最大独立集问题

2024-04-21 19:42:06 114

当独立集是所有二叉树节点的子集，而该子集中的任何两个节点之间都没有边缘时。

现在，从一组元素中，我们将找到最长的独立集合。即，如果将元素用于形成二叉树，则所有最大子集，其中该子集中没有元素相互连接。

输入输出

Input:
A binary tree.Output:
Size of the Largest Independent Set is: 5

算法

longSetSize(root)

在这种算法中，将形成二叉树，该树的每个节点将保存数据和setSize。

输入- 二叉树的根节点。

输出-最长集合的大小。

Begin
   if root = φ, then
      return 0
   if setSize(root) ≠ 0, then
      setSize(root)
   if root has no child, then
      setSize(root) := 1
      return setSize(root)
   setSizeEx := longSetSize(left(root)) + longSetSize(right(root)) //excluding root
   setSizeIn := 1

   if left child exists, then
      setSizeIn := setSizeIn + longSetSize(left(left(root))) + longSetSize(left(right(root)))

   if right child exists, then
      setSizeIn := setSizeIn + longSetSize(right(left(root))) + longSetSize(right(right(root)))

   if setSizeIn > setSizeEx, then
      setSize(root) := setSizeIn
   else
      setSize(root) := setSizeEx

   return setSize(root)
End

示例

#include <iostream>
using namespace std;

struct node {
   int data;
   int setSize;
   node *left, *right;
};

int longSetSize(node *root) {
   if (root == NULL)
      return 0;

   if (root->setSize != 0)
      return root->setSize;

   if (root->left == NULL && root->right == NULL)    //when there is no child
      return (root->setSize = 1);

   //设置大小独占根是设置左边的大小和设置右边的大小

   int setSizeEx = longSetSize(root->left) + longSetSize(root->right);
   int setSizeIn = 1;             //inclusive root node

   if (root->left)               //if left sub tree is present
      setSizeIn += longSetSize(root->left->left) + longSetSize(root->left->right);

   if (root->right)                //if right sub tree is present
      setSizeIn += longSetSize(root->right->left) +longSetSize(root->right->right);
   root->setSize = (setSizeIn>setSizeEx)?setSizeIn:setSizeEx;

   return root->setSize;
}

struct node* getNode(int data) {          //create a new node with given data
   node* newNode = new node;
   newNode->data = data;
   newNode->left = newNode->right = NULL;
   newNode->setSize = 0;

   return newNode;
}

int main() {
   node *root = getNode(20);
   root->left = getNode(8);
   root->left->left = getNode(4);
   root->left->right = getNode(12);
   root->left->right->left = getNode(10);
   root->left->right->right = getNode(14);
   root->right = getNode(22);

   root->right->right = getNode(25);
   cout << "Size of the Largest Independent Set is: " << longSetSize(root);
}

输出结果

Size of the Largest Independent Set is − 5

最大独立集问题

输入输出

算法

示例

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