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Question 1: Counting Balanced Clips

Description:

Given a video clip of certain length and a difficulty tolerance, calculate the number of "balanced" clips possible. A clip is defined as a sequence of characters, and it is considered balanced if each consecutive pair of characters differs in their alphabet position by no more than a given tolerance diff.

Implement a function to return the total number of balanced clips possible, given the clip length and difficulty tolerance.

Input:

• clipLength (int): An integer indicating the length of the clip.
• diff (int): An integer defining the maximum allowed difference in position between consecutive characters.

Output:

• Returns the count of balanced clips, modulo 10^9 + 7.

Code Example:

def countBalancedClips(clipLength, diff):
    dp = [[0] * 26 for _ in range(2)]
    MOD = 10**9 + 7
    for i in range(26):
        dp[0][i] = 1
    for i in range(1, clipLength):
        cur = i % 2
        prev = (i+1) % 2
        dp[cur] = [0] * 26
        for j in range(26):
            for k in range(26):
                if abs(j - k) <= diff:
                    dp[cur][j] = (dp[cur][j] + dp[prev][k]) % MOD
    return sum(dp[(clipLength - 1) % 2]) % MOD

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Question 2: Minimizing TikTok Server Network Cost

Description:

Given coordinates of servers in a 2D plane, implement an efficient function to calculate the minimum network cost needed to connect all servers. The cost of connecting two servers is determined by the minimum of their x or y coordinate differences.

Use an algorithm to compute the minimal cost to connect the network of servers, where each server must be connected to at least one other server.

Input:

• x (List[int]): List of x-coordinates of the servers.
• y (List[int]): List of y-coordinates of the servers.

Output:

• Returns the minimum network connection cost to connect all servers.

Code Example:

import heapq
from collections import defaultdict

def getMinTikTokServerNetworkCost(x, y):
    n = len(x)
    servers = [(x[i], y[i], i) for i in range(n)]
    g = defaultdict(list)
    for i in [0, 1]:
        servers.sort(key=lambda server: server[i])
        for j in range(1, n):
            x1, y1, idx1 = servers[j-1]
            x2, y2, idx2 = servers[j]
            cost = min(abs(x1 - x2), abs(y1 - y2))
            g[idx1].append((cost, idx2))
            g[idx2].append((cost, idx1))
    res = 0
    visited = set()
    h = [(0, 0)]
    while len(visited) < n:
        cost, cur = heapq.heappop(h)
        if cur in visited:
            continue
        visited.add(cur)
        res += cost
        for c, v in g[cur]:
            if v not in visited:
                heapq.heappush(h, (c, v))
    return res