#
# @lc app=leetcode.cn id=74 lang=python3
#
# [74] 搜索二维矩阵
#
# https://leetcode-cn.com/problems/search-a-2d-matrix/description/
#
# algorithms
# Medium (37.62%)
# Likes:    166
# Dislikes: 0
# Total Accepted:    39.3K
# Total Submissions: 104.1K
# Testcase Example:  '[[1,3,5,7],[10,11,16,20],[23,30,34,50]]\n3'
#
# 编写一个高效的算法来判断 m x n 矩阵中，是否存在一个目标值。该矩阵具有如下特性：
# 
# 
# 每行中的整数从左到右按升序排列。
# 每行的第一个整数大于前一行的最后一个整数。
# 
# 
# 示例 1:
# 
# 输入:
# matrix = [
# ⁠ [1,   3,  5,  7],
# ⁠ [10, 11, 16, 20],
# ⁠ [23, 30, 34, 50]
# ]
# target = 3
# 输出: true
# 
# 
# 示例 2:
# 
# 输入:
# matrix = [
# ⁠ [1,   3,  5,  7],
# ⁠ [10, 11, 16, 20],
# ⁠ [23, 30, 34, 50]
# ]
# target = 13
# 输出: false
# 
#

# @lc code=start
class Solution:
    def searchMatrix(self, matrix: List[List[int]], target: int) -> bool:
        if not matrix:
            return False
        m, n = len(matrix), len(matrix[0])
        p, q = 0, m*n-1
        while p <= q:
            mid = (p+q)//2
            if matrix[mid//n][mid%n] == target:
                return True
            elif matrix[mid//n][mid%n] > target:
                q = mid-1
            else:
                p = mid+1
        return False

# @lc code=end

