74. Search a 2D Matrix

Write an efficient algorithm that searches for a value in an m x n matrix. This matrix has the following properties:

    Integers in each row are sorted from left to right.
    The first integer of each row is greater than the last integer of the previous row.

Example 1:

Input:
matrix = [
  [1,   3,  5,  7],
  [10, 11, 16, 20],
  [23, 30, 34, 50]
]
target = 3
Output: true

Example 2:

Input:
matrix = [
  [1,   3,  5,  7],
  [10, 11, 16, 20],
  [23, 30, 34, 50]
]
target = 13
Output: false
  • Binary Search
public boolean searchMatrix(int[][] matrix, int target) {
    if(matrix.length == 0 || matrix[0].length == 0) return false;
    int n = matrix.length, m = matrix[0].length;
    int l = 0, r = n * m - 1;
    while(l <= r) {
        int mid = l + (r-l) / 2;
        int i = mid / m, j = mid - i * m;
        if(matrix[i][j] == target)
            return true;
        else if(matrix[i][j] < target) {
            l = mid + 1;
        else
            r = mid - 1;
    }
    return false;
}