Search a 2D Matrix II
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
从右上角开始, 比较target 和 matrix[i][j]的值。如果小于target, 则该行不可能有此数, 所以i++; 如果大于target, 则该列不可能有此数, 所以j--。遇到边界则表明该矩阵不含target.
代码
// Search a 2D Matrix II
// 时间复杂度O(m + n)，空间复杂度O(1)
public class Solution {
public boolean searchMatrix(int[][] matrix, int target) {
if(matrix.length==0 || matrix[0].length==0) return false;
int i = 0;
int j = matrix[0].length-1;
while(i < matrix.length && j >= 0) {
final int x = matrix[i][j];
if(target == x) {
return true;
} else if (x < target) {
++i;
} else {
--j;
}
}
return false;
}
}