Leetcode 二分查找 Search a 2D Matrix

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Search a 2D Matrix

  Total Accepted: 10871  Total Submissions: 35629

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.

For example,

Consider the following matrix:

[
  [1,   3,  5,  7],
  [10, 11, 16, 20],
  [23, 30, 34, 50]
]

Given target = 3, return true.

题意：在一个二维矩阵中找到给定的值。矩阵从上到下从左到右有序
思路：二维空间的二分查找 
先在一维里找中间位置，再将该位置转为二维空间里的下标
注：下标比较难弄，得注意点
复杂度： 时间O(log n)，空间O(1)

相关题目：

Search Insert Position

bool searchMatrix(const vector<vector<int> > &matrix, int target){
	if (matrix.empty()) return false;
	int m = matrix.size(), n = matrix.front().size();
	int begin = 0, end = m * n, middle, row, col;
	while(begin < end){
		middle = begin + (end - begin) / 2;
		int row = middle / n;
		int col = middle % n;
		if(matrix[row][col] == target) return true;
		else if(matrix[row][col] < target) begin = middle + 1;
		else end = middle;
	}
	return false;
}