LeetCode 113 Conquer Path Sum II- Finding All Target Sum Paths

Level Up Your Skills: Mastering LeetCode 113 - Path Sum II (C++)
Welcome, coders, to this advanced guide on tackling LeetCode problem 113! We'll embark on a journey to find all possible paths in a binary tree where the sum of the node values along the path equals a given target value. This video equips you with the skills to solve this variation of the path sum problem in C++.
Understanding the Problem:
LeetCode problem 113 builds upon the concept of path sum. Here, the task is to find all possible paths from the root node to leaf nodes (nodes with no children) where the sum of the node values along each path equals a specific target value. Unlike the previous challenge, we need to identify all such paths, not just confirm their existence.
Binary Tree Fundamentals (Recap):
Before diving into the solution, let's briefly revisit binary trees. These hierarchical structures consist of nodes connected by pointers. Each node holds data (typically a value) and can have zero, one, or two child nodes (left and right). Understanding tree structure is crucial for this algorithm.
Visualizing All Path Sums:
Imagine a binary tree. A path sum refers to the sum of the values of nodes along a specific path from the root to a leaf node. This challenge requires finding all possible sequences of nodes from the root that lead to leaf nodes, with each sequence's sum equaling the target value. We'll use clear diagrams throughout the video to illustrate this concept.
Crafting the C++ Solution:
Now, let's explore how to solve the "Path Sum II" problem in C++. We'll present a recursive backtracking approach that explores all possible paths in the tree, building and storing valid paths that meet the target sum criteria.
Building the Recursive Backtracking C++ Solution:
Defining a TreeNode structure for a binary tree node with val (data) and left and right pointers to child nodes.
Creating a Solution class with a pathSum method to find all paths with the target sum.
The pathSum function takes a TreeNode pointer (representing the root of the subtree to be explored), the target sum, and an empty vector paths (to store the found paths) as input.
If the node is null (empty subtree), it's not a valid path, so return.
If the node is a leaf node (no child nodes) and its value equals the remaining target sum (after reaching the leaf), create a new vector representing the path (including the current node's value), add it to the paths vector, and return (signifying a valid path found).
Recursively call pathSum on the left and right child nodes, passing the remaining target sum minus the current node's value (similar to the previous problem) and including the current node's value in a temporary vector representing the current path being explored.
After recursion on both children, the function returns since we've explored all possible paths from the current node.
Explanation of the Recursive Backtracking Approach:
This approach works by recursively exploring both the left and right subtrees of each node. At each node, we subtract its value from the remaining target sum and pass the updated target and a path vector (including the current node) down the recursion. If a leaf node is reached with a remaining target sum of zero, a valid path is found, and the constructed path vector is added to the final results. Backtracking ensures we explore all possible paths from the current node.
Time and Space Complexity Analysis:
This solution has a time complexity of O(n * pathLength), where n is the number of nodes and pathLength is the maximum length of a path in the tree. In the worst case (all paths lead to leaves), we might visit each node multiple times. The space complexity is also O(n) in the worst case, due to the recursion call stack and the vector storing all paths (which could potentially hold all nodes in the tree).
Conclusion:
By conquering LeetCode problem 113, you've gained valuable experience in using backtracking to find all possible solutions that meet specific criteria within a tree structure. This is a fundamental technique for various tree search and optimization problems. Remember, practice is key to mastering these concepts. So, keep exploring and solving coding challenges!