流中元素的排名

给定整数流，查找给定整数x的等级。整数插播广告的排名为“小于或等于x(不包括x)的元素总数”。
如果在流中找不到元素或元素在流中最小，则返回-1。
例子：

Input :  arr[] = {10, 20, 15, 3, 4, 4, 1}
              x = 4;
Output : Rank of 4 in stream is: 3
There are total three elements less than
or equal to x (and not including x)

Input : arr[] = {5, 1, 14, 4, 15, 9, 7, 20, 11}, 
           x = 20;
Output : Rank of 20 in stream is: 8

一个相对简单的实现方法是使用一个数组，该数组按排序顺序保存所有元素。当插入一个新元素时，我们将移动这些元素。然后，我们在数组上执行二进制搜索以获取x的最右边的索引并返回该索引。 getRank(x)可以在O(log n)中使用，但是插入会很昂贵。
一种有效的方法是使用二进制搜索树。每个节点将保留其左子树的数据值和大小。
我们从根开始遍历树并将根值与x进行比较。

1. 如果root-> data == x，则返回root的左子树的大小。
2. 如果x data，返回getRank(root-> left)
3. 如果x> root-> data，则返回getRank(root-> right)+ leftSubtree的大小+ 1。

下面是解决方案。

C++

// CPP program to find rank of an
// element in a stream.
#include 
using namespace std;
 
struct Node {
    int data;
    Node *left, *right;
    int leftSize;
};
 
Node* newNode(int data)
{
    Node *temp = new Node;
    temp->data = data;
    temp->left = temp->right = NULL;
    temp->leftSize = 0;
    return temp;
}
 
// Inserting a new Node.
Node* insert(Node*& root, int data)
{
    if (!root)
        return newNode(data);
 
    // Updating size of left subtree.
    if (data <= root->data) {
        root->left = insert(root->left, data);
        root->leftSize++;
    }
    else
        root->right = insert(root->right, data);
 
    return root;
}
 
// Function to get Rank of a Node x.
int getRank(Node* root, int x)
{
    // Step 1.
    if (root->data == x)
        return root->leftSize;
 
    // Step 2.
    if (x < root->data) {
        if (!root->left)
            return -1;
        else
            return getRank(root->left, x);
    }
 
    // Step 3.
    else {
        if (!root->right)
            return -1;
        else {
            int rightSize = getRank(root->right, x);
              if(rightSize == -1 ) return -1;
            return root->leftSize + 1 + rightSize;
        }
    }
}
 
// Driver code
int main()
{
    int arr[] = { 5, 1, 4, 4, 5, 9, 7, 13, 3 };
    int n = sizeof(arr) / sizeof(arr[0]);
    int x = 4;
 
    Node* root = NULL;
    for (int i = 0; i < n; i++)
        root = insert(root, arr[i]);
 
    cout << "Rank of " << x << " in stream is: "
         << getRank(root, x) << endl;
 
    x = 13;
    cout << "Rank of " << x << " in stream is: "
         << getRank(root, x) << endl;
 
    x = 8;
    cout << "Rank of " << x << " in stream is: "
         << getRank(root, x) << endl;
    return 0;
}

Java

// Java program to find rank of an
// element in a stream.
class GfG {
 
static class Node {
    int data;
    Node left, right;
    int leftSize;
}
 
static Node newNode(int data)
{
    Node temp = new Node();
    temp.data = data;
    temp.left = null;
    temp.right = null;
    temp.leftSize = 0;
    return temp;
}
 
// Inserting a new Node.
static Node insert(Node root, int data)
{
    if (root == null)
        return newNode(data);
 
    // Updating size of left subtree.
    if (data <= root.data) {
        root.left = insert(root.left, data);
        root.leftSize++;
    }
    else
        root.right = insert(root.right, data);
 
    return root;
}
 
// Function to get Rank of a Node x.
static int getRank(Node root, int x)
{
    // Step 1.
    if (root.data == x)
        return root.leftSize;
 
    // Step 2.
    if (x < root.data) {
        if (root.left == null)
            return -1;
        else
            return getRank(root.left, x);
    }
 
    // Step 3.
    else {
        if (root.right == null)
            return -1;
        else {
            int rightSize = getRank(root.right, x);
          if(rightSize == -1) return -1;
            return root.leftSize + 1 + rightSize;
        }
    }
}
 
// Driver code
public static void main(String[] args)
{
    int arr[] = { 5, 1, 4, 4, 5, 9, 7, 13, 3 };
    int n = arr.length;
    int x = 4;
 
    Node root = null;
    for (int i = 0; i < n; i++)
        root = insert(root, arr[i]);
 
    System.out.println("Rank of " + x + " in stream is : "+getRank(root, x));
 
    x = 13;
    System.out.println("Rank of " + x + " in stream is : "+getRank(root, x));
 
}
}

Python3

# Python3 program to find rank of an
# element in a stream.
 
class newNode:
    def __init__(self, data):
        self.data = data
        self.left = self.right = None
        self.leftSize = 0
 
# Inserting a new Node.
def insert(root, data):
    if root is None:
        return newNode(data)
 
    # Updating size of left subtree.
    if data <= root.data:
        root.left = insert(root.left, data)
        root.leftSize += 1
    else:
        root.right = insert(root.right, data)
    return root
 
