机试小课堂丨搜索周·例题讲解②《Prime Path》

2021-01-25 00:27 作者:苏世考研 0人读过 | 我要投稿

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公主号：苏世学社考研苏世计算机考研

Prime Path

Description

The ministers of the cabinet were quite upset by the message from the Chief of Security stating that they would all have to change the four-digit room numbers on their offices.

— It is a matter of security to change such things every now and then, to keep the enemy in the dark.

— But look, I have chosen my number 1033 for good reasons. I am the Prime minister, you know!

— I know, so therefore your new number 8179 is also a prime. You will just have to paste four new digits over the four old ones on your office door.

— No, it’s not that simple. Suppose that I change the first digit to an 8, then the number will read 8033 which is not a prime!

— I see, being the prime minister you cannot stand having a non-prime number on your door even for a few seconds.

— Correct! So I must invent a scheme for going from 1033 to 8179 by a path of prime numbers where only one digit is changed from one prime to the next prime.

Now, the minister of finance, who had been eavesdropping, intervened.

— No unnecessary expenditure, please! I happen to know that the price of a digit is one pound.

— Hmm, in that case I need a computer program to minimize the cost. You don't know some very cheap software gurus, do you?

— In fact, I do. You see, there is this programming contest going on... Help the prime minister to find the cheapest prime path between any two given four-digit primes! The first digit must be nonzero, of course. Here is a solution in the case above.

1033

1733

3733

3739

3779

8779

8179

The cost of this solution is 6 pounds. Note that the digit 1 which got pasted over in step 2 can not be reused in the last step – a new 1 must be purchased.

Input

One line with apositive number: the number of test cases (at most 100). Then for each testcase, one line with two numbers separated by a blank. Both numbers arefour-digit primes (without leading zeros).

Output

One line for each case,either with a number stating the minimal cost or containing the wordImpossible.

Sample Input

1033 8179

1373 8017

1033 1033

Sample Output

答案

①读题:

给出两个四位数a和b，将a变成b需要多少步，要求每个只能改变a的某一位数，即改变后的数和改变前的数只有一位不同，并且每次改变后的数都是素数，且不能重复，求从a变到b最少需要的次数，无法变换就输出Impossible。

②想出思路：

筛选素数+BFS，枚举每一位数字进行修改，如果是素数就进入队列，循环出队队列。