74. Search a 2D Matrix**

74. Search a 2D Matrix**

​​https://leetcode.com/problems/search-a-2d-matrix/​​

题目描述

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 from left to right.
• The first integer of each row is greater than the last integer of the previous row.
  Example 1:

Input:
matrix = [
  [1,   3,  5,  7],
  [10, 11, 16, 20],
  [23, 30, 34, 50]
]
target = 3
Output: true

Example 2:

Input:
matrix = [
  [1,   3,  5,  7],
  [10, 11, 16, 20],
  [23, 30, 34, 50]
]
target = 13
Output: false

解题思路

把二维矩阵当成一维的 list 即可, 使用二分查找.

C++ 实现 1

class Solution {
public:
    bool searchMatrix(vector<vector<int>>& matrix, int target) {
        if (matrix.empty() || matrix[0].empty()) return false;
        int m = matrix.size(), n = matrix[0].size();
        int i = 0, j = m * n - 1;
        while (i <= j) {
            int mid = i + (j - i) / 2;
            int p = mid / n, q = mid % n;
            if (matrix[p][q] == target) return true;
            else if (matrix[p][q] < target) ++ i;
            else -- j;
        }
        return false;
    }
};