# Function to get Rank of a Node x.
def getRank(root, x):
     
    # Step 1.
    if root.data == x:
        return root.leftSize
 
    # Step 2.
    if x < root.data:
        if root.left is None:
            return -1
        else:
            return getRank(root.left, x)
 
    # Step 3.
    else:
        if root.right is None:
            return -1
        else:
            rightSize = getRank(root.right, x)
            if rightSize == -1:
                # x not found in right sub tree, i.e. not found in stream
                return -1
            else:
                return root.leftSize + 1 + rightSize
 
# Driver code
if __name__ == '__main__':
    arr = [5, 1, 4, 4, 5, 9, 7, 13, 3]
    n = len(arr)
    x = 4
 
    root = None
    for i in range(n):
        root = insert(root, arr[i])
 
    print("Rank of", x, "in stream is:",
                       getRank(root, x))
    x = 13
    print("Rank of", x, "in stream is:",
                       getRank(root, x))
    x = 8
    print("Rank of", x, "in stream is:",
                       getRank(root, x))
         
# This code is contributed by PranchalK

C#

// C# program to find rank of an
// element in a stream.
using System;
     
class GFG
{
public class Node
{
    public int data;
    public Node left, right;
    public int leftSize;
}
 
static Node newNode(int data)
{
    Node temp = new Node();
    temp.data = data;
    temp.left = null;
    temp.right = null;
    temp.leftSize = 0;
    return temp;
}
 
// Inserting a new Node.
static Node insert(Node root, int data)
{
    if (root == null)
        return newNode(data);
 
    // Updating size of left subtree.
    if (data <= root.data)
    {
        root.left = insert(root.left, data);
        root.leftSize++;
    }
    else
        root.right = insert(root.right, data);
 
    return root;
}
 
// Function to get Rank of a Node x.
static int getRank(Node root, int x)
{
    // Step 1.
    if (root.data == x)
        return root.leftSize;
 
    // Step 2.
    if (x < root.data)
    {
        if (root.left == null)
            return -1;
        else
            return getRank(root.left, x);
    }
 
    // Step 3.
    else
    {
        if (root.right == null)
            return -1;
        else
        {
            int rightSize = getRank(root.right, x);
              if(rightSize == -1) return -1;
            return root.leftSize + 1 + rightSize;
        }
    }
}
 
// Driver code
public static void Main(String[] args)
{
    int []arr = { 5, 1, 4, 4, 5, 9, 7, 13, 3 };
    int n = arr.Length;
    int x = 4;
 
    Node root = null;
    for (int i = 0; i < n; i++)
        root = insert(root, arr[i]);
 
    Console.WriteLine("Rank of " + x +
                      " in stream is : " +
                      getRank(root, x));
 
    x = 13;
    Console.WriteLine("Rank of " + x +
                      " in stream is : " +
                      getRank(root, x));
}
}
 
// This code is contributed by PrinciRaj1992

输出

Rank of 4 in stream is: 3
Rank of 13 in stream is: 8
Rank of 8 in stream is: -1

另一种方法：
从头开始遍历数组。遍历时，对等于或小于给定键的节点计数，打印count(Rank)。

C++

// C++ program to find rank of an
// element in a stream.
#include 
using namespace std;
 
// Driver code
int main()
{
    int a[] = {5, 1, 14, 4, 15, 9, 7, 20, 11};
    int key = 20;
    int arraySize = sizeof(a)/sizeof(a[0]);
    int count = 0;
    for(int i = 0; i < arraySize; i++)
    {
        if(a[i] <= key)
        {
            count += 1;
        }
    }
    cout << "Rank of " << key << " in stream is: "
            << count-1 << endl;
    return 0;
}
 
// This code is contributed by
// Ashwin Loganathan.

Java

// Java program to find rank of an
// element in a stream.
class GFG
{
 
// Driver code
public static void main(String[] args)
{
    int a[] = {5, 1, 14, 4, 15, 9, 7, 20, 11};
    int key = 20;
    int arraySize = a.length;
    int count = 0;
    for(int i = 0; i < arraySize; i++)
    {
        if(a[i] <= key)
        {
            count += 1;
        }
    }
    System.out.println("Rank of " + key +
                    " in stream is: " + (count - 1));
}
}
 
// This code has been contributed by 29AjayKumar

Python3

# Python3 program to find rank of an
# element in a stream.
 
# Driver code
if __name__ == '__main__':
    a = [5, 1, 14, 4, 15,
            9, 7, 20, 11]
    key = 20
    arraySize = len(a)
    count = 0
    for i in range(arraySize):
        if a[i] <= key:
            count += 1
             
    print("Rank of", key,
          "in stream is:", count - 1)
 
# This code is contributed by PranchalK

C＃

// C# program to find rank of an
// element in a stream.
using System;
 
class GFG
{
// Driver code
public static void Main()
{
    int []a = {5, 1, 14, 4, 15, 9, 7, 20, 11};
    int key = 20;
    int arraySize = a.Length;
    int count = 0;
    for(int i = 0; i < arraySize; i++)
    {
        if(a[i] <= key)
        {
            count += 1;
        }
    }
    Console.WriteLine("Rank of " + key +
                      " in stream is: " +
                            (count - 1));
}
}
 
// This code is contributed by
// Akanksha Rai

输出：

Rank of 20 in stream is: 8