Code Question 1
Amazon operates a network of n distribution centers, each located in a different city. The cities are numbered from 1 to n. Given a list of orders, where each order is destined for a city specified in orderCityList[i]:

• Delivery from the distribution center in the same city takes 1 day.
• Delivery from a distribution center in another city takes 2 days due to the longer distance.

Each distribution center can handle one order at a time, and orders from the same center are processed sequentially — only one order is delivered at a time, and the next order will be processed once the previous one has been delivered. Multiple centers can process orders simultaneously.

Task: Determine the minimum number of days to fulfill all orders by optimally assigning them to the distribution centers.

Example:
Given n = 3 and orderCityList = [1, 1, 3, 1, 1, 1]

• Center 1: orders 1, 2, 4 → all same city, each takes 1 day → total 3 days.
• Center 2: order 5 → to city 3 (different city) → takes 2 days.
• Center 3: order 3 → same city → 1 day.

All orders delivered in 3 days.

Constraints:
1 ≤ n ≤ 2×10^5
1 ≤ orderCityList[i] ≤ n

Code Question 2
Amazon’s database stores numbers as strings of binary characters '0' and '1'. Accidentally, a '!' appears in some positions, representing an unknown character that can be replaced with either '0' or '1'.

Due to internal faults:

• Every subsequence "01" generates x errors.
• Every subsequence "10" generates y errors.

A subsequence of a string is obtained by deleting zero or more characters without changing the order of the remaining characters.

Task: Determine the minimum total errors possible after optimally replacing each '!'. Return the result modulo 10^9+7.

Example:
errorString = "0!111", x = 2, y = 3

If '!' → '0':

• String: "00111"
• "01" subsequences = 9 → errors = 9×x = 18
• "10" subsequences = 0 → errors = 0×y = 0
• Total = 18

If '!' → '1':

• String: "01111"
• "01" subsequences = 3 → errors = 3×x = 6
• "10" subsequences = 0 → errors = 0×y = 0
• Total = 6

Minimum errors = 6 (modulo 10^9+7).

Constraints:
1 ≤ length(errorString) ≤ 10^5
1 ≤ x, y ≤ 10^5

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