Given a K-ary tree, where each node is having K children and each edge has some weight. All the edges i.e. K, that goes from a particular node to all its children have weights in ascending order 1, 2, 3, …, K. Find the number of paths having total weight as W (sum of all edge weights in the path) starting from root and containing atleast one edge of weight atleast M.
Input : W = 3, K = 3, M = 2 Output : 3 Explanation : One path can be (1 + 2), second can be (2 + 1) and third is 3. Input : W = 4, K = 3, M = 2 Output : 6
Approach: This problem can be solved using dynamic programming approach. The idea is to maintain two states, one for the current weight to be required and other one for a boolean variable which denotes that the current path has included an edge of weight atleast M or not. Iterate over all possible edge weights i.e. K and recursively solve for the weight W – i for 1 ≤ i ≤ K. If the current edge weight is more than or equal to M, set the boolean variable as 1 for the next call.
Below is the implementation of above approach.
Time Complexity: O(W * K)
- Count number of paths whose weight is exactly X and has at-least one edge of weight M
- Number of unique paths in tree such that every path has a value greater than K
- Count the nodes in the given tree whose weight is even
- Count the nodes of the given tree whose weight has X as a factor
- Count the nodes in the given tree whose sum of digits of weight is odd
- Count the nodes in the given tree whose weight is prime
- Find the weight of the minimum spanning tree
- Count the nodes in the given tree whose weight is even parity
- Count the nodes in the given tree whose weight is a power of two
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- Sum of lengths of all paths possible in a given tree
- Count all k-sum paths in a Binary Tree
- Print all k-sum paths in a binary tree
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- Print all the paths from root, with a specified sum in Binary tree
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