给定一个BST，任务是找到所有大于和等于第k个最大元素的元素之和。
例子：
Input : K = 3
8
/ \
7 10
/ / \
2 9 13
Output : 32
Explanation: 3rd largest element is 9 so sum of all
elements greater than or equal to 9 are
9 + 10 + 13 = 32.
Input : K = 2
8
/ \
5 11
/ \
2 7
\
3
Output : 19
Explanation: 2nd largest element is 8 so sum of all
elements greater than or equal to 8 are
8 + 11 = 19.
方法：
这个想法是以相反的方式(右向左)遍历BST的顺序遍历。
请注意，BST的有序遍历以排序(或递增)顺序访问元素，因此有序遍历的逆向将以有序顺序(递减)进行。遍历时，请跟踪已访问节点的数量，并继续添加节点，直到数量变为k。
C++
// C++ program to find Sum Of All Elements larger
// than or equal to Kth Largest Element In BST
#include
using namespace std;
struct Node {
int data;
Node *left, *right;
};
// utility function new Node of BST
struct Node* cNode(int data)
{
Node* node = new Node;
node->left = NULL;
node->right = NULL;
node->data = data;
return node;
}
// A utility function to insert a new Node
// with given key in BST
struct Node* add(Node* root, int key)
{
// If the tree is empty, return a new Node
if (root == NULL)
return cNode(key);
// Otherwise, recur down the tree
if (root->data > key)
root->left = add(root->left, key);
else if (root->data < key)
root->right = add(root->right, key);
// return the (unchanged) Node pointer
return root;
}
// function to return sum of all elements larger than
// and equal to Kth largest element
int klargestElementSumUtil(Node* root, int k, int& c)
{
// Base cases
if (root == NULL)
return 0;
if (c > k)
return 0;
// Compute sum of elements in right subtree
int ans = klargestElementSumUtil(root->right, k, c);
if (c >= k)
return ans;
// Add root's data
ans += root->data;
// Add current Node
c++;
if (c >= k)
return ans;
// If c is less than k, return left subtree Nodes
return ans + klargestElementSumUtil(root->left, k, c);
}
// Wrapper over klargestElementSumRec()
int klargestElementSum(struct Node* root, int k)
{
int c = 0;
klargestElementSumUtil(root, k, c);
}
// Drivers code
int main()
{
/* 19
/ \
7 21
/ \
3 11
/ \
9 13
*/
Node* root = NULL;
root = add(root, 19);
root = add(root, 7);
root = add(root, 3);
root = add(root, 11);
root = add(root, 9);
root = add(root, 13);
root = add(root, 21);
int k = 2;
cout << klargestElementSum(root, k) << endl;
return 0;
} Java
// Java program to find Sum Of All Elements larger
// than or equal to Kth Largest Element In BST
import java.util.*;
class GFG
{
static class Node
{
int data;
Node left, right;
};
static int c;
// Utility function new Node of BST
static Node cNode(int data)
{
Node node = new Node();
node.left = null;
node.right = null;
node.data = data;
return node;
}
// A utility function to insert a new Node
// with given key in BST
static Node add(Node root, int key)
{
// If the tree is empty, return a new Node
if (root == null)
return cNode(key);
// Otherwise, recur down the tree
if (root.data > key)
root.left = add(root.left, key);
else if (root.data < key)
root.right = add(root.right, key);
// return the (unchanged) Node pointer
return root;
}
// function to return sum of all elements larger than
// and equal to Kth largest element
static int klargestElementSumUtil(Node root, int k)
{
// Base cases
if (root == null)
return 0;
if (c > k)
return 0;
// Compute sum of elements in right subtree
int ans = klargestElementSumUtil(root.right, k);
if (c >= k)
return ans;
// Add root's data
ans += root.data;
// Add current Node
c++;
if (c >= k)
return ans;
// If c is less than k, return left subtree Nodes
return ans + klargestElementSumUtil(root.left, k);
}
// Wrapper over klargestElementSumRec()
static int klargestElementSum(Node root, int k)
{
c = 0;
return klargestElementSumUtil(root, k);
}
// Drivers code
