Path Through Graph

Author: keshavsingh3197

Codevita/2020/Zone 2/Path Through Graph.cpp

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+/*
+
+Path Through Graph
+Problem Description
+You are given two natural numbers. Imagine these natural numbers as nodes on a graph. On this graph, a number is connected to its largest factor other than itself. You have to find the shortest path between them and print the number of edges on that path.
+
+If the two numbers do not have any common factor, then construct a path through 1. For better understanding refer to the examples below:
+
+Example 1: Input numbers: 2 4
+The numbers are directly connected as follows on the graph. 2 is the largest factor of 4, other than itself.
+We can also see that there is only on edge between them.
+4 <--> 2
+Hence the number of edges in shortest path is 1.
+Output: 1
+
+Example 2: Input numbers: 18 19
+The graph for number 18 and 19 will look like this. Here we have 4 edges in the path.
+18 <--> 9 <--> 3 <--> 1 <--> 19
+Output: 4
+
+Example 3: Input numbers: 9 9
+The number of edges in shortest path is zero since the numbers correspond to the same node.
+Output: 0
+
+Constraints
+0 < M, N <= 10 ^ 9
+
+Input
+Single line containing two space separated integers M, N
+
+Output
+Number of edges in the shortest path.
+
+Time Limit
+1
+
+Examples
+Example 1
+
+Input
+
+15689 28
+
+Output
+
+5
+
+Explanation :
+
+The graph for number 15689 and 28 will look like this.
+
+Since we know that largest factor of 15689 other than itself is 541.
+
+Since 541 is a prime number, it’s largest factor other than itself is 1.
+
+For number 28, it’s largest factor other than itself is 14.
+
+Largest factor of 14, other than itself is 7.
+
+Since 7 is a prime number, it’s largest factor other than itself is 1.
+
+So, the graph will look like this:
+
+15689 <--> 541 <--> 1 <--> 7 <--> 14 <--> 28
+
+Since there are 5 edges in this graph, output will be 5.
+
+Example 2
+
+Input
+
+16 4
+
+Output
+
+2
+
+Explanation :
+
+The graph for number 16 and 4 will look like this.
+
+Since we know that largest factor of 16 other than itself is 8.
+
+Largest factor of 8 other than itself is 4. That’s the other input number, so we will stop here.
+
+So, the graph will look like this:
+
+16<-->8<-->4
+
+Since there are 2 edges in this graph, output will be 2.
+
+
+*/
+
+
+#include <bits/stdc++.h>
+using namespace std;
+                     
+#define int             long long
+#define endl            '\n'
+
+int get(int x)
+{
+    for(int i=2;i*i<=x;i++)
+    {
+        if(x%i==0)return x/i;
+    }
+    return 1;
+}
+
+void sol()
+{   
+    int x,y;
+    cin>>x>>y;
+    if(x<y)swap(x,y);
+    if(x==y){cout<<0;return;}
+    map<int,int> m;
+    
+    int c=0;
+    while(x!=1)
+    {
+        c++;
+        x=get(x);
+        m[x]=c;
+    } 
+    c=0;
+    while(!m.count(y))
+    {
+        c++;
+        y=get(y);
+    }
+    cout<<c+m[y];
+}
+int32_t main()
+{   
+ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
+    sol();
+    return 0;
+}   

Codevita/2020/Zone 2/Path Through Graph.py

@@ -0,0 +1,125 @@
+'''
+Path Through Graph
+Problem Description
+You are given two natural numbers. Imagine these natural numbers as nodes on a graph. On this graph, a number is connected to its largest factor other than itself. You have to find the shortest path between them and print the number of edges on that path.
+
+If the two numbers do not have any common factor, then construct a path through 1. For better understanding refer to the examples below:
+
+Example 1: Input numbers: 2 4
+The numbers are directly connected as follows on the graph. 2 is the largest factor of 4, other than itself.
+We can also see that there is only on edge between them.
+4 <--> 2
+Hence the number of edges in shortest path is 1.
+Output: 1
+
+Example 2: Input numbers: 18 19
+The graph for number 18 and 19 will look like this. Here we have 4 edges in the path.
+18 <--> 9 <--> 3 <--> 1 <--> 19
+Output: 4
+
+Example 3: Input numbers: 9 9
+The number of edges in shortest path is zero since the numbers correspond to the same node.
+Output: 0
+
+Constraints
+0 < M, N <= 10 ^ 9
+
+Input
+Single line containing two space separated integers M, N
+
+Output
+Number of edges in the shortest path.
+
+Time Limit
+1
+
+Examples
+Example 1
+
+Input
+
+15689 28
+
+Output
+
+5
+
+Explanation :
+
+The graph for number 15689 and 28 will look like this.
+
+Since we know that largest factor of 15689 other than itself is 541.
+
+Since 541 is a prime number, it’s largest factor other than itself is 1.
+
+For number 28, it’s largest factor other than itself is 14.
+
+Largest factor of 14, other than itself is 7.
+
+Since 7 is a prime number, it’s largest factor other than itself is 1.
+
+So, the graph will look like this:
+
+15689 <--> 541 <--> 1 <--> 7 <--> 14 <--> 28
+
+Since there are 5 edges in this graph, output will be 5.
+
+Example 2
+
+Input
+
+16 4
+
+Output
+
+2
+
+Explanation :
+
+The graph for number 16 and 4 will look like this.
+
+Since we know that largest factor of 16 other than itself is 8.
+
+Largest factor of 8 other than itself is 4. That’s the other input number, so we will stop here.
+
+So, the graph will look like this:
+
+16<-->8<-->4
+
+Since there are 2 edges in this graph, output will be 2.
+
+'''
+from collections import defaultdict
+def greatest_divisor_n(n):
+    if n % 2 == 0:             
+        return n//2
+    else:
+        i = 3                   
+        while i * i <= n:
+            if n % i  == 0:
+                return n//i
+            i = i + 2
+    return 1
+def path_of_graph(var1,var2):
+    map_d=defaultdict(int)
+    if var1==var2:
+        return 0
+    count=0
+    # swap
+    if var1<var2:
+        temp=var1
+        var1=var2
+        var2=temp
+    count=0
+    while var1!=1:
+        var1=greatest_divisor_n(var1)
+        count+=1
+        map_d[var1]=count
+    count=0
+    while not map_d[var2]:
+        var2=greatest_divisor_n(var2)
+        count+=1
+    return  map_d[var2]+count
+        
+var1,var2=map(int,input().split())
+print(path_of_graph(var1,var2))