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Print the node with the maximum degree in the prufer sequence
The node with the greatest degree within the Prufer grouping is the one that appears most often within the grouping. To discover it, we emphasise it through grouping and keep track of the frequencies of each hub. Once we have the frequencies, we select the hub with the most noteworthy recurrence as the hub with the maximum degree. This hub speaks to the leaf within the labelled tree. The Prufer grouping may be a one-of-a-kind representation of a labelled tree, where the maximum degree hub compares to the leaf that's included final amid the development preparation. By distinguishing this hub, we are able to pick up bits of knowledge about the structure and properties of the initial tree.
Methods Used
Frequency counting
Set Representation
Frequency Counting
Within the setting of finding the hub with the most extreme degree in a Prufer grouping, recurrence checking includes effectively emphasising through the grouping and tallying the events of each hub. By keeping track of how numerous times each hub shows up, we will decide which hub has the most noteworthy recurrence, showing the greatest degree. This approach permits us to recognise the hub that speaks to the leaf added last amid the development preparation. By effectively following and comparing frequencies, we are able to proficiently pinpoint the hub with the greatest degree, picking up profitable experiences in the structure of the initial tree.
Algorithm
Begin by characterising a purge outline or cluster to store the frequencies of each node.
Iterate through the Prufer grouping, one component at a time.
For each component, check if it exists within the map or array.
If it exists, increase its recurrence by 1.
If it doesn't exist, include it in the map or array with a beginning recurrence of 1.
Once the emphasis is total, initialise factors for maxDegree and maxNode.
Iterate through the map or array and compare the frequencies of each node.
If the recurrence is more noteworthy than maxDegree, upgrade maxDegree to the modern recurrence and maxNode to the comparing node.
At the conclusion of the cycle, maxNode will contain the hub to the greatest degree.
Print or utilise the value of maxNode as required.
Example
#include <iostream>
#include <vector>
#include <map>
int findMaxDegree(const std::vector<int>& prufer) {
std::map<int, int> freq; // Map to store frequencies
for (int node : prufer) {
freq[node]++;
}
int maxDegree = 0;
int maxNode = -1;
for (const auto& entry : freq) {
if (entry.second > maxDegree) {
maxDegree = entry.second;
maxNode = entry.first;
}
}
return maxNode;
}
int main() {
std::vector<int> prufer = {2, 3, 1, 0, 2, 4}; // Example Prufer sequence
int maxNode = findMaxDegree(prufer);
std::cout << "Node with maximum degree: " << maxNode << std::endl;
return 0;
}
Output
Node with maximum degree: 2
Set Representation
Within the setting of recognising the hub with the greatest degree in a Prufer arrangement, set representation includes changing over the Prufer grouping into a set information structure. This change makes a difference. You can evacuate copies and get a one-of-a kind set of hubs displayed within the grouping. By repeating through this set, we will number the events of each hub within the unique arrangement. Ultimately, we are ready to decide the node with the most extreme degree by selecting the hub with the most elevated check. Set representation streamlines the method by giving a brief and effective way to analyse the nodes' frequencies within the Prufer arrangement.
Algorithm
Initialise a purge set called "uniqueNodes" to store the special hubs from the Prufer sequence.
Iterate through each component "hub" within the Prufer sequence.
a. Include "hub" in the "uniqueNodes" set.
Initialise a lexicon called "nodeCount" to keep track of the number of each node.
Iterate through each component "hub" within the "uniqueNodes" set.
a. Set the number of "hub" in "nodeCount" to the number of events of "hub" within the Prufer sequence.
Initialise factors "maxDegreeNode" and "maxDegreeCount" to store the hub with the maximum degree and its tally, respectively.
Iterate through each key-value combination "node"-"count" within the "nodeCount" dictionary.
a. In the event that the tally is more noteworthy than maxDegreeCount,"
i. Overhaul "maxDegreeNode" to the current "node".
ii. Upgrade "maxDegreeCount" to the current "count".
"maxDegreeNode" speaks to the hub with the greatest degree within the Prufer arrangement.
Example
#include <iostream>
#include <map>
#include <set>
#include <vector>
int main() {
std::vector<int> pruferSeq = {1, 2, 3, 4, 3, 2};
std::set<int> uniqueNodes;
std::map<int, int> nodeCount;
int maxDegreeNode = -1;
int maxDegreeCount = -1;
// Step 1: Initialize an empty set and iterate through the Prufer sequence
for (int node : pruferSeq) {
uniqueNodes.insert(node);
}
// Step 2: Count the occurrences of each node in the Prufer sequence using a dictionary
for (int node : pruferSeq) {
nodeCount[node]++;
}
// Step 3: Find the node with the maximum degree in the Prufer sequence
for (const auto& pair : nodeCount) {
if (pair.second > maxDegreeCount) {
maxDegreeNode = pair.first;
maxDegreeCount = pair.second;
}
}
// Step 4: Print the results
std::cout << "Unique nodes:";
for (int node : uniqueNodes) {
std::cout << " " << node;
}
std::cout << std::endl;
std::cout << "Node count:" << std::endl;
for (const auto& pair : nodeCount) {
std::cout << "Node " << pair.first << ": " << pair.second << std::endl;
}
std::cout << "Node with the maximum degree: " << maxDegreeNode << std::endl;
return 0;
}
Output
Unique nodes: 1 2 3 4 Node count: Node 1: 1 Node 2: 2 Node 3: 2 Node 4: 1 Node with the maximum degree: 2
Conclusion
This article clarifies how to recognise the hub with the greatest degree in a Prufer grouping, which speaks to an interesting representation of a labelled tree. The article talks about two strategies: recurrence checking and set representation. In recurrence checking, the events of each hub within the Prufer arrangement are numbered to determine the hub with the most noteworthy recurrence, showing the most extreme degree. In set representation, the Prufer arrangement is changed over into a set to get an interesting set of hubs, and their frequencies are calculated. The hub with the most noteworthy number represents the greatest degree within the Prufer arrangement. Code cases are given to illustrate these strategies.
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