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2564. Substring XOR Queries 👍

  • Time: $O(30n) = O(n)$
  • Space: $O(n)$
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class Solution {
 public:
  vector<vector<int>> substringXorQueries(string s,
                                          vector<vector<int>>& queries) {
    constexpr int kMaxBit = 30;
    vector<vector<int>> ans;
    // {val: (left, right)} := s[left..right]'s decimal value = val
    unordered_map<int, pair<int, int>> valToLeftAndRight;

    for (int left = 0; left < s.length(); ++left) {
      int val = 0;
      if (s[left] == '0') {
        // edge case: Save the index of the first 0.
        if (!valToLeftAndRight.contains(0))
          valToLeftAndRight[0] = {left, left};
        continue;
      }
      const int maxRight = min(static_cast<int>(s.length()), left + kMaxBit);
      for (int right = left; right < maxRight; ++right) {
        val = val * 2 + s[right] - '0';
        if (!valToLeftAndRight.contains(val))
          valToLeftAndRight[val] = {left, right};
      }
    }

    for (const vector<int>& query : queries) {
      const int first = query[0];
      const int second = query[1];
      const int val = first ^ second;
      const auto it = valToLeftAndRight.find(val);
      if (it == valToLeftAndRight.cend()) {
        ans.push_back({-1, -1});
      } else {
        const auto [left, right] = it->second;
        ans.push_back({left, right});
      }
    }

    return ans;
  }
};

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class Solution {
  public int[][] substringXorQueries(String s, int[][] queries) {
    final int MAX_BIT = 30;
    int[][] ans = new int[queries.length][2];
    // {val: (left, right)} := s[left..right]'s decimal value = val
    Map<Integer, Pair<Integer, Integer>> valToLeftAndRight = new HashMap<>();

    for (int left = 0; left < s.length(); ++left) {
      int val = 0;
      if (s.charAt(left) == '0') {
        // edge case: Save the index of the first 0.
        if (!valToLeftAndRight.containsKey(0))
          valToLeftAndRight.put(val, new Pair<>(left, left));
        continue;
      }
      final int maxRight = Math.min(s.length(), left + MAX_BIT);
      for (int right = left; right < maxRight; ++right) {
        val = val * 2 + s.charAt(right) - '0';
        if (!valToLeftAndRight.containsKey(val))
          valToLeftAndRight.put(val, new Pair<>(left, right));
      }
    }

    for (int i = 0; i < queries.length; ++i) {
      final int first = queries[i][0];
      final int second = queries[i][1];
      final int val = first ^ second;
      Pair<Integer, Integer> leftAndRight = valToLeftAndRight.get(val);
      if (leftAndRight == null) {
        ans[i] = new int[] {-1, -1};
      } else {
        final int left = leftAndRight.getKey();
        final int right = leftAndRight.getValue();
        ans[i] = new int[] {left, right};
      }
    }

    return ans;
  }
}

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class Solution:
  def substringXorQueries(self, s: str, queries: list[list[int]]) -> list[list[int]]:
    MAX_BIT = 30
    # {val: [left, right]} := s[left..right]'s decimal value = val
    valToLeftAndRight = collections.defaultdict(lambda: [-1, -1])

    for left, c in enumerate(s):
      val = 0
      if c == '0':
        # edge case: Save the index of the first 0.
        if 0 not in valToLeftAndRight:
          valToLeftAndRight[0] = [left, left]
        continue
      for right in range(left, min(len(s), left + MAX_BIT)):
        val = val * 2 + int(s[right])
        if val not in valToLeftAndRight:
          valToLeftAndRight[val] = [left, right]

    return [valToLeftAndRight[first, right]
            for first, right in queries]