【LeetCode】74. 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.

For example,

Consider the following matrix:

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

Given target = 3, return true.

解题思路

二分查找
先对行进行二分查找，找到比目标小一点的数字。
再对找到的行进行列的二分查找。

AC代码

class Solution {public:    bool searchMatrix(vector<vector<int>>& matrix, int target) {        int m = matrix.size(); if (!m) return false;        int n = matrix[0].size(); if (!n) return false;        //binary search for row index        int begin = 0, end = m - 1;        int mid;        while (begin < end) {            mid = (begin + end) / 2 + 1;            if (matrix[mid][0] == target) return true;            if (matrix[mid][0] < target) begin = mid;            else end = mid - 1;        }        int i = begin;        //binary search for column        begin = 0; end = n;        while (begin < end) {            mid = (begin + end) / 2;            if (matrix[i][mid] == target) return true;            if (matrix[i][mid] <  target) begin = mid + 1;            else end = mid;        }        return false;    }};