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();
}

Python3

# Python3 implementation to generate
# test-case for the Tree
import random

# Maximum Number Of Nodes
MAXNODE = 10

# Maximum Number Of testCases
MAXT = 10

# Maximum weight
MAXWEIGHT = 100

# Function for the path
# compression technique
def find(parent, 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
def merge(parent, size, x, y):
    r1 = find(parent, x)
    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
def generate():

    # Number of testcases
    t = random.randint(1, MAXT)
    print(t)
    for _ in range(t):
        # for 2<=Number of Nodes<=MAXNODE

        # Randomly generate number of edges
        n = random.randint(2, MAXNODE)
        print(n)
        parent = [i for i in range(n + 1)]
        size = [1 for _ in range(n + 1)]
        Edges = []
        weights = []

        # Now We have add N-1 edges
        for i in range(n - 1):
            x = random.randint(1, n)
            y = random.randint(1, n)

            # Find edges till it does not
            # forms a cycle
            while find(parent, x) == find(parent, y):
                x = random.randint(1, n)
                y = random.randint(1, n)

            # Merge the nodes in tree
            merge(parent, size, x, y)

            # Store the current edge and weight
            Edges.append((x, y))
            w = random.randint(1, MAXWEIGHT)
            weights.append(w)

        # Print the set of edges
        # with weight
        for i in range(len(Edges)):
            print(Edges[i][0], Edges[i][1], weights[i])

# Driver Code
if __name__ == "__main__":

    # Uncomment the below line to store
    # the test data in a file
    # open("output.txt", "w").close()
    # open("output.txt", "w").write(generate())

    # For random values every time
    random.seed(None)

    generate()

# This code is contributed by Potta Lokesh

Output:

1
10
4 2 67
8 3 64
6 5 31
7 6 77
8 2 64
9 2 44
5 9 10
1 6 71
10 7 32

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