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
saketag007: 2018-09-11 10:56:25

easy bfs 0.07

tanardi gunawan: 2018-08-31 08:27:47

easy problem using string ac in 0,19s!!!

masterchef2209: 2018-08-24 13:11:26

Pretty Straightforward problem
wasted 3 hours trying different implementation for calculating shortest distance but error was in logic to check 'one digit difference' between prime numbers; *ultimate facepalm moment*
but still AC in 1 go :P

shivan11: 2018-07-26 18:36:20

Good bfs problem. Store the sieve of prime numbers beforehand so you dont have to calculate all the prime numbers for every test case.

kkislay20: 2018-06-30 08:26:10

OMG this problem...I don't know about you guys but this was a really nice problem. The bfs,graph,sieve and concept was really good. I was getting WA even though all my answers were correct but there was one testcase which was not giving correct ans...I dont know why, After hitting walls for few hours I replaced the memset with loop and got AC.If you want to know the test case..this was the one-
4241 6101
5099 7159
1559 9437
Correct ans- 5 5 4
My ans was- 5 5 5
And lastly I though I will be getting TLE but we have big enough time space.

dennislo: 2018-06-29 03:27:40

Good problem

nitish235: 2018-06-16 11:34:41

took 2 hrs to think this as bfs then got AC 0.15

aman9598: 2018-06-08 21:09:37

wrong testcases
1033 8179
correct output is 7

atharva_sarage: 2018-06-07 12:53:48

AC in first shot
must do bfs problem

flyingduchman_: 2018-05-12 19:57:17

BFS tag ... What is the graph ?
It's the puzzle, try to figure it out.
For attitude :I am a programmer, not a puzzle solver ,The graph is
conceptual and you can't see all vertices & edges as a first snapshot like many other problems.But the graph is describeable in gradual order. As first snapshot : you know the source vertex and it's neighbour vertices, destination vertex. Each vertex's
neighbour verties are = all prime number from the Set {All numbers i.e. each one is a permutation of source number with only one digit difference} . Cost of each edge = 1.
So, neighbour vertices of 1033 is = Prime numbers among( 1033...9033, 1133..1933, 1003...1093, 1030....1039) , for clearity (1_ _ _ ... 9 _ _ _, _0_ _ ... _9_ _, _ _ 0 _..._ _ 9_, _ _ _ 0... _ _ _ 9), '_' remain unchanged in the permutation.

Task : Find shortest path between source and destination vertex, if no path exists print "Impossible".

Last edit: 2018-05-12 19:59:56

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