Shortest path to reach one prime to other by changing single digit at…

Samsung D

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+// CPP program to reach a prime number from
+// another by changing single digits and
+// using only prime numbers.
+#include <bits/stdc++.h>
+
+using namespace std;
+
+class graph {
+	int V;
+	list<int>* l;
+public:
+	graph(int V)
+	{
+		this->V = V;
+		l = new list<int>[V];
+	}
+	void addedge(int V1, int V2)
+	{
+		l[V1].push_back(V2);
+		l[V2].push_back(V1);
+	}
+	int bfs(int in1, int in2);
+};
+
+// Finding all 4 digit prime numbers
+void SieveOfEratosthenes(vector<int>& v)
+{
+	// Create a boolean array "prime[0..n]" and initialize
+	// all entries it as true. A value in prime[i] will
+	// finally be false if i is Not a prime, else true.
+	int n = 9999;
+	bool prime[n + 1];
+	memset(prime, true, sizeof(prime));
+
+	for (int p = 2; p * p <= n; p++) {
+
+		// If prime[p] is not changed, then it is a prime
+		if (prime[p] == true) {
+
+			// Update all multiples of p
+			for (int i = p * p; i <= n; i += p)
+				prime[i] = false;
+		}
+	}
+
+	// Forming a vector of prime numbers
+	for (int p = 1000; p <= n; p++)
+		if (prime[p])
+			v.push_back(p);
+}
+
+// in1 and in2 are two vertices of graph which are
+// actually indexes in pset[]
+int graph::bfs(int in1, int in2)
+{
+	int visited[V];
+	memset(visited, 0, sizeof(visited));
+	queue<int> que;
+	visited[in1] = 1;
+	que.push(in1);
+	list<int>::iterator i;
+	while (!que.empty()) {
+		int p = que.front();
+		que.pop();
+		for (i = l[p].begin(); i != l[p].end(); i++) {
+			if (!visited[*i]) {
+				visited[*i] = visited[p] + 1;
+				que.push(*i);
+			}
+			if (*i == in2) {
+				return visited[*i] - 1;
+			}
+		}
+	}
+}
+
+// Returns true if num1 and num2 differ
+// by single digit.
+bool compare(int num1, int num2)
+{
+	// To compare the digits
+	string s1 = to_string(num1);
+	string s2 = to_string(num2);
+	int c = 0;
+	if (s1[0] != s2[0])
+		c++;
+	if (s1[1] != s2[1])
+		c++;
+	if (s1[2] != s2[2])
+		c++;
+	if (s1[3] != s2[3])
+		c++;
+
+	// If the numbers differ only by a single
+	// digit return true else false
+	return (c == 1);
+}
+
+int shortestPath(int num1, int num2)
+{
+	// Generate all 4 digit
+	vector<int> pset;
+	SieveOfEratosthenes(pset);
+
+
+	// Create a graph where node numbers are indexes
+	// in pset[] and there is an edge between two
+	// nodes only if they differ by single digit.
+	graph g(pset.size());
+	for (int i = 0; i < pset.size(); i++)
+		for (int j = i + 1; j < pset.size(); j++)
+			if (compare(pset[i], pset[j]))
+				g.addedge(i, j);	
+
+
+	// Since graph nodes represent indexes of numbers
+	// in pset[], we find indexes of num1 and num2.
+	int in1, in2;
+	for (int j = 0; j < pset.size(); j++)
+		if (pset[j] == num1)
+			in1 = j;
+	for (int j = 0; j < pset.size(); j++)
+		if (pset[j] == num2)
+			in2 = j;
+
+	return g.bfs(in1, in2);
+}
+
+// Driver code
+int main()
+{
+	int num1 = 1033, num2 = 8179;
+	cout << shortestPath(num1, num2);
+	return 0;
+}