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2387. Median of a Row Wise Sorted Matrix 👍

  • Time: $O(\log(10^6) \cdot m\log n) = O(m\log n)$
  • Space: $O(1)$
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class Solution {
 public:
  int matrixMedian(vector<vector<int>>& grid) {
    const int noGreaterThanMedianCount = grid.size() * grid[0].size() / 2 + 1;
    int l = 1;
    int r = 1e6;

    while (l < r) {
      const int m = (l + r) / 2;
      if (numsNoGreaterThan(grid, m) >= noGreaterThanMedianCount)
        r = m;
      else
        l = m + 1;
    }

    return l;
  }

 private:
  int numsNoGreaterThan(const vector<vector<int>>& grid, int m) {
    int count = 0;
    for (const vector<int>& row : grid)
      count += upper_bound(row.begin(), row.end(), m) - row.begin();
    return count;
  }
};

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class Solution {
  public int matrixMedian(int[][] grid) {
    final int noGreaterThanMedianCount = grid.length * grid[0].length / 2 + 1;
    int l = 1;
    int r = (int) 1e6;

    while (l < r) {
      final int m = (l + r) / 2;
      if (numsNoGreaterThan(grid, m) >= noGreaterThanMedianCount)
        r = m;
      else
        l = m + 1;
    }

    return l;
  }

  private int numsNoGreaterThan(int[][] grid, int m) {
    int count = 0;
    for (int[] row : grid)
      count += firstGreater(row, m);
    return count;
  }

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

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class Solution:
  def matrixMedian(self, grid: List[List[int]]) -> int:
    noGreaterThanMedianCount = len(grid) * len(grid[0]) // 2 + 1
    l = 1
    r = int(1e6)

    while l < r:
      m = (l + r) // 2
      if sum(bisect_right(row, m) for row in grid) >= \
              noGreaterThanMedianCount:
        r = m
      else:
        l = m + 1

    return l