public static void main(String[] args)
{
/* 19
/ \
7 21
/ \
3 11
/ \
9 13
*/
Node root = null;
root = add(root, 19);
root = add(root, 7);
root = add(root, 3);
root = add(root, 11);
root = add(root, 9);
root = add(root, 13);
root = add(root, 21);
int k = 2;
System.out.print(klargestElementSum(root, k) +"\n");
}
}
// This code is contributed by PrinciRaj1992Python3
# Python3 program to find sum of all elements larger
# than or equal to Kth largest element In BST
c = 0
class cNode:
def __init__(self, data):
self.data = data
self.left = None
self.right = None
# A utility function to insert a new Node
# with given key in BST
def add(root, key):
# If the tree is empty, return a new Node
if (root == None):
return cNode(key)
# Otherwise, recur down the tree
if (root.data > key):
root.left = add(root.left, key)
elif(root.data < key):
root.right = add(root.right, key)
# return the (unchanged) Node pointer
return root
# Function to return sum of all elements
# larger than and equal to Kth largest element
def klargestElementSumUtil(root, k):
global c
# Base cases
if (root == None):
return 0
if (c > k):
return 0
# Compute sum of elements in right subtree
ans = klargestElementSumUtil(root.right, k)
if (c >= k):
return ans
# Add root's data
ans += root.data
# Add current Node
c += 1
if (c >= k):
return ans
# If c is less than k, return left subtree Nodes
return ans + klargestElementSumUtil(root.left, k)
# Wrapper over klargestElementSumRec()
def klargestElementSum(root, k):
return klargestElementSumUtil(root, k)
# Driver code
if __name__ == '__main__':
'''
/* 19
/ \
7 21
/ \
3 11
/ \
9 13
*/ '''
root = None
root = add(root, 19)
root = add(root, 7)
root = add(root, 3)
root = add(root, 11)
root = add(root, 9)
root = add(root, 13)
root = add(root, 21)
k = 2
print(klargestElementSum(root, k))
# This code is contributed by bgangwar59C#
// C# program to find Sum Of All Elements larger
// than or equal to Kth Largest Element In BST
using System;
class GFG
{
class Node
{
public int data;
public Node left, right;
};
static int c;
// Utility function new Node of BST
static Node cNode(int data)
{
Node node = new Node();
node.left = null;
node.right = null;
node.data = data;
return node;
}
// A utility function to insert a new Node
// with given key in BST
static Node add(Node root, int key)
{
// If the tree is empty, return a new Node
if (root == null)
return cNode(key);
// Otherwise, recur down the tree
if (root.data > key)
root.left = add(root.left, key);
else if (root.data < key)
root.right = add(root.right, key);
// return the (unchanged) Node pointer
return root;
}
// function to return sum of all elements larger than
// and equal to Kth largest element
static int klargestElementSumUtil(Node root, int k)
{
// Base cases
if (root == null)
return 0;
if (c > k)
return 0;
// Compute sum of elements in right subtree
int ans = klargestElementSumUtil(root.right, k);
if (c >= k)
return ans;
// Add root's data
ans += root.data;
// Add current Node
c++;
if (c >= k)
return ans;
// If c is less than k, return left subtree Nodes
return ans + klargestElementSumUtil(root.left, k);
}
// Wrapper over klargestElementSumRec()
static int klargestElementSum(Node root, int k)
{
c = 0;
return klargestElementSumUtil(root, k);
}
// Drivers code
public static void Main(String[] args)
{
/* 19
/ \
7 21
/ \
3 11
/ \
9 13
*/
Node root = null;
root = add(root, 19);
root = add(root, 7);
root = add(root, 3);
root = add(root, 11);
root = add(root, 9);
root = add(root, 13);
root = add(root, 21);
int k = 2;
Console.Write(klargestElementSum(root, k) +"\n");
}
}
// This code is contributed by PrinciRaj1992输出：
40