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📜  节点值从1到N的二叉树的两个节点之间的距离

📅  最后修改于: 2021-05-25 03:47:00             🧑  作者: Mango

给定一个二叉树

1

作为其根源并为任何父母

i

它的左孩子将是2 * i ,右孩子将是2 * i + 1 。任务是找到两个节点n1n2之间的最小距离。

1
            /      \
           2        3
         /  \      / \
        4    5    6   7
      /  \  / \  / \ / \
     .  .  .  . .  .  .  . 

例子

Input : n1 = 7, n2 = 10
Output : 5

Input : n1 = 6, n2 = 7
Output : 4

找到二叉树的两个给定节点之间的最小距离的方法有很多。
这是在给定节点的二进制表示的帮助下找到相同内容的有效方法。对于任何节点,请仔细查看其二进制表示形式。例如,考虑节点99的二进制表示形式是1001 。因此,要找到从根到节点的路径,请找到该节点的二进制表示形式,并在该二进制表示形式中从左向右移动,如果遇到1则移动到树中的右子节点,如果遇到0则移动到左子节点。 。

Path of 9 as per bit representation
        1
       / \
      2   3
     /\   /\
    4  5 6  7
   /\ 
  8  9.

因此,为了找到两个节点之间的最小距离,我们将尝试找到两个节点的二进制表示形式的公共部分,它实际上是从根到LCA的公共路径。让两个节点的前k位相同。同样,如果二进制形式为n位,则表明从根到该节点的路径距离为n长度。因此,根据以上陈述,我们可以轻松得出以下结论:如果m和n是两个节点的位长,并且两个节点的值的k个起始位相同,则两个节点之间的最小距离为: m + n – 2 * k
注意:最后类似的位显示LCA在给定的二叉树中的位置。
下面是上述方法的实现:

C++
// C++ program to find minimum distance between
// two nodes in binary tree
 
#include 
using namespace std;
 
// Function to get minimum path distance
int minDistance(int n1, int n2)
{
    /** find the 1st dis-similar bit **/
    // count bit length of n1 and n2
    int bitCount1 = floor(log2(n1)) + 1;
    int bitCount2 = floor(log2(n2)) + 1;
 
    // find bit difference and maxBit
    int bitDiff = abs(bitCount1 - bitCount2);
    int maxBitCount = max(bitCount1, bitCount2);
 
    if (bitCount1 > bitCount2) {
        n2 = n2 * pow(2, bitDiff);
    }
    else {
        n1 = n1 * pow(2, bitDiff);
    }
 
    int xorValue = n1 ^ n2;
    int bitCountXorValue;
   
      if( xorValue == 0)
      bitCountXorValue = 1;
    else
    {
       bitCountXorValue = floor(log2(xorValue)) + 1;
    }
    int disSimilarBitPosition = maxBitCount -
                                     bitCountXorValue;
   
    // calculate result by formula
    int result = bitCount1 + bitCount2 -
                         2 * disSimilarBitPosition;
    return result;
}
 
// Driver program
int main()
{
    int n1 = 12, n2 = 5;
 
    cout << minDistance(n1, n2);
 
    return 0;
}


Java
// Java program to find minimum distance between
// two nodes in binary tree
import java.util.*;
 
class GFG
{
    // Function to get minimum path distance
    static int minDistance(int n1, int n2)
    {
        /** find the 1st dis-similar bit **/
        // count bit length of n1 and n2
     
        int bitCount1 =(int) Math.floor((Math.log(n1) /
                        Math.log(2))) + 1;
        int bitCount2 = (int)Math.floor((Math.log(n2) /
                        Math.log(2))) + 1;
 
        // find bit difference and maxBit
        int bitDiff = Math.abs(bitCount1 - bitCount2);
        int maxBitCount = Math.max(bitCount1, bitCount2);
 
        if (bitCount1 > bitCount2)
        {
            n2 = n2 *(int) Math.pow(2, bitDiff);
        }
        else   
        {
            n1 = n1 *(int) Math.pow(2, bitDiff);
        }
       
       
        int xorValue = n1 ^ n2;
        int bitCountXorValue;
       
        if( xorValue == 0)
          bitCountXorValue = 1;
        else
        {
           bitCountXorValue = (int)Math.floor((Math.log(xorValue) /
                                Math.log(2))) + 1;
        }
        int disSimilarBitPosition = maxBitCount -
                                         bitCountXorValue;
        
