Formatted question description:

2070. Most Beautiful Item for Each Query (Medium)

You are given a 2D integer array items where items[i] = [pricei, beautyi] denotes the price and beauty of an item respectively.

You are also given a 0-indexed integer array queries. For each queries[j], you want to determine the maximum beauty of an item whose price is less than or equal to queries[j]. If no such item exists, then the answer to this query is 0.

Return an array answer of the same length as queries where answer[j] is the answer to the jth query.


Example 1:

Input: items = [[1,2],[3,2],[2,4],[5,6],[3,5]], queries = [1,2,3,4,5,6]
Output: [2,4,5,5,6,6]
- For queries[0]=1, [1,2] is the only item which has price <= 1. Hence, the answer for this query is 2.
- For queries[1]=2, the items which can be considered are [1,2] and [2,4]. 
  The maximum beauty among them is 4.
- For queries[2]=3 and queries[3]=4, the items which can be considered are [1,2], [3,2], [2,4], and [3,5].
  The maximum beauty among them is 5.
- For queries[4]=5 and queries[5]=6, all items can be considered.
  Hence, the answer for them is the maximum beauty of all items, i.e., 6.

Example 2:

Input: items = [[1,2],[1,2],[1,3],[1,4]], queries = [1]
Output: [4]
The price of every item is equal to 1, so we choose the item with the maximum beauty 4. 
Note that multiple items can have the same price and/or beauty.  

Example 3:

Input: items = [[10,1000]], queries = [5]
Output: [0]
No item has a price less than or equal to 5, so no item can be chosen.
Hence, the answer to the query is 0.



  • 1 <= items.length, queries.length <= 105
  • items[i].length == 2
  • 1 <= pricei, beautyi, queries[j] <= 109

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Solution 1. Offline Query

Sort both items and queries in ascending order of price. Traverse queries. Use a pointer i to cover all the items with a price <= the current query, and compute the maximum beauty among them. In this way, we traverse both array only once.

// OJ:
// Time: O(NlogN + MlogM + M + N) where `N`/`M` is the length of `items`/`queries`.
// Space: O(M)
class Solution {
    vector<int> maximumBeauty(vector<vector<int>>& A, vector<int>& Q) {
        vector<pair<int, int>> queries;
        for (int i = 0; i < Q.size(); ++i) queries.push_back({Q[i],i});
        sort(begin(queries), end(queries));
        sort(begin(A), end(A));
        int i = 0, N = A.size(), maxBeauty = 0;
        vector<int> ans(Q.size());
        for (auto q : queries) {
            auto &[query, index] = q;
            for (; i < N && A[i][0] <= query; ++i) maxBeauty = max(maxBeauty, A[i][1]);
            ans[index] = maxBeauty;
        return ans;


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