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2070. Most Beautiful Item for Each Query 👍

  • Time: $O(\texttt{sort} + q\log n)$
  • Space: $O(n)$
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class Solution {
 public:
  vector<int> maximumBeauty(vector<vector<int>>& items, vector<int>& queries) {
    vector<int> ans;
    vector<int> prices;
    vector<int> maxBeautySoFar(items.size() + 1);

    ranges::sort(items);

    for (const vector<int>& item : items)
      prices.push_back(item[0]);

    for (int i = 0; i < items.size(); ++i)
      maxBeautySoFar[i + 1] = max(maxBeautySoFar[i], items[i][1]);

    for (const int query : queries) {
      const int i = ranges::upper_bound(prices, query) - prices.begin();
      ans.push_back(maxBeautySoFar[i]);
    }

    return ans;
  }
};

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class Solution {
  public int[] maximumBeauty(int[][] items, int[] queries) {
    int[] ans = new int[queries.length];
    int[] prices = new int[items.length];
    int[] maxBeautySoFar = new int[items.length + 1];

    Arrays.sort(items, (a, b) -> Integer.compare(a[0], b[0]));

    for (int i = 0; i < items.length; ++i)
      maxBeautySoFar[i + 1] = Math.max(maxBeautySoFar[i], items[i][1]);

    for (int i = 0; i < queries.length; ++i) {
      final int index = firstGreater(items, queries[i]);
      ans[i] = maxBeautySoFar[index];
    }

    return ans;
  }

  private int firstGreater(int[][] items, int q) {
    int l = 0;
    int r = items.length;
    while (l < r) {
      final int m = (l + r) / 2;
      if (items[m][0] > q)
        r = m;
      else
        l = m + 1;
    }
    return l;
  }
}

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class Solution:
  def maximumBeauty(
      self,
      items: list[list[int]],
      queries: list[int],
  ) -> list[int]:
    prices, beauties = zip(*sorted(items))
    maxBeautySoFar = [0] * (len(beauties) + 1)

    for i, beauty in enumerate(beauties):
      maxBeautySoFar[i + 1] = max(maxBeautySoFar[i], beauty)

    return [maxBeautySoFar[bisect_right(prices, query)] for query in queries]