Problem
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.
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]
]
Example 1:
Input: matrix, target = 5
Output: true
Example 2:
Input: matrix, target = 20
Output: false
Solution (Java)
class Solution {
public boolean searchMatrix(int[][] matrix, int target) {
int r = 0;
int c = matrix[0].length - 1;
while (r < matrix.length && c >= 0) {
if (matrix[r][c] == target) {
return true;
} else if (matrix[r][c] > target) {
c--;
} else {
r++;
}
}
return false;
}
}
Solution (Javascript)
/**
* @param {number[][]} matrix
* @param {number} target
* @return {boolean}
*/
var searchMatrix = function(matrix, target) {
var n = matrix.length;
var m = (matrix[0] || []).length;
var x = m - 1;
var y = 0;
var tmp = 0;
while (x >= 0 && y < n) {
tmp = matrix[y][x];
if (target === tmp) {
return true;
} else if (target > tmp) {
y++;
} else {
x--;
}
}
return false;
};
Explain:
nope.
Complexity:
- Time complexity : O(n + m).
n行m列。 - Space complexity : O(1).