This set Snowflake OA is a set that has just been tested recently. The overall difficulty can be said to be on the upper level among OA from major manufacturers. The format is 3 questions in 120 minutes, all of which are mid+ or above in intensity, and the questions are geared towards algorithm modeling capabilities rather than simple templates. Almost all three questions require complete thinking + boundary processing + performance optimization. If the pace is slow, it is easy to be pressed for time. Let’s break down the structure of this set of real questions completely.
1. String Patterns
Introduction to the topic
Given word length WordLen And the maximum number of consecutive vowels allowed MaxVowels, count the number of legal words composed of English letters (a-z). The vowels are {a,e,i,o,u} (5 in total) and the consonants are the remaining 21 letters. A legal word means any number of consecutive vowels not exceeding MaxVowels, the result needs to be taken modulo 10⁹+7.
Problem-solving ideas
Use dynamic programming: dp[i][j] represents the number of legal strings of length i and ending with j consecutive vowels.
- Play consonants: dp[i][0] = (sum of all states of the previous length) × 21
- Put vowels: dp[i][j] = dp[i-1][j-1] × 5 (j ≤ maxVowels) Recurse from dp[0][0]=1 to wordLen, and finally sum up all j modulo 10⁹+7.
2. Paint the ceiling
Introduction to the topic
The construction company will generate a set of side lengths s according to a recursive formula. We need to select two side lengths from this set (you can choose the same one, equivalent to a square) to be the length and width of the house respectively. It is required that the product of these two side lengths (that is, the ceiling area) cannot exceed the given a. Finally, figure out how many legal options there are.
Problem-solving ideas
First, according to the formula s[i]=((k∗s[i−1]+b)modm)+1+s[i−1], starting from s[0], a length set s is generated according to the formula provided in the question, and a total of n side lengths are obtained; then, To avoid repeated calculations, s can be deduplicated and sorted in ascending order. The problem is then transformed into counting the number of rectangular combinations in the set that satisfy x ≤ y and x × y ≤ a. You can enumerate each smaller side x, then find all y's on its right side that satisfy the area constraint, and count the qualifying combinations into the answer. You can also use the double pointer method. A pointer Left Starting from the minimum length, another pointer Right Start with maximum length. If S[left]×S[right]≤aS[left]×S[right]≤A , then for the current Left, all from Left Arrive Right The elements of all satisfy the conditions, then Left Move right. Otherwise Right Shift left.
3. Task Scheduling
Introduction to the topic
There are two servers: paid server (task time-consuming Time[i],cost Cost[i]) and free servers (tasks take 1 and cost 0, but are only available when paid servers are occupied). Find the minimum cost to complete all tasks.
Problem-solving ideas
The key to this question is to understand the usage rules of the free server: as long as the paid server is running, the free server can process tasks in parallel, and each free task only takes 1 unit of time. So, if we put a certain task on a paid server, it will not only complete its task, but also generate Time[i] A free task quota is equivalent to one "coverage" Time[i] + 1 Task. The problem is transformed into: select a number of tasks and place them on the paid server so that all tasks are covered (total number of coverage ≥ n), while the total cost is minimized. This is essentially a 0/1 knapsack problem. Just use DP to find the minimum cost.
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