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");
}
}
}Input
1033 8179
1373 8017
1033 1033
Output
7
0
Demonstration
SPOJ Solution-Prime Path-Solution in C, C++, Java, Python