240. Search a 2D Matrix II

1. Question

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

• Integers in each row are sorted in ascending from left to right.
• Integers in each column are sorted in ascending from top to bottom.

2. Examples

Example 1:

Input: matrix = [[1,4,7,11,15],[2,5,8,12,19],[3,6,9,16,22],[10,13,14,17,24],[18,21,23,26,30]], target = 5
Output: true

Example 2:

Input: matrix = [[1,4,7,11,15],[2,5,8,12,19],[3,6,9,16,22],[10,13,14,17,24],[18,21,23,26,30]], target = 20
Output: false

3. Constraints

• m == matrix.length
• n == matrix[i].length
• 1 <= n, m <= 300
• -10⁹ <= matrix[i][j] <= 10⁹
• All the integers in each row are sorted in ascending order.
• All the integers in each column are sorted in ascending order.
• -10⁹ <= target <= 10⁹

4. References

来源：力扣（LeetCode） 链接：https://leetcode-cn.com/problems/search-a-2d-matrix-ii 著作权归领扣网络所有。商业转载请联系官方授权，非商业转载请注明出处。

5. Solutions

5.1. 暴力枚举

class Solution {
  public boolean searchMatrix(int[][] matrix, int target) {
    for (int i = 0; i < matrix.length; i++) {
      for (int j = 0; j < matrix[0].length; j++) {
        if (matrix[i][j] == target) {
          return true;
        } 
      }
    }
    return false;
  }
}

5.2. 二分的变种

class Solution {
  public boolean searchMatrix(int[][] matrix, int target) {
    int m = matrix.length;
    int n = matrix[0].length;
    int x = 0;
    int y = m - 1;
    while (x < n && y >= 0) {
      if (matrix[y][x] == target) {
        return true;
      } else if (matrix[y][x] < target) {
        x++;
      } else {
        y--;
      }
    }
    return false;
  }
}