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
javafreak: 2017-09-28 15:41:38

AC in 0.00s :) Pre populate the prime array using sieve of eratosthenes, next use bfs by considering each number as a node, and prime numbers reachable from it as connected edges , don't form a graph beforehand , that is not necessary, just keep on connecting edges on the go...

jaykay12: 2017-09-26 10:23:59

AC in one Go. :) Nice Implementation of BFS :)

parthendo: 2017-09-18 20:45:07

AC in one go ;)

vishesh197: 2017-09-02 07:56:09

just think it as a graph with prime number as nodes of graph and two nodes will have a edge only if they have 1 digit different.Use bfs to find shortest path
AC in 4th go...

aronzx: 2017-08-24 11:51:58

Nice problem teaching 2 concepts at once. AC in one go !

rohit1507: 2017-07-24 10:26:28

Easy. Think Simple. Nice!!

nikhil2504: 2017-07-10 17:48:59

AC 0.0 <3

leafbebop: 2017-06-02 14:27:04

Note: No leading Zero allowed. I do not understand why...

akashmandal21: 2017-05-24 20:34:16

Took a long time but AC in a single shot :)
Though implementation is not that easy!!!

Last edit: 2017-05-24 20:36:30
akash619j: 2017-05-02 14:21:37

Got AC in first go! Was fearing a TLE :p

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