1409. Queries on a Permutation With Key

• Time: $O(q\log m)$
• Space: $O(q + m)$

C++JavaPython

class FenwickTree {
 public:
  FenwickTree(int n) : sums(n + 1) {}

  void add(int i, int delta) {
    while (i < sums.size()) {
      sums[i] += delta;
      i += lowbit(i);
    }
  }

  int get(int i) const {
    int sum = 0;
    while (i > 0) {
      sum += sums[i];
      i -= lowbit(i);
    }
    return sum;
  }

 private:
  vector<int> sums;

  static inline int lowbit(int i) {
    return i & -i;
  }
};

class Solution {
 public:
  vector<int> processQueries(vector<int>& queries, int m) {
    vector<int> ans;
    // Map [-m, m] to [0, 2 * m].
    FenwickTree tree(2 * m + 1);
    unordered_map<int, int> numToIndex;

    for (int num = 1; num <= m; ++num) {
      numToIndex[num] = num + m;
      tree.add(num + m, 1);
    }

    int nextEmptyIndex = m;  // Map 0 to m.

    for (const int query : queries) {
      const int index = numToIndex[query];
      ans.push_back(tree.get(index - 1));
      // Move `query` from `index` to `nextEmptyIndex`.
      tree.add(index, -1);
      tree.add(nextEmptyIndex, 1);
      numToIndex[query] = nextEmptyIndex--;
    }

    return ans;
  }
};

class FenwickTree {
  public FenwickTree(int n) {
    sums = new int[n + 1];
  }

  public void add(int i, int delta) {
    while (i < sums.length) {
      sums[i] += delta;
      i += lowbit(i);
    }
  }

  public int get(int i) {
    int sum = 0;
    while (i > 0) {
      sum += sums[i];
      i -= lowbit(i);
    }
    return sum;
  }

  private int[] sums;

  private static int lowbit(int i) {
    return i & -i;
  }
}

class Solution {
  public int[] processQueries(int[] queries, int m) {
    int[] ans = new int[queries.length];
    // Map [-m, m] to [0, 2 * m].
    FenwickTree tree = new FenwickTree(2 * m + 1);
    Map<Integer, Integer> numToIndex = new HashMap<>();

    for (int num = 1; num <= m; ++num) {
      numToIndex.put(num, num + m);
      tree.add(num + m, 1);
    }

    int nextEmptyIndex = m; // Map 0 to m.

    for (int i = 0; i < queries.length; ++i) {
      final int query = queries[i];
      final int index = numToIndex.get(query);
      ans[i] = tree.get(index - 1);
      // Move `query` from `index` to `nextEmptyIndex`.
      tree.add(index, -1);
      tree.add(nextEmptyIndex, 1);
      numToIndex.put(query, nextEmptyIndex--);
    }

    return ans;
  }
}

class FenwickTree:
  def __init__(self, n: int):
    self.sums = [0] * (n + 1)

  def add(self, i: int, delta: int) -> None:
    while i < len(self.sums):
      self.sums[i] += delta
      i += FenwickTree.lowbit(i)

  def get(self, i: int) -> int:
    summ = 0
    while i > 0:
      summ += self.sums[i]
      i -= FenwickTree.lowbit(i)
    return summ

  @staticmethod
  def lowbit(i: int) -> int:
    return i & -i


class Solution:
  def processQueries(self, queries: list[int], m: int) -> list[int]:
    ans = []
    # Map [-m, m] to [0, 2 * m].
    tree = FenwickTree(2 * m + 1)
    numToIndex = {num: num + m for num in range(1, m + 1)}

    for num in range(1, m + 1):
      tree.add(num + m, 1)

    nextEmptyIndex = m  # Map 0 to m.

    for query in queries:
      index = numToIndex[query]
      ans.append(tree.get(index - 1))
      # Move `query` from `index` to `nextEmptyIndex`.
      tree.add(index, -1)
      tree.add(nextEmptyIndex, 1)
      numToIndex[query] = nextEmptyIndex
      nextEmptyIndex -= 1

    return ans