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Minimalus apsikeitimas reikalingas norint konvertuoti dvejetainį medį į dvejetainį paieškos medį

Duotas masyvas arr[] kuri reiškia a Pilnas dvejetainis medis y. jei indeksas i yra tėvas indeksas 2*i + 1 yra paliktas vaikas ir indeksas 2*i + 2 yra teisingas vaikas. Užduotis yra surasti minimumas skaičius apsikeitimo sandoriais reikia konvertuoti į a Dvejetainis paieškos medis.

Pavyzdžiai:  

Įvestis: arr[] = [5 6 7 8 9 10 11]
Išvestis: 3
Paaiškinimas:
Duoto masyvo dvejetainis medis:



Minimalus apsikeitimo poreikis, norint konvertuoti dvejetainį medį į dvejetainį paieškos medį-1' title=

1 apsikeitimas: sukeiskite 8 mazgą su 5 mazgu.
2 keitimas: sukeiskite 9 mazgą su 10 mazgu.
3 keitimas: sukeiskite 10 mazgą su 7 mazgu.

Taigi, norint gauti žemiau esantį dvejetainį paieškos medį, reikia atlikti mažiausiai 3 apsikeitimo sandorius:

kiek yra filmų apie neįmanomą misiją
Minimalus apsikeitimo poreikis, norint konvertuoti dvejetainį medį į dvejetainį paieškos medį-3' loading='lazy' title=


Įvestis: arr[] = [1 2 3]
Išvestis: 1
Paaiškinimas:
Duoto masyvo dvejetainis medis:

Minimalus apsikeitimo poreikis, norint konvertuoti dvejetainį medį į dvejetainį paieškos medį-2' loading='lazy' title=

Pakeitę 1 mazgą 2 mazgu, gaukite toliau pateiktą dvejetainės paieškos medį:

Minimalus apsikeitimo poreikis, norint konvertuoti dvejetainį medį į dvejetainį paieškos medį-4' loading='lazy' title=

Prieiga:

css pabrauktas tekstas

Idėja yra pasinaudoti tuo įsakymo perėjimas Dvejetainis paieškos medis yra didėja jų vertės tvarka. 
Taigi suraskite įsakymo perėjimas dvejetainio medžio ir saugokite jį masyve ir stengtis rūšiuoti masyvas. The minimalus apsikeitimo sandorių skaičius, reikalingas norint surūšiuoti masyvą bus atsakymas.

