PPATH - Prime Path

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.

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.


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


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


1033 8179
1373 8017
1033 1033


hide comments
jrseinc: 2020-08-21 09:10:16

It is such a good question. I had no idea this type of question can be solved using BFS, worth solving.

Last edit: 2020-08-21 09:10:35
gnomegeek: 2020-08-04 14:19:54

AC in one go !!!!! Main task is to prepare the adj list :)

anonymousamigo: 2020-08-03 11:07:54

BFS will be good way to solve

noobiesag_0206: 2020-07-18 20:48:27

Beautiful problem :)

kumar_anubhav: 2020-07-03 14:10:00

Good Problem !!
SSSD variant on src to dest with constraint that only one digit will change :)

adikrmishra_1: 2020-06-24 05:25:39

for solution go to this link
*** Edit : no spoil allowed ***

Last edit: 2020-06-24 09:11:11
mercuto: 2020-06-12 12:01:45

Tourist power activated
AC in one Go!!!!

nandadeep_2001: 2020-06-11 18:24:36

a gentle reminder to all pls stop posting comments like "AC in one go!!" ... etc this session is for doubt clarification not for expressing your personal feelings

Last edit: 2020-06-11 18:28:17
kgargdunregret: 2020-06-04 21:03:14

one of the best questions ever

chaudhary_19: 2020-04-22 19:45:38

There is no impossible case

Added by:overwise
Time limit:2s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO NODEJS PERL6 VB.NET
Resource:ACM ICPC NWERC 2006