给定M×N矩阵,每一行、每一列都按升序排列,请编写代码找出某元素。

示例:

现有矩阵 matrix 如下:

[
  [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]
]
给定 target = 5,返回 true。

给定 target = 20,返回 false。

方法一:直接遍历(O(n*m))略。

方法二:对于每行采用二分,复杂度(O(nlog(m)))

class Solution {
    public boolean searchMatrix(int[][] matrix, int target) {

        if(matrix.length==0) return false;

        int n = matrix.length;
        int m = matrix[0].length;

        for (int i = 0; i < n; i++) {
            int l = 0, r = m - 1;
            while (l <= r) {
                int mid = (l + r) / 2;
                if (matrix[i][mid] < target)
                    l = mid + 1;
                else if (matrix[i][mid] == target)
                    return true;
                else
                    r = mid - 1;
            }
        }

        return false;

    }
}

方法三:从右上角开始找。复杂度(O(n+m))

class Solution {
    public boolean searchMatrix(int[][] matrix, int target) {

        if (matrix.length == 0) return false;

        int n = matrix.length;
        int m = matrix[0].length;

        int row = 0, col = m - 1;

        while (row < n && col >= 0) {
            if (matrix[row][col] < target)
                row++;
            else if (matrix[row][col] > target)
                col--;
            else
                return true;
        }

        return false;

    }
}