Perform the given queries on the rooted tree
Given a rooted tree and not necessarily binary. The tree contains N nodes, labeled 1 to N. You are given the tree in the form of an array A[1..N] of size N. A[i] denotes label of the parent of node labeled i. For clarity, you may assume that the tree satisfies the following conditions.
- The root of the tree is labeled 1. Hence A is set to 0.
- The parent of node T will always have a label less than T.
The task is to perform the following operations according to the type of query given.
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- ADD, X, Y: add Y to the value at node X.
- ADDUP, X, Y: add Y to the value at node X. Then, add Y to the value at A[X] (i.e. the parent of X). The, add Y to the value at A[A[X]] (i.e. the parent of A[X]).. and so on, till you add Y to the value at root.
After you have performed all the given operations, you are asked to answer several queries of the following type
- VAL, X: print the value at node X.
- VALTREE, X: print the sum of values at all nodes in the subtree rooted at X (including X).
Source: Directi Interview | Set 13
N = 7, M = 4, Q = 5
0 1 2 2 2 1 2
ADD 6 76
ADDUP 1 49
ADD 4 48
ADDUP 2 59
N = 5, M = 5, Q = 3
0 1 1 1 3
ADD 1 10
ADD 2 20
ADD 3 30
ADD 4 40
ADDUP 5 50
Explanation: This problem is a slight variation of dfs. In this, we have stored the node’s original value and addup value in the vector of the pair. We did 2 times dfs.
- dfs1 for offline queries i.e to calculate the addup sum for each node.
- dfs2 to store the subtree sum in an array.
Now all the queries can be answered in a constant time.
Graph before dfs1
Graph after dfs1
Below is the required implementation:
291 0 0 107 59
Time Complexity: O(1) per query, O(N) for preprocessing is taken by dfs1() and dfs2() function.
Auxiliary Space: O(N)