Algorithm


Problem link- https://www.spoj.com/problems/PPATH/

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.

    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.

Example

Input:
3
1033 8179
1373 8017
1033 1033

Output:
6
7
0

 

Code Examples

#1 Code Example with C++ Programming

Code - C++ Programming

#include <iostream>
#include <cstdio>
#include <vector>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <sstream>
#include <map>
#include <list>
#include <queue>
#include <utility>

using namespace std;

struct node{
	int val;
	int count;
	node(int x,int y):val(x),count(y){};
};

bool isPrime[10000];
bool isVisited[10000];
queue<node> q;

void prime(){
	isPrime[0]=false;
	isPrime[1]=false;
	for(int i=2;i<=(int)sqrt(9999);i++){
		if(isPrime[i]){
			for(int j=i*i;j<=9999;j+=i){
				isPrime[j]=false;
			}
		}
	}
}

int getcombinations(int start,int end,int count){
	isVisited[start]=true;
	stringstream ss;
	ss<<start;
	string s,t;
	s=ss.str();
	for(int i=0;i<4;i++){
		t=s;
		for(char j='0';j<='9';j++){
			if(i==0&&j=='0')continue;
			t[i]=j;
			stringstream ss1(t);
			int st;
			ss1>>st;
			if(st==end){
				return count;
			}
			if(isPrime[st]&&(isVisited[st]==false)){
				isVisited[st]=true;
				q.push(node(st,count));
			}
		}
	}
	return -1;
}

int getpath(int start,int end){
	int count=0;
	q.push(node(start,count));
	while(!q.empty()){
		node temp=q.front();
		q.pop();
		int result=getcombinations(temp.val,end,(temp.count)+1);
		if(result!=-1){
			return result;
		}
	}
	return -1;
}

int main(){
	memset(isPrime,true,sizeof(isPrime));
	prime();
	int t;
	scanf("%d",&t);
	while(t--){
		q=queue<node>();
		memset(isVisited,false,sizeof(isVisited));
		int start,end;
		scanf("%d%d",&start,&end);
		if(start==end){
			printf("0\n");
			continue;
		}
		int finalresult=getpath(start,end);
		if(finalresult!=-1){
			printf("%d\n",finalresult);
		}
		else{
			printf("Impossible\n");
		}
	}
}
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Input

x
+
cmd
3
1033 8179
1373 8017
1033 1033

Output

x
+
cmd
6
7
0
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SPOJ Solution-Prime Path-Solution in C, C++, Java, Python

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