Given a tree, and the weights of all the nodes, the task is to count the number of nodes whose weight is a perfect Square.
Only the weights of nodes 1, 4 and 5 are perfect squares.
Approach: Perform dfs on the tree and for every node, check if it’s weight is a perfect square or not.
Below is the implementation of the above approach:
- Time Complexity: O(N*logV) where V is the maximum weight of a node in the tree.
In DFS, every node of the tree is processed once and hence the complexity due to the DFS is O(N) for N nodes in the tree. Also, while processing every node, in order to check if the node value is a perfect square or not, the inbuilt sqrt(V), is being called where V is the weight of the node and this function has a complexity of O(log V). Hence for every node, there is an added complexity of O(log V). Therefore, the total time complexity is O(N*logV).
- Auxiliary Space: O(1).
Any extra space is not required, so the space complexity is constant.
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- Count the nodes in the given Tree whose weight is a Perfect Number
- Count number of paths whose weight is exactly X and has at-least one edge of weight M
- Count the nodes in the given tree whose weight is even
- Count the nodes in the given tree whose weight is a power of two
- Count the nodes in the given tree whose weight is even parity
- Count the nodes in the given tree whose sum of digits of weight is odd
- Count the nodes of the given tree whose weight has X as a factor
- Count nodes in the given tree whose weight is a fibonacci number
- Count the nodes in the given tree whose weight is a powerful number
- Count the nodes in the given tree whose weight is prime
- Count of all prime weight nodes between given nodes in the given Tree
- Count of Nodes which has Prime Digit sum weight in a Tree
- Query to find the maximum and minimum weight between two nodes in the given tree using LCA.
- Queries to find the Minimum Weight from a Subtree of atmost D-distant Nodes from Node X
- Permutation of numbers such that sum of two consecutive numbers is a perfect square
- Count all pairs of adjacent nodes whose XOR is an odd number
- Count the nodes whose sum with X is a Fibonacci number
- Count the nodes of the given tree whose weighted string is a palindrome
- Count the nodes of the tree whose weighted string contains a vowel
- Count the nodes of a tree whose weighted string does not contain any duplicate characters
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