items, (a, b) => a[0] - b[0]);
7 int[] maxBeauties = new int[items.Length];
8 int maxBeauty = 0;
9
10 for (int i = 0; i < items.Length; i++) {
11 maxBeauty = Math.Max(maxBeauty, items[i][1]);
12 maxBeauties[i] = maxBeauty;
13 }
14
15 int[] result = new int[queries.Length];
16 for (int i = 0; i < queries.Length; i++) {
17 int idx = Array.BinarySearch(items, new int[]{queries[i], int.MaxValue}, Comparer<int[]>.Create((a, b) => a[0] - b[0]));
18 if (idx < 0) idx = ~idx - 1;
19 result[i] = idx >= 0 ? maxBeauties[idx] : 0;
20 }
21 return result;
22 }
23
24 public static void Main(string[] args) {
25 var solution = new Solution();
26 int[][] items = new int[][] { new int[] {1,2}, new int[] {3,2}, new int[] {2,4}, new int[] {5,6}, new int[] {3,5} };
27 int[] queries = new int[] { 1, 2, 3, 4, 5, 6 };
28 int[] result = solution.MaxBeautyForQueries(items, queries);
29 Console.WriteLine(string.Join(" ", result));
30 }
31}
This method leverages C# collections and algorithms to supply a projected maximum beauty for sorted item data. Here, a binary search optimizes query resolution by narrowing potential indexes efficiently.
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.