I attended an interview with an IT company today, but I didn't get two open-ended questions. Who can help me explain the answer and the truth?

A: After switching 100 times, the locks are 1, 4, 9, 16... 100, and * * * 10.

If K locks are arranged in the corridor in turn, then after the K-th pass, there are locks 1, 4, 9, 16 ..., | sqrt (k) | locks have been opened.

Proof: 100 locks are marked as S 1, S2, S3, ..., Si, ..., respectively.

S 1 only switches in 1 pass;

If I is a prime number, si only switches at 1 and I times, and the switching times are even;

If I is a compound of non-square numbers, it can always be decomposed into I = m * n = q * p =...= r * u (m! =n，q！ =p，....，r！ =u), si is only at time 1, i, m, n, q, p, ..., r, u, and the switching times are even;

If I is a square number, I = m * n = q * p =...= r * u = x * x (m! =n，q！ =p，....，r！ =u), si is only at 1, i, m, n, q, p, ..., r, u, x times, and the switching times are odd;

The lock head is locked before switching, and it is still locked after switching several times;

Before switching, the lock is locked, and after odd switching, the lock becomes open.

Therefore, only when I is a square number will the lock be opened.

Algorithm: From the operation steps of solving puzzles, we can get inspiration and get the square number in this way.

Step 1: Set the status value of the number to-1;

Step 2: Make all numbers 1, 2, 3, ..., 100 according to this module, and change the state if the result is 0;

Step 3: Print out the number with the status value of 1.

Procedure: The following is the procedure for finding the square of the interval [1, 100] by this method. The code runs successfully on vc++6.0 platform.

/* * Author: Cartography

Date: February 2007.15

FindSquareNumber。 cpp**/

# include & ltiostream & gt

# include & ltprocess.h & gt

Use namespace std

void main()

{

int a；

int I；

for(I = 1； I<= 100; i++)

{

a =- 1；

for(int j = 1； j & lt= I； j++)

{

If (i%j==0)

a =(- 1)* a；

}

If (a== 1)

Cout & lt& lt "square number:"<& lt me<& ltendl.

}

System ("suspended");

}