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;
}
}