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,
— 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 8179The 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.
Input: 3 1033 8179 1373 8017 1033 1033 Output: 6 7 0
good question ,,beginners must give it a try
nice problem ....test cases are weak...
very good application of BFS :)
Ac in one go!
Accepted in one go, use bfs and sieve :-)
Pretty sweet ;)
NICE BFS + BIT TRICKS + Sieve of eratosthenes :)Last edit: 2017-03-04 15:20:10
nice one , Hint: Convert to graph
30 minutes. AC in one go!
enjoyed solving the problem ,very good question ,, it took some time ,, my 100th on spoj .............