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
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 .............
Very Good Question!!
Can someone please explain me the line - "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."