Check sum of Covered and Uncovered nodes of Binary Tree

• Difficulty Level : Medium
• Last Updated : 25 Jun, 2021

Given a binary tree, you need to check whether sum of all covered elements is equal to sum of all uncovered elements or not.
In a binary tree, a node is called Uncovered if it appears either on left boundary or right boundary. Rest of the nodes are called covered.

For example, consider below binary tree

In above binary tree,
Covered node:     6, 5, 7
Uncovered node:   9, 4, 3, 17, 22, 20

The output for this tree should be false as
sum of covered and uncovered node is not same

We strongly recommend you to minimize your browser and try this yourself first.
For calculating sum of Uncovered nodes we will follow below steps:
1) Start from root, go to left and keep going until left child is available, if not go to right child and again follow same procedure until you reach a leaf node.

2) After step 1 sum of left boundary will be stored, now for right part again do the same procedure but now keep going to right until right child is available, if not then go to left child and follow same procedure until you reach a leaf node.
After above 2 steps sum of all Uncovered node will be stored, we can subtract it from total sum and get sum of covered elements and check for equines of binary tree.

C++

 // C++ program to find sum of Covered and Uncovered node of// binary tree#include using namespace std; /* A binary tree node has key, pointer to left   child and a pointer to right child */struct Node{    int key;    struct Node* left, *right;}; /* To create a newNode of tree and return pointer */struct Node* newNode(int key){    Node* temp = new Node;    temp->key = key;    temp->left = temp->right = NULL;    return (temp);} /* Utility function to calculate sum of all node of tree */int sum(Node* t){    if (t == NULL)        return 0;    return t->key + sum(t->left) + sum(t->right);} /* Recursive function to calculate sum of left boundary   elements  */int uncoveredSumLeft(Node* t){    /*  If leaf node, then just return its key value   */    if (t->left == NULL && t->right == NULL)        return t->key;     /*  If left is available then go left otherwise go right  */    if (t->left != NULL)        return t->key + uncoveredSumLeft(t->left);    else        return t->key + uncoveredSumLeft(t->right);} /* Recursive function to calculate sum of right boundary   elements  */int uncoveredSumRight(Node* t){    /*  If leaf node, then just return its key value   */    if (t->left == NULL && t->right == NULL)        return t->key;     /*  If right is available then go right otherwise go left  */    if (t->right != NULL)        return t->key + uncoveredSumRight(t->right);    else        return t->key + uncoveredSumRight(t->left);} // Returns sum of uncovered elementsint uncoverSum(Node* t){    /* Initializing with 0 in case we don't have       left or right boundary  */    int lb = 0, rb = 0;     if (t->left != NULL)        lb = uncoveredSumLeft(t->left);    if (t->right != NULL)        rb = uncoveredSumRight(t->right);     /* returning sum of root node, left boundary       and right boundary*/    return t->key + lb + rb;} // Returns true if sum of covered and uncovered elements// is same.bool isSumSame(Node *root){    // Sum of uncovered elements    int sumUC = uncoverSum(root);     // Sum of all elements    int sumT = sum(root);     // Check if sum of covered and uncovered is same    return (sumUC == (sumT - sumUC));} /* Helper function to print inorder traversal of   binary tree   */void inorder(Node* root){    if (root)    {        inorder(root->left);        printf("%d ", root->key);        inorder(root->right);    }} // Driver program to test above functionsint main(){    // Making above given diagram's binary tree    Node* root = newNode(8);    root->left = newNode(3);     root->left->left = newNode(1);    root->left->right = newNode(6);    root->left->right->left = newNode(4);    root->left->right->right = newNode(7);     root->right = newNode(10);    root->right->right = newNode(14);    root->right->right->left = newNode(13);     if (isSumSame(root))        printf("Sum of covered and uncovered is same\n");    else        printf("Sum of covered and uncovered is not same\n");}

