POJ 3126 Prime Path (BFS digital processing), pojbfs

POJ 3126 Prime Path (BFS digital processing), pojbfs

Here are two 4-digit prime numbers, a. B. You can change the single-digit number of a each time. However, after changing the number, you still need to calculate how many times a must change to B.

The basic bfs pay attention to the number of processing on the line of a number, and then join all the prime numbers that can be changed by this prime number after a change know to get B

# Include <cstdio> # include <cstring> using namespace std; const int N = 10000; int p [N], v [N], d [N], q [N], a, B; void initPrime () {memset (v, 0, sizeof (v); for (int I = 2; I * I <N; ++ I) if (! V [I]) for (int j = I; I * j <N; ++ j) v [I * j] = 1; for (int I = 2; I <N; ++ I) p [I] =! V [I];} int bfs () {int c, t, le = 0, ri = 0; memset (v, 0, sizeof (v )); q [ri ++] = a, v [a] = 1, d [a] = 0; while (le <ri) {c = q [le ++]; if (c = B) return d [c]; for (int I = 1; I <N; I * = 10) {for (int j = 0; j <10; ++ j) // change the number of I-th orders of magnitude in c to j {if (I = 1000 & j = 0) continue; t = c/(I * 10) * I * 10 + I * j + c % I; if (p [t] &! V [t]) v [t] = 1, d [t] = d [c] + 1, q [ri ++] = t ;}}} return-1 ;}int main () {int cas; scanf ("% d", & cas); initPrime (); while (cas --) {scanf ("% d", & a, & B); if (a = bfs ())! =-1) printf ("% d \ n", a); else puts ("Impossible") ;}return 0 ;}

Prime Path

Description

The ministers of the cabinet were quite upset by the message from the Chief of Security stating that they wowould 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! Also 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.

1033
1733
3733
3739
3779
8779
8179

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.

Input

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 ).

Output

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

Sample Input

31033 81791373 80171033 1033

Sample Output

670