38 · Search a 2D Matrix II - LintCode

# Description

Write an efficient algorithm that searches for a value in an m x n matrix, return The number of occurrence of it.

This matrix has the following properties:

  • Integers in each row are sorted from left to right.
  • Integers in each column are sorted from up to bottom.
  • No duplicate integers in each row or column.

# Example

Example 1:

Input:

matrix = [[3,4]]
target = 3

Output:

1

Explanation:

There is only one 3 in the matrix.

Example 2:

Input:

matrix = [
      [1, 3, 5, 7],
      [2, 4, 7, 8],
      [3, 5, 9, 10]
    ]
target = 3

Output:

2

Explanation:

There are two 3 in the matrix.

# Challenge

O(m+n) time and O(1) extra space

# Solution

可以從矩陣的右上角 (0, row - 1) 開始搜,直到左下角結束
要注意的是搜索範圍不能越界,找到一個 target 就 count + 1

public class Solution {
    /**
     * @param matrix: A list of lists of integers
     * @param target: An integer you want to search in matrix
     * @return: An integer indicate the total occurrence of target in the given matrix
     */
    public int searchMatrix(int[][] matrix, int target) {
        if (matrix == null || matrix.length == 0 || matrix[0].length == 0 || matrix[0] == null) {
            return 0;
        }
        int rows = matrix.length;
        int cols = matrix[0].length;
        int x = 0;
        int y = cols - 1;
        int count = 0;
        while (x < rows && y >= 0) {
            if (matrix[x][y] < target) {
                x++;
            } else if (matrix[x][y] > target) {
                y--;
            } else {
                count++;
                x++;
                y--;
            }
        }
        return count;
    }
}

# 時間複雜度

  • O(m+n)
    m 在這代表 row, n = cols, 搜索時沒有找到 target 時,那麼 y 就要 - 1,能減少 n 次;x+1,能增加 m 次。

# 空間複雜度

O(1)