Java

 // Java program to find sum of covered and uncovered nodes// of a binary tree /* A binary tree node has key, pointer to left child and   a pointer to right child */class Node{    int key;    Node left, right;     public Node(int key)    {        this.key = key;        left = right = null;    }} class BinaryTree{    Node root;     /* Utility function to calculate sum of all node of tree */    int sum(Node t)    {        if (t == null)            return 0;        return t.key + sum(t.left) + sum(t.right);    }     /* Recursive function to calculate sum of left boundary       elements  */    int uncoveredSumLeft(Node t)    {        /*  If left node, then just return its key value   */        if (t.left == null && t.right == null)            return t.key;         /*  If left is available then go left otherwise go right  */        if (t.left != null)            return t.key + uncoveredSumLeft(t.left);         else            return t.key + uncoveredSumLeft(t.right);    }     /* Recursive function to calculate sum of right boundary       elements  */    int uncoveredSumRight(Node t)    {        /*  If left node, then just return its key value   */        if (t.left == null && t.right == null)            return t.key;         /*  If right is available then go right otherwise go left  */        if (t.right != null)            return t.key + uncoveredSumRight(t.right);        else            return t.key + uncoveredSumRight(t.left);    }     // Returns sum of uncovered elements    int uncoverSum(Node t)    {        /* Initializing with 0 in case we don't have           left or right boundary  */        int lb = 0, rb = 0;         if (t.left != null)            lb = uncoveredSumLeft(t.left);        if (t.right != null)            rb = uncoveredSumRight(t.right);         /* returning sum of root node, left boundary           and right boundary*/        return t.key + lb + rb;    }     // Returns true if sum of covered and uncovered elements    // is same.    boolean isSumSame(Node root)    {        // Sum of uncovered elements        int sumUC = uncoverSum(root);         // Sum of all elements        int sumT = sum(root);         // Check if sum of covered and uncovered is same        return (sumUC == (sumT - sumUC));    }     /* Helper function to print inorder traversal of       binary tree   */    void inorder(Node root)    {        if (root != null)        {            inorder(root.left);            System.out.print(root.key + " ");            inorder(root.right);        }    }     // Driver program to test above functions    public static void main(String[] args)    {         BinaryTree tree = new BinaryTree();         // Making above given diagram's binary tree        tree.root = new Node(8);        tree.root.left = new Node(3);        tree.root.left.left = new Node(1);        tree.root.left.right = new Node(6);        tree.root.left.right.left = new Node(4);        tree.root.left.right.right = new Node(7);         tree.root.right = new Node(10);        tree.root.right.right = new Node(14);        tree.root.right.right.left = new Node(13);         if (tree.isSumSame(tree.root))            System.out.println("Sum of covered and uncovered is same");         else            System.out.println("Sum of covered and uncovered is not same");    }} // This code has been contributed by Mayank Jaiswal(mayank_24)

Python3

 # Python3 program to find sum of Covered and# Uncovered node of binary tree # To create a newNode of tree and return pointerclass newNode:    def __init__(self, key):        self.key = key        self.left = self.right = None # Utility function to calculate sum# of all node of treedef Sum(t):    if (t == None):        return 0    return t.key + Sum(t.left) + Sum(t.right) # Recursive function to calculate sum# of left boundary elementsdef uncoveredSumLeft(t):         # If leaf node, then just return    # its key value    if (t.left == None and t.right == None):        return t.key     # If left is available then go    # left otherwise go right    if (t.left != None):        return t.key + uncoveredSumLeft(t.left)    else:        return t.key + uncoveredSumLeft(t.right) # Recursive function to calculate sum of# right boundary elementsdef uncoveredSumRight(t):         # If leaf node, then just return    # its key value    if (t.left == None and t.right == None):        return t.key     # If right is available then go right    # otherwise go left    if (t.right != None):        return t.key + uncoveredSumRight(t.right)    else:        return t.key + uncoveredSumRight(t.left) # Returns sum of uncovered elementsdef uncoverSum(t):         # Initializing with 0 in case we    # don't have left or right boundary    lb = 0    rb = 0     if (t.left != None):        lb = uncoveredSumLeft(t.left)    if (t.right != None):        rb = uncoveredSumRight(t.right)     # returning sum of root node,    # left boundary and right boundary    return t.key + lb + rb # Returns true if sum of covered and# uncovered elements is same.def isSumSame(root):         # Sum of uncovered elements    sumUC = uncoverSum(root)     # Sum of all elements    sumT = Sum(root)     # Check if sum of covered and    # uncovered is same    return (sumUC == (sumT - sumUC)) # Helper function to prinorder# traversal of binary treedef inorder(root):    if (root):        inorder(root.left)        print(root.key, end = " ")        inorder(root.right) # Driver Codeif __name__ == '__main__':         # Making above given diagram's    # binary tree    root = newNode(8)    root.left = newNode(3)     root.left.left = newNode(1)    root.left.right = newNode(6)    root.left.right.left = newNode(4)    root.left.right.right = newNode(7)     root.right = newNode(10)    root.right.right = newNode(14)    root.right.right.left = newNode(13)     if (isSumSame(root)):        print("Sum of covered and uncovered is same")    else:        print("Sum of covered and uncovered is not same")         # This code is contributed by PranchalK

