Specialist Programmer

You are given a tree T with N nodes (numbered 0 to N-1) and a string S where S[i] is the lowercase letter written on node i.

You must answer Q queries of two types:

Type 1 (Update): 1 U X - Change the letter on node U to the X-th letter of the alphabet (0-indexed, 'a'=0, 'b'=1, ...).

Type 2 (Query): 2 U V - Count the number of distinct letters on the unique simple path from node U to node V.

After processing all queries, you need to calculate a final weighted sum. Let the answers to the Type 2 queries be C1, C2, ..., Ck. The final result is (C1 * 3^1 + C2 * 3^2 + ... + Ck * 3^k).

Return this final sum modulo 1,000,000,007.

A group of N people are seated in chairs numbered 1 to N arranged in a circle. You are given an array A, where A[i-1] represents the jump distance for the person on chair i.

From any chair i, a person can jump A[i-1] chairs in either a clockwise (right) or counter-clockwise (left) direction.

Bob starts at chair X and needs to reach chair Y. Your task is to find the minimum number of jumps required to get from chair X to chair Y. If it's impossible to reach chair Y, return -1.

You are given three integers: N, M, and K. Your task is to find the number of "great" arrays of length N.

An array A of length X is considered great if for all i from 2 to X, the condition bitcount(A[i-1] & A[i]) = K holds true. The elements A[i] of the array must satisfy 0 <= A[i] < 2^M.

Since the total number of great arrays can be very large, you must return the count modulo 1,000,000,007.

You are given a positive integer N. Your task is to calculate the total number of times the digit '0' appears in the decimal representations of all integers from 1 to N, inclusive.

You are given a binary tree consisting of 'n' nodes.

Convert the given binary tree into a linked list where the linked list nodes follow the same order as the pre-order traversal of the given binary tree.

Use the right pointer of the binary tree as the “next” pointer for the linked list and set the left pointer to NULL.

Use these nodes only. Do not create extra nodes.

Example :

Input: Let the binary be as shown in the figure:

Output: Linked List: 15 -> 40 -> 62 -> 10 -> 20 -> NULL

Explanation: As shown in the figure, the right child of every node points to the next node, while the left node points to null.

Also, the nodes are in the same order as the pre-order traversal of the binary tree.

There are 25 horses among which you need to find out the fastest 3 horses. You can conduct a race among at most 5 to find out their relative speed. At no point can you find out the actual speed of the horse in a race.
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