 
        // calculate result by formula
        int result = bitCount1 + bitCount2 - 2 * disSimilarBitPosition;
        return result;
    }
 
    // Driver program
    public static void main(String args[])
    {
        int n1 = 12, n2 = 5;
        System.out.println(minDistance(n1, n2));
    }
}
 
// This code is contributed by
// Sanjit_Prasad


Python3
# Python 3 program to find minimum distance
# between two nodes in binary tree
from math import log2
 
# Function to get minimum path distance
def minDistance(n1, n2):
     
    # find the 1st dis-similar bit
    # count bit length of n1 and n2
    bitCount1 = int(log2(n1)) + 1
    bitCount2 = int(log2(n2)) + 1
 
    # find bit difference and maxBit
    bitDiff = abs(bitCount1 - bitCount2)
    maxBitCount = max(bitCount1, bitCount2)
 
    if (bitCount1 > bitCount2):
        n2 = int(n2 * pow(2, bitDiff))
     
    else:
        n1 = int(n1 * pow(2, bitDiff))
 
    xorValue = n1 ^ n2
    if xorValue == 0:
        bitCountXorValue = 1
    else:
        bitCountXorValue = int(log2(xorValue)) + 1
    disSimilarBitPosition = (maxBitCount -
                             bitCountXorValue)
 
    # calculate result by formula
    result = (bitCount1 + bitCount2 - 2 *
                   disSimilarBitPosition)
    return result
 
# Driver Code
if __name__ == '__main__':
    n1 = 12
    n2 = 5
 
    print(minDistance(n1, n2))
 
# This code is contributed by
# Surendra_Gangwar


C#
// C# program to find minimum distance between
// two nodes in binary tree
using System;
     
class GFG
{
    // Function to get minimum path distance
    static int minDistance(int n1, int n2)
    {
        /** find the 1st dis-similar bit **/
        // count bit length of n1 and n2
     
        int bitCount1 =(int) Math.Floor((Math.Log(n1) /
                        Math.Log(2))) + 1;
        int bitCount2 = (int)Math.Floor((Math.Log(n2) /
                        Math.Log(2))) + 1;
 
        // find bit difference and maxBit
        int bitDiff = Math.Abs(bitCount1 - bitCount2);
        int maxBitCount = Math.Max(bitCount1, bitCount2);
 
        if (bitCount1 > bitCount2)
        {
            n2 = n2 *(int) Math.Pow(2, bitDiff);
        }
        else
        {
            n1 = n1 *(int) Math.Pow(2, bitDiff);
        }
 
        int xorValue = n1 ^ n2;
        
       
        int bitCountXorValue;
       
        if( xorValue == 0)
          bitCountXorValue = 1;
        else
        {
           bitCountXorValue = (int)Math.Floor((Math.Log(xorValue) /
                                Math.Log(2))) + 1;
        }
         
        int disSimilarBitPosition = maxBitCount - bitCountXorValue;
 
        // calculate result by formula
        int result = bitCount1 + bitCount2 - 2 * disSimilarBitPosition;
        return result;
    }
 
    // Driver code
    public static void Main(String []args)
    {
        int n1 = 12, n2 = 5;
        Console.WriteLine(minDistance(n1, n2));
    }
}
 
/* This code contributed by PrinciRaj1992 */


PHP
 $bitCount2)
    {
        $n2 = $n2 * pow(2, $bitDiff);
    }
    else
    {
        $n1 = $n1 * pow(2, $bitDiff);
    }
 
    $xorValue = $n1 ^ $n2;
    $bitCountXorValue = floor(log($xorValue, 2)) + 1;
    $disSimilarBitPosition = $maxBitCount -
                             $bitCountXorValue;
 
    // calculate result by formula
    $result = $bitCount1 + $bitCount2 - 2 *
              $disSimilarBitPosition;
    return $result;
}
 
// Driver Code
$n1 = 12;
$n2 = 5;
 
echo minDistance($n1, $n2);
 
// This code is contributed by akt_mit
?>


Javascript


输出:
5