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It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions. Point Jumper hack. The Jump pointer algorithm is a design technique for parallel algorithms that operate on pointer structures, such as arrays or linked list.

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This algorithm is normally used to determine the root of the forest of a rooted tree. In the jump pointer algorithm, we pre-process a tree so that one can able to answer the queries to find any parent of any node in the tree in time complexity of O(log n) . The jump pointer algorithm associates up to log 2 n pointers to each vertex of the tree. These pointers are called jump pointers because they jump up the tree towards the root node of the tree. For any node of the processing tree, the algorithm stores an array of length l jumpers where l = log2(depth(v)) . The ith element of this array points to the 2ith parent of the node v . This data structure helps us to jump halfway up the tree from any given node. When the algorithm is asked to process a query to find any parent of any node in the tree, we repeatedly jump up the tree using these pointers. The number of jumps will be at most log n and therefore any problem to find the parent of any node in the tree can be answered in O(log n) time complexity. In jump pointer, there is a pointer from node N to N’s j-th parent, for j = 1, 2, 4, 8, …, and so on. So we store 2 ith parent of each node. The jump pointer algorithm basically works on the approach of dynamic programming where we use the pre-computed result to find the next result . By doing some simple calculations we can compute the mathematical formula that for any node k, 2 j th parent of k is equal to 2 j-1 th parent of 2 j-1 th parent of k . The brief explanation of this formula is given below in the algorithm section. The most common use of this algorithm is to solve the queries in which we need to find the ancestor of any node in O(log n) time complexity. Graph to implement Jump Pointer Algorithm: Representation of jump array that stores 2^i th parent of all nodes: Examples: Input: 0th parent of node 2 Output: 0th parent of node 2 is = 2 Input: 2nd parent of node 4 Output: 2nd parent of node 4 is = 2 Input: 3rd parent of node 8 Output: 3rd parent of node 8 is = 1. Algorithm : Here is the algorithm to implement the jump pointer algorithm to find any parent of any node in the graph. We determine the jump matrix using dynamic programming . Here, we denote the root node as R and initially assume the parent of the root node as 0 which means there is no parent of this node . Now looking at the graph and the array is shown in the above diagram we can easily understand the above formula to determine the 2 i th parent of each node. If we look at the node with value 8 we can see that its 2 0 th parent is 10 , now to find its 2 1 th parent we see that it’s 2 1 th parent is 2 0 th parent of the node with value 10 and here 10 is 2 0 th parent of 8 it means 2 1 th parent of node 8 is 2 0 th parent of 2 0 th parent of node 8 . Similarly, we can also see that 2 2 th parent of node 8 is 5 which is 2 1 th parent of 2 1 th parent of node 8 i.e 2 1 th parent of node with value 9 . Thus in this way we can compute the array of jump pointers for all the nodes to store their 2 i th parents. Below is the pseudo code to calculate the jump pointer matrix that store 2 i th parent of all the nodes in the tree. jump[k][j] = it points 2^jth parent of k = 2^j-1th parent of (2^j-1th parent of k) = jump[jump[i][j-1][j-1] Implementation : Below is the code to implement the above algorithm to find any parent of any node in O( logn ) time complexity.