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.
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
Constraints:
m == matrix.length
n == matrix[i].length
1 <= n, m <= 300
-109 <= matix[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
我的答案：
一下子就想到binary search，好久不写也觉得有点陌生了
class Solution {
public:
bool searchMatrix(vector>& matrix, int target) {
int row_end = matrix.size();
int col_end = matrix[0].size();
for (int r=0; r& matrix_row, const int& col_end, const int& target) {
if (target > matrix_row[col_end-1])
return col_end-1;
int c_left = 0;
int c_right = col_end;
int c_mid = (c_left+c_right)/2;
while (c_left < c_right) {
if (matrix_row[c_mid] == target)
return c_mid;
else if (matrix_row[c_mid] > target) {
c_right = c_mid;
}
else {
c_left = c_mid+1;
}
c_mid = (c_left+c_right)/2;
}
return c_left;
}
};
Runtime: 264 ms, faster than 19.54% of C++ online submissions for Search a 2D Matrix II.
Memory Usage: 11.1 MB, less than 17.69% of C++ online submissions for Search a 2D Matrix II.
性能一般，应该是O(nlogn)
看答案：
https://zxi.mytechroad.com/blog/two-pointers/leetcode-240-search-a-2d-matrix-ii/
只需要从右上角开始往left或者bottom搜索就可以了，不用binary search。O(n)
我的默写：
class Solution {
public:
bool searchMatrix(vector>& matrix, int target) {
int row_end = matrix.size();
int col_end = matrix[0].size();
int r = 0, c = col_end-1;
while (r=0) {
if (matrix[r][c] == target)
return true;
else if (matrix[r][c] > target)
--c;
else
++r;
}
return false;
}
};
Runtime: 104 ms, faster than 75.42% of C++ online submissions for Search a 2D Matrix II.
Memory Usage: 10.9 MB, less than 55.95% of C++ online submissions for Search a 2D Matrix II.
想了想为什么比binary search快，binary search快在没有每一层联系的时候