74. Search a 2D Matrix

1. Description

You are given an m x n integer matrix matrix with the following two properties:

• Each row is sorted in non-decreasing order.
• The first integer of each row is greater than the last integer of the previous row.

Given an integer target, return true if target is in matrix or false otherwise.
You must write a solution in O(log(m * n)) time complexity.

2. Example

Example 1

Input: matrix = [[1,3,5,7],[10,11,16,20],[23,30,34,60]], target = 3
Output: true

Example 2

Input: matrix = [[1,3,5,7],[10,11,16,20],[23,30,34,60]], target = 13
Output: false

3. Constraints

• m == matrix.length
• n == matrix[i].length
• 1 <= m, n <= 100
• -$10^4$ <= matrix[i][j], target <= $10^4$

4. Solutions

Binary Search

m = matrix.size(), n = matrix.front().size()
Time complexity: O(logmn)
Space complexity: O(1)

class Solution {
public:
    bool searchMatrix(const vector<vector<int>> &matrix, int target) {
        const int m = matrix.size(), n = matrix.front().size();
        int left = 0, right = m * n;
        while (left < right) {
            int middle = left + (right - left) / 2;
            int value = matrix[middle / n][middle % n];
            if (value < target) {
                left = middle + 1;
            } else if (value == target) {
                return true;
            } else {
                right = middle;
            }
        }

        return false;
    }
};