C++
// C++ program for Minimum swap required // to convert binary tree to binary search tree #include   using namespace std; // Function to perform inorder traversal of the binary tree // and store it in vector v void inorder(vector<int>& arr vector<int>& inorderArr int index) {    int n = arr.size();    // If index is out of bounds return  if (index >= n)  return;  // Recursively visit left subtree  inorder(arr inorderArr 2 * index + 1);    // Store current node value in vector  inorderArr.push_back(arr[index]);    // Recursively visit right subtree  inorder(arr inorderArr 2 * index + 2); } // Function to calculate minimum swaps  // to sort inorder traversal int minSwaps(vector<int>& arr) {  int n = arr.size();  vector<int> inorderArr;    // Get the inorder traversal of the binary tree  inorder(arr inorderArr 0);    // Create an array of pairs to store value  // and original index  vector<pair<int int>> t(inorderArr.size());  int ans = 0;    // Store the value and its index  for (int i = 0; i < inorderArr.size(); i++)  t[i] = {inorderArr[i] i};    // Sort the pair array based on values   // to get BST order  sort(t.begin() t.end());    // Find minimum swaps by detecting cycles  for (int i = 0; i < t.size(); i++) {    // If the element is already in the   // correct position continue  if (i == t[i].second)  continue;    // Otherwise perform swaps until the element  // is in the right place  else {    // Swap elements to correct positions  swap(t[i].first t[t[i].second].first);  swap(t[i].second t[t[i].second].second);  }    // Check if the element is still not  // in the correct position  if (i != t[i].second)  --i;     // Increment swap count  ans++;  }    return ans; } int main() {    vector<int> arr = { 5 6 7 8 9 10 11 };  cout << minSwaps(arr) << endl; } 
Java
// Java program for Minimum swap required // to convert binary tree to binary search tree import java.util.Arrays; class GfG {    // Function to perform inorder traversal of the binary tree  // and store it in an array  static void inorder(int[] arr int[] inorderArr   int index int[] counter) {  int n = arr.length;    // Base case: if index is out of bounds return  if (index >= n)  return;    // Recursively visit left subtree  inorder(arr inorderArr 2 * index + 1 counter);    // Store current node value in the inorder array  inorderArr[counter[0]] = arr[index];  counter[0]++;    // Recursively visit right subtree  inorder(arr inorderArr 2 * index + 2 counter);  }  // Function to calculate minimum swaps   // to sort inorder traversal  static int minSwaps(int[] arr) {  int n = arr.length;  int[] inorderArr = new int[n];  int[] counter = new int[1];    // Get the inorder traversal of the binary tree  inorder(arr inorderArr 0 counter);    // Create an array of pairs to store the value   // and its original index  int[][] t = new int[n][2];  int ans = 0;    // Store the value and its original index  for (int i = 0; i < n; i++) {  t[i][0] = inorderArr[i];  t[i][1] = i;  }    // Sort the array based on values to get BST order  Arrays.sort(t (a b) -> Integer.compare(a[0] b[0]));    // Find minimum swaps by detecting cycles  boolean[] visited = new boolean[n];    // Iterate through the array to find cycles  for (int i = 0; i < n; i++) {    // If the element is already visited or in  // the correct place continue  if (visited[i] || t[i][1] == i)  continue;    // Start a cycle and find the number of  // nodes in the cycle  int cycleSize = 0;  int j = i;    while (!visited[j]) {  visited[j] = true;  j = t[j][1];  cycleSize++;  }    // If there is a cycle we need (cycleSize - 1)  // swaps to sort the cycle  if (cycleSize > 1) {  ans += (cycleSize - 1);  }  }    // Return the total number of swaps  return ans;  }  public static void main(String[] args) {  int[] arr = {5 6 7 8 9 10 11};   System.out.println(minSwaps(arr));  } } 
Python
# Python program for Minimum swap required # to convert binary tree to binary search tree # Function to perform inorder traversal of the binary tree # and store it in an array def inorder(arr inorderArr index): # If index is out of bounds return n = len(arr) if index >= n: return # Recursively visit left subtree inorder(arr inorderArr 2 * index + 1) # Store current node value in inorderArr inorderArr.append(arr[index]) # Recursively visit right subtree inorder(arr inorderArr 2 * index + 2) # Function to calculate minimum swaps  # to sort inorder traversal def minSwaps(arr): inorderArr = [] # Get the inorder traversal of the binary tree inorder(arr inorderArr 0) # Create a list of pairs to store value and original index t = [(inorderArr[i] i) for i in