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2031. Count Subarrays With More Ones Than Zeros 👍

  • Time: $O(n\log n)$
  • Space: $O(n)$
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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:
  int subarraysWithMoreZerosThanOnes(vector<int>& nums) {
    constexpr int kMod = 1'000'000'007;
    const int n = nums.size();
    int ans = 0;
    int prefix = 0;
    // Map [-n, n] to [1, 2 * n + 1].
    FenwickTree tree(2 * n + 1);
    tree.add(remap(0, n), 1);

    for (const int num : nums) {
      prefix += num == 0 ? -1 : 1;
      // If prefix[j] > prefix[i], where 0 <= i < j < |prefix|, that means that
      // there are more ones than zeros in nums[i + 1, j].
      ans += tree.get(remap(prefix - 1, n));
      ans %= kMod;
      tree.add(remap(prefix, n), 1);
    }

    return ans;
  }

 private:
  int remap(int i, int n) {
    return i + n + 1;
  }
};

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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 subarraysWithMoreZerosThanOnes(int[] nums) {
    final int kMod = 1_000_000_007;
    final int n = nums.length;
    int ans = 0;
    int prefix = 0;
    FenwickTree tree = new FenwickTree(2 * n + 1);
    tree.add(remap(0, n), 1);

    for (final int num : nums) {
      prefix += num == 0 ? -1 : 1;
      ans += tree.get(remap(prefix - 1, n));
      ans %= kMod;
      tree.add(remap(prefix, n), 1);
    }

    return ans;
  }

  private int remap(int i, int n) {
    return i + n + 1;
  }
}

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class FenwichTree:
  def __init__(self, n: int):
    self.n = n
    self.sums = [0] * (2 * n + 1)

  def add(self, i: int, delta: int) -> None:
    i += self.n + 1  # re-mapping
    while i < len(self.sums):
      self.sums[i] += delta
      i += i & -i

  def get(self, i: int) -> int:
    i += self.n + 1  # re-mapping
    summ = 0
    while i > 0:
      summ += self.sums[i]
      i -= i & -i
    return summ


class Solution:
  def subarraysWithMoreZerosThanOnes(self, nums: list[int]) -> int:
    kMod = 1_000_000_007
    ans = 0
    prefix = 0
    tree = FenwichTree(len(nums))
    tree.add(0, 1)

    for num in nums:
      prefix += -1 if num == 0 else 1
      ans += tree.get(prefix - 1)
      ans %= kMod
      tree.add(prefix, 1)

    return ans