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

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;
}
}