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Question 1: Path Concatenation Sum in a Binary Tree
Problem Statement:
Consider a binary tree with N nodes (1 Root and N-1 descendants). Each node, X is related to the Root by some relations such as L, R, LL, LR... and so on, where X is left (L) to Root or left-left (LL) or right-left (RL) to Root and so on.
Perform the following operations to find the value of Sum.
- If the given tree has M leaf nodes, there will be M minimum paths from root to M leaf nodes. Each path, Path_i, is the path from root to i^{th} leaf node, where 1 <= i <= M. Find all such paths.
- Concatenate all node values along the Path_i to form an integer P_i, where 1 <= i <=M.
- Calculate Sum, where Sum = P_1 + P_2 +....... + P_M.
Write a program to print Sum.
Constraints:
- Node values are always greater than or equal to 0.
Question 2: Maximum Carrots in a Matrix (Rabbit's Journey)
Problem Statement:
A field, represented as cells of an M * N matrix, is given. There are some carrots in every cell, and a rabbit is trying to cross the field while eating the carrots available on the way. He starts from the top-left cell and moves right or down in each step, and finally reaches the bottom-right cell.
Write a program to find the maximum number of carrots the rabbit can eat during the trip from the top-left cell to the bottom-right cell.
Note: The Rabbit always moves either to downfield or right field, and always consumes all the carrots available in the cells on its path.
Input Format:
- The first line of input contains two integers M and N separated by a single white space, where M and N represent the size of the field.
- Next M lines have N integers, separated by a single white space, which represents the number of carrots in each cell.
