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118:Search a 2D Matrix

題目:Write an efficient algorithm that searches for a value in an mn 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.
For example, Consider the following matrix:
[
[1, 3, 5, 7],
[10, 11, 16, 20],
[23, 30, 34, 50]
]
Given target = 3, return true.

可以用二分查詢解決,程式碼如下:

// 時間複雜度 O(log(nm)),空間複雜度 O(1)
class Solution {
public:
        bool searchMatrix(vector<vector<int>>& matrix, int target) {
                if (matrix.empty()) return false;
                const size_t m = matrix.size();
                const size_t n = matrix[0].size();

                int
first = 0; int last = m * n; while (first != last) { int mid = first + (last - first) / 2; int value = matrix[mid / n][mid % n]; if (value == target) return true; else
if (value < target) first = mid + 1; else last = mid; } return false; } };