Search a 2D Matrix

描述

Write an efficient algorithm that searches for a value in an m × 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.

分析

二分查找。

代码

Java

// Search a 2D Matrix
// 时间复杂度O(logn)，空间复杂度O(1)
public class Solution {
    public boolean searchMatrix(int[][] matrix, int target) {
        if (matrix.length == 0) return false;
        final int  m = matrix.length;
        final int n = matrix[0].length;

        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;
    }
}

C++

// Search a 2D Matrix
// 时间复杂度O(logn)，空间复杂度O(1)
class Solution {
public:
    bool searchMatrix(const vector<vector<int>>& matrix, int target) {
        if (matrix.empty()) return false;
        const size_t  m = matrix.size();
        const size_t n = matrix.front().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;
    }
};

相关题目

• Search a 2D Matrix II