Test case generator for Tree using Disjoint-Set Union

In this article, we will generate test cases such that given set edges form a Tree. Below are the two conditions of the Tree:

It should have one less edge than the number of vertices.
There should be no cycle in it.

Approach: The idea is to run a loop and add one edge each time that is generated randomly, and for adding each edge we will check whether it is forming cycle or not. We can ensure that cycle is present or not with the help of Disjoint-Set Union. If adding any edges form cycle then ignore the current edges and generate the new set of edges. Else print the edges with randomly generated weight.

Below is the implementation of the above approach:

C++

// C++ implementation to generate 
// test-case for the Tree 
  
#include <bits/stdc++.h> 
using namespace std; 
  
typedef long long int ll; 
#define fast ios_base::sync_with_stdio(false); 
#define MOD 1000000007 
  
// Maximum Number Of Nodes 
#define MAXNODE 10; 
  
// Maximum Number Of testCases 
#define MAXT 10; 
  
// Maximum weight 
#define MAXWEIGHT 100; 
  
// Function for the path 
// compression technique 
ll find(ll parent[], ll x) 
{ 
    // If parent found 
    if (parent[x] == x) 
        return x; 
  
    // Find parent recursively 
    parent[x] = find(parent, parent[x]); 
  
    // Return the parent node of x 
    return parent[x]; 
} 
  
// Function to compute the union 
// by rank 
void merge(ll parent[], ll size[], 
           ll x, ll y) 
{ 
    ll r1 = find(parent, x); 
    ll r2 = find(parent, y); 
  
    if (size[r1] < size[r2]) { 
        parent[r1] = r2; 
        size[r2] += size[r1]; 
    } 
    else { 
        parent[r2] = r1; 
        size[r1] += size[r2]; 
    } 
} 
  
// Function to generate the 
// test-cases for the tree 
void generate() 
{ 
    ll t; 
    t = 1 + rand() % MAXT; 
  
    // Number of testcases 
    cout << t << "\n"; 
    while (t--) { 
  
        // for 2<=Number of Nodes<=MAXNODE 
  
        // Randomly generate number of edges 
        ll n = 2 + rand() % MAXNODE; 
        ll i; 
        cout << n << "\n"; 
        ll parent[n + 1]; 
        ll size[n + 1]; 
  
        // Initialise parent and 
        // size arrays 
        for (i = 1; i <= n; i++) { 
            parent[i] = i; 
            size[i] = 1; 
        } 
  
        vector<pair<ll, ll> > Edges; 
        vector<ll> weights; 
  
        // Now We have add N-1 edges 
        for (i = 1; i <= n - 1; i++) { 
            ll x = 1 + rand() % n; 
            ll y = 1 + rand() % n; 
  
            // Find edges till it does not 
            // forms a cycle 
            while (find(parent, x) 
                   == find(parent, y)) { 
  
                x = 1 + rand() % n; 
                y = 1 + rand() % n; 
            } 
  
            // Merge the nodes in tree 
            merge(parent, size, x, y); 
  
            // Store the current edge and weight 
            Edges.push_back(make_pair(x, y)); 
            ll w = 1 + rand() % MAXWEIGHT; 
            weights.push_back(w); 
        } 
  
        // Print the set of edges 
        // with weight 
        for (i = 0; i < Edges.size(); i++) { 
  
            cout << Edges[i].first << " "
                 << Edges[i].second; 
            cout << " " << weights[i]; 
            cout << "\n"; 
        } 
    } 
} 
  
// Driver Code 
int main() 
{ 
    // Uncomment the below line to store 
    // the test data in a file 
    // freopen ("output.txt", "w", stdout); 
  
    // For random values every time 
    srand(time(NULL)); 
  
    fast; 
  
    generate(); 
} 

Output:

Time Complexity: O(N*logN)
Auxiliary Space: O(1)

My Personal Notes

C++

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