LeetCode——Search a 2D Matrix II
2024-10-01 06:36:33
Description:
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
.
首先想到的就是遍历整个矩阵,时间复杂度是O(m*n),肯定是Timeout。
public class Solution {
public boolean searchMatrix(int[][] matrix, int target) { for(int i=0; i<matrix.length; i++) {
for(int j=0; j<matrix[i].length; j++) {
if(matrix[i][j] == target) {
return true;
}
}
} return false;
}
}
然后在优化的话就想到了二分。对每一行进行二分。时间复杂度是O(n*logm),还是Timeout,二分用的越多时间复杂度就越高,所以行列都二分(有点递归分治的意思)更会Timeout。
public class Solution { public boolean binarySearch(int[] arr, int terget) { int left = 0, int right = arr.length - 1;
while(left <= right) {
int mid = left + (right - left) / 2;
if(target == arr[mid]) {
return true;
}
if(target > arr[mid]) {
left = mid + 1;
}
else {
right = mid - 1;
}
} return false;
} public boolean searchMatrix(int[][] matrix, int target) { for(int i=0; i<matrix.length; i++) {
if(binarySearch(matrix[i], target)) {
return true;
}
} return false;
} }
这么看来时间复杂度必须在线性的基础上才行。观察一下矩阵不难发现把矩阵逆时针旋转45度类似一棵二叉查找树。所以就可以模仿二叉查找树的方法来做了。
这样的话时间复杂度就是O(m + n);AC。
public class Solution { public boolean searchMatrix(int[][] matrix, int target) { if(matrix.length==0 || matrix[0].length==0) {
return false;
} int i = 0, j = matrix[0].length - 1; while(i < matrix.length && j >= 0) {
int cur = matrix[i][j];
if(cur == target) {
return true;
}
else if(cur < target) {
i ++;
}
else {
j --;
} }
return false; } }
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