C#

 // C# program to find sum of covered// and uncovered nodes of a binary treeusing System; /* A binary tree node has key, pointerto left child and a pointer to right child */public class Node{    public int key;    public Node left, right;     public Node(int key)    {        this.key = key;        left = right = null;    }} class GFG{public Node root; /* Utility function to calculatesum of all node of tree */public virtual int sum(Node t){    if (t == null)    {        return 0;    }    return t.key + sum(t.left) +                   sum(t.right);} /* Recursive function to calculatesum of left boundary elements */public virtual int uncoveredSumLeft(Node t){    /* If left node, then just return       its key value */    if (t.left == null && t.right == null)    {        return t.key;    }     /* If left is available then go       left otherwise go right */    if (t.left != null)    {        return t.key + uncoveredSumLeft(t.left);    }    else    {        return t.key + uncoveredSumLeft(t.right);    }} /* Recursive function to calculate   sum of right boundary elements */public virtual int uncoveredSumRight(Node t){    /* If left node, then just return       its key value */    if (t.left == null && t.right == null)    {        return t.key;    }     /* If right is available then go       right otherwise go left */    if (t.right != null)    {        return t.key + uncoveredSumRight(t.right);    }    else    {        return t.key + uncoveredSumRight(t.left);    }} // Returns sum of uncovered elementspublic virtual int uncoverSum(Node t){    /* Initializing with 0 in case we    don't have left or right boundary */    int lb = 0, rb = 0;     if (t.left != null)    {        lb = uncoveredSumLeft(t.left);    }    if (t.right != null)    {        rb = uncoveredSumRight(t.right);    }     /* returning sum of root node,    left boundary and right boundary*/    return t.key + lb + rb;} // Returns true if sum of covered// and uncovered elements is same.public virtual bool isSumSame(Node root){    // Sum of uncovered elements    int sumUC = uncoverSum(root);     // Sum of all elements    int sumT = sum(root);     // Check if sum of covered and    // uncovered is same    return (sumUC == (sumT - sumUC));} /* Helper function to print inordertraversal of binary tree */public virtual void inorder(Node root){    if (root != null)    {        inorder(root.left);        Console.Write(root.key + " ");        inorder(root.right);    }} // Driver Codepublic static void Main(string[] args){     GFG tree = new GFG();     // Making above given diagram's binary tree    tree.root = new Node(8);    tree.root.left = new Node(3);    tree.root.left.left = new Node(1);    tree.root.left.right = new Node(6);    tree.root.left.right.left = new Node(4);    tree.root.left.right.right = new Node(7);     tree.root.right = new Node(10);    tree.root.right.right = new Node(14);    tree.root.right.right.left = new Node(13);     if (tree.isSumSame(tree.root))    {        Console.WriteLine("Sum of covered and " +                            "uncovered is same");    }    else    {        Console.WriteLine("Sum of covered and " +                        "uncovered is not same");    }}} // This code is contributed by Shrikant13

Javascript



Output :

Sum of covered and uncovered is not same