题目描述
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 in ascending from left to right.
- Integers in each column are sorted in ascending from top to bottom.
For example,
Consider the following 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]
]
Given target = 5, return true.
Given target = 20, return false.
分析
参考《剑指offer》,每一次排除一行或一列。
查找数字7:
- 首先寻找matrix的左上角的元素9, 9>7,所以排除掉9所在的列,因为9以下的列,肯定比9大
- 再次寻找剩余matrix的左上角的元素8, 8>7,所以排除掉8所在的列
- 再次寻找剩余matrix的左上角的元素2, 2<7,所以排除掉2所在的行,因为2所在行,之前的元素都比2小
- 依次递推
代码
public boolean searchMatrix(int[][] matrix, int target) {
if (matrix == null || matrix.length == 0 || matrix[0].length == 0) {
return false;
}
int m = matrix.length;
int n = matrix[0].length;
int x = 0, y = n - 1;
while (x < m && y >= 0) {
if (matrix[x][y] == target) {
return true;
} else if (matrix[x][y] < target) {
x++;
} else {
y--;
}
}
return false;
}