Given $a > 0, a\neq 1$, $\forall n \in \mathbb{N}$, we have

$$ \frac{1+a^2+a^4+\cdots + a^{2n}}{a+a^3+\cdots+a^{2n-1}} > \frac{n+1}{n} $$

很久以前在 FB 上看到的這題

求證不等式 對於實數 $x$，$\cos(\sin x) > \sin(\cos x)$

題目如下：

Given an array nums of n integers, are there elements a, b, c in nums such that a + b + c = 0? Find all unique triplets in the array which gives the sum of zero.

Notice that the solution set must not contain duplicate triplets.

題目如下：

Given the root of a binary tree, return an array of the largest value in each row of the tree (0-indexed).

題目如下：

Given two arrays, write a function to compute their intersection.

題目如下：

Write a SQL query for a report that provides the following information for each person in the Person table, regardless if there is an address for each of those people:

FirstName, LastName, City, State

題目如下：

Given two integers dividend and divisor, divide two integers without using multiplication, division and mod operator.

Return the quotient after dividing dividend by divisor.

The integer division should truncate toward zero, which means losing its fractional part. For example, truncate(8.345) = 8 and truncate(-2.7335) = -2.

題目如下：

And then read line by line: "PAHNAPLSIIGYIR"

Write the code that will take a string and make this conversion given a number of rows:

string convert(string s, int numRows);

題目如下：

Given a 32-bit signed integer, reverse digits of an integer.

題目如下：

Given a string s, find the length of the longest substring without repeating characters.