437. Path Sum III

You are given a binary tree in which each node contains an integer value.

Find 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).

The tree has no more than 1,000 nodes and the values are in the range -1,000,000 to 1,000,000.

Example:

root = [10,5,-3,3,2,null,11,3,-2,null,1], sum = 8

      10
     /  \
    5   -3
   / \    \
  3   2   11
 / \   \
3  -2   1

Return 3. The paths that sum to 8 are:

1.  5 -> 3
2.  5 -> 2 -> 1
3. -3 -> 11

An interested prefix sum solution. for reference

Key: Remove current sum from the map when this substree is visited.

public int pathSum(TreeNode root, int sum) {
     HashMap<Integer, Integer> preSum = new HashMap();
     preSum.put(0,1);
     return helper(root, 0, sum, preSum);
 }

 public int helper(TreeNode root, int currSum, int target, HashMap<Integer, Integer> preSum) {
     if (root == null) {
         return 0;
     }

     currSum += root.val;
     int res = preSum.getOrDefault(currSum - target, 0);
     preSum.put(currSum, preSum.getOrDefault(currSum, 0) + 1);

     res += helper(root.left, currSum, target, preSum) + helper(root.right, currSum, target, preSum);
     preSum.put(currSum, preSum.get(currSum) - 1);
     return res;
 }

// path sum of this tree
public int pathSum(TreeNode root, int sum) {
    if(root == null) return 0;
    return withRoot(root, sum) + pathSum(root.left, sum) + pathSum(root.right, sum);
}
// path sum of this tree must include the root
public int withRoot(TreeNode root, int sum) {
    if(root == null) return 0;
    return (root.val == sum ? 1 : 0) + withRoot(root.left, sum-root.val) + withRoot(root.right, sum-root.val);
}

Return all sums with current root

int result = 0;
public int pathSum(TreeNode root, int sum) {
    traverse(root, sum);
    return result;
}

public ArrayList<Integer> traverse(TreeNode root, int sum) {
    if(root == null) return new ArrayList<>();
    ArrayList<Integer> left = traverse(root.left, sum);
    ArrayList<Integer> right = traverse(root.right, sum);
    ArrayList<Integer> total = new ArrayList<>();
    total.addAll(left);
    total.addAll(right);

    for(int i = 0; i < total.size(); i++) {
        total.set(i, total.get(i)+root.val);
        if(total.get(i) == sum) result++;
    }
    total.add(root.val);
    if(root.val == sum) result++;
    return total;
}