Paths with Sum


Related: LeetCode - Path Sum
Related: LeetCode 437 - Path Sum III
https://github.com/careercup/CtCI-6th-Edition/tree/master/Java/Ch%2004.%20Trees%20and%20Graphs/Q4_12_Paths_with_Sum
You are given a binary tree in which each node contains an integer value (which
might be positive or negative). Design an algorithm to count the number of paths that sum to a
given value. The path does not need to start or end at the root or a leaf, but it must go downwards

(traveling only from parent nodes to child nodes).

int countPathsWithSum(TreeNode root, int targetSum) {
        return countPathsWithSum(root, targetSum, 0, new HashMap<Integer, Integer>());
}

int countPathsWithSum(TreeNode node, int targetSum, int runningSum,
                      HashMap<Integer, Integer> pathCount) {
        if (node == null) return 0;   // Base case

        /* Count paths with sum ending at the current node. */
        runningSum += node.data;
        int sum= runningSum - targetSum;
        int totalPaths = pathCount.getOrDefault(sum, 0);

        /* If runningSum equals targetSum, then one additional path starts at root.
         * Add in this path.*/
        if (runningSum == targetSum) {
                totalPaths++;
        }

        /* Increment pathCount, recurse, then decrement pathCount. */
        incrementHashTable(pathCount, runningSum, 1);   // Increment pathCount
        totalPaths += countPathsWithSum(node.left, targetSum, runningSum, pathCount);
        totalPaths += countPathsWithSum(node.right, targetSum, runningSum, pathCount);
        incrementHashTable(pathCount, runningSum, -1);   // Decrement pathCount

        return totalPaths;
}

void incrementHashTable(HashMap<Integer, Integer> hashTable, int key, int delta) {
        int newCount = hashTable.getOrDefault(key, 0) + delta;
        if (newCount == 0) {//Remove when zero to reduce space usage
                hashTable.remove(key);
        } else {
                hashTable.put(key, newCount);
        }
}

Brute Force - O(nlogn)
int countPathsWithSum(TreeNode root, int targetSum) {
        if (root == null) return 0;

        /* Count paths with sum starting from the root. */
        int pathsFromRoot = countPathsWithSumFromNode(root, targetSum, 0);
        /* Try the nodes on the left and right. */
        int pathsOnleft = countPathsWithSum(root.left, targetSum);
        int pathsOnRight = countPathsWithSum(root.right, targetSum);

        return pathsFromRoot + pathsOnLeft + pathsOnRight;
}

int countPathsWithSumFromNode(TreeNode node, int targetSum, int currentSum) {
        if (node == null) return 0;

        currentSum += node.data;

        int totalPaths = 0;
        if (currentSum == targetSum) { // Found a path from the root
                totalPaths++;
        }

        totalPaths += countPathsWithSumFromNode(node.left, targetSum, currentSum);
        totalPaths += countPathsWithSumFromNode(node.right, targetSum, currentSum);
        return totalPaths;
}



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