range(len(inorderArr))] ans = 0 # Sort the list of pairs based on values # to get BST order t.sort() # Initialize visited array visited = [False] * len(t) # Find minimum swaps by detecting cycles for i in range(len(t)): # If already visited or already in the # correct place skip if visited[i] or t[i][1] == i: continue # Start a cycle and find the number of  # nodes in the cycle cycleSize = 0 j = i # Process all elements in the cycle while not visited[j]: visited[j] = True j = t[j][1] cycleSize += 1 # If there is a cycle of size `cycle_size` we  # need `cycle_size - 1` swaps if cycleSize > 1: ans += (cycleSize - 1) # Return total number of swaps return ans if __name__ == '__main__': arr = [5 6 7 8 9 10 11] print(minSwaps(arr)) 
C#
// C# program for Minimum swap required // to convert binary tree to binary search tree using System; using System.Linq; class GfG {    // Function to perform inorder traversal of the binary tree  // and store it in an array  static void Inorder(int[] arr int[] inorderArr int index ref int counter) {  int n = arr.Length;  // Base case: if index is out of bounds return  if (index >= n)  return;  // Recursively visit left subtree  Inorder(arr inorderArr 2 * index + 1 ref counter);  // Store current node value in inorderArr  inorderArr[counter] = arr[index];  counter++;  // Recursively visit right subtree  Inorder(arr inorderArr 2 * index + 2 ref counter);  }  // Function to calculate minimum  // swaps to sort inorder traversal  static int MinSwaps(int[] arr) {  int n = arr.Length;  int[] inorderArr = new int[n];  int counter = 0;  // Get the inorder traversal of the binary tree  Inorder(arr inorderArr 0 ref counter);  // Create an array of pairs to store value   // and original index  var t = new (int int)[n];  for (int i = 0; i < n; i++) {  t[i] = (inorderArr[i] i);  }  // Sort the array based on values to get BST order  Array.Sort(t (a b) => a.Item1.CompareTo(b.Item1));  // Initialize visited array  bool[] visited = new bool[n];  int ans = 0;  // Find minimum swaps by detecting cycles  for (int i = 0; i < n; i++) {    // If already visited or already in   // the correct place skip  if (visited[i] || t[i].Item2 == i)  continue;  // Start a cycle and find the number   // of nodes in the cycle  int cycleSize = 0;  int j = i;  // Process all elements in the cycle  while (!visited[j]) {  visited[j] = true;  j = t[j].Item2;  cycleSize++;  }  // If there is a cycle of size `cycle_size` we  // need `cycle_size - 1` swaps  if (cycleSize > 1)  {  ans += (cycleSize - 1);  }  }  // Return total number of swaps  return ans;  }  static void Main(string[] args) {    int[] arr = { 5 6 7 8 9 10 11 };  Console.WriteLine(MinSwaps(arr));  } } 
JavaScript
// Javascript program for Minimum swap required // to convert binary tree to binary search tree // Inorder traversal to get values in sorted order function inorder(arr inorderArr index) {  // If index is out of bounds return  if (index >= arr.length)  return;  // Recursively visit left subtree  inorder(arr inorderArr 2 * index + 1);  // Store current node value in array  inorderArr.push(arr[index]);  // Recursively visit right subtree  inorder(arr inorderArr 2 * index + 2); } // Function to calculate minimum swaps to sort inorder // traversal function minSwaps(arr) {  let inorderArr = [];  // Get the inorder traversal of the binary tree  inorder(arr inorderArr 0);  // Create an array of pairs to store value and original  // index  let t = inorderArr.map((val i) => [val i]);  let ans = 0;  // Sort the pair array based on values to get BST order  t.sort((a b) => a[0] - b[0]);  // Find minimum swaps by detecting cycles  let visited = Array(arr.length)  .fill(false);  for (let i = 0; i < t.length; i++) {    // If the element is already in the correct  // position continue  if (visited[i] || t[i][1] === i)  continue;  // Otherwise perform swaps until the element is in  // the right place  let cycleSize = 0;  let j = i;  while (!visited[j]) {  visited[j] = true;  j = t[j][1];  cycleSize++;  }  // If there is a cycle we need (cycleSize - 1)  // swaps to sort the cycle  if (cycleSize > 1) {  ans += (cycleSize - 1);  }  }  // Return total number of swaps  return ans; } let arr = [ 5 6 7 8 9 10 11 ]; console.log(minSwaps(arr)); 

Išvestis
3 

Laiko sudėtingumas: O(n*logn) kur n yra elementų skaičius masyve.
Pagalbinė erdvė: O(n), nes ji naudoja papildomos vietos masyvei 

Pratimas: Ar galime tai išplėsti į įprastą dvejetainį medį, t. y. dvejetainį medį, pavaizduotą naudojant kairiąją ir dešiniąją rodykles ir nebūtinai baigtą?

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