There are n lockers in a hallway numbered sequentially from 1 to n. Initially, all the locker doors are closed. You make n passes by the lockers, each time starting with locker #1. On the ith pass, i = 1, 2, ..., n, you toggle the door of every ith locker: if the door is closed, you open it, if it is open, you close it. For example, after the first pass every door is open; on the second pass you only toggle the even-numbered lockers (#2, #4, ...) so that after the second pass the even doors are closed and the odd ones are opened; the third time through you close the door of locker #3 (opened from the first pass), open the door of locker #6 (closed from the second pass), and so on. After the last pass, which locker doors are open and which are closed? How many of them are open?
Your task is write a program to output How many doors are open after the last pass? Assumptions all doors are closed at first.
Input
a positive numbers n, total doors. n<=100000
Output
a positive numbers ，the total of doors opened after the last pass.
Sample Input
10
Sample Output
3
Solution:
ALGORITHM Lockerdoors(n)
//Solve the Lockerdoors problem
//Input: An positive interger n
//Output: An nonnegative interger m of the total of doors opened after the last pass
for x←1 to n do A[x] = true
for i←2 to n do
for j←i to n do
if j mod i = 0 do
A[j]←not A[j]
m←0
for i←1 to n do
if A[i] do
m←m+1
return m
这是一个比较直接的解决的算法.算法时间复杂度是θ(n^2)