# Integrated Algorithm Design Practice

Computer Science I · Algorithmics · https://tryals.app/learn/computer-science-i/integrated-algorithm-design-practice

## Designing a Solution

Real algorithm design draws on every unit concept at once: choose a strategy, back it with data structures, argue correctness, and analyze complexity.

A practical **design workflow**:

| Step | Action | Key Question |
| --- | --- | --- |
| 1 | **Understand** | What are the exact inputs, outputs, and edge cases? |
| 2 | **Strategy** | **Divide-and-conquer**, **dynamic programming**, **greedy**, or **graph traversal**? |
| 3 | **Structures** | Which structures make hot operations fast (heap, hash table)? |
| 4 | **Verify** | Correctness proof and complexity analysis vs constraints. |

> **Common pitfall:** reaching for an exotic technique when a simple approach works, or brute-forcing a problem whose size demands a better strategy.

## Integrated Practice

These techniques are not separate exam topics but an **integrated design toolkit**. A strong algorithmist moves fluidly among them to balance correctness and efficiency.

**Worked Example:** Find the $k$ most frequent words in a huge text.

- **Count:** Use a **hash table** in $O(n)$ time.
- **Select:** Use a **heap** of size $k$ in $O(m \log k)$ time over $m$ distinct words.

Rather than fully sorting, this design consciously combines a strategy (selection via heap) with the right structures, justified by its $O(n + m \log k)$ complexity.

## Practice questions

6 of this lesson's 11 practice questions, with answers. The full set is in the app.

### 1. A problem is shown to be NP-complete. Why is that useful news rather than merely bad news?

A. Because it guarantees an efficient algorithm exists but has not been found
B. Because it redirects the effort toward approximation or heuristics
C. Because it proves the problem cannot be solved on any computer
D. Because NP-complete problems have no solutions at all

**Answer:** B. Because it redirects the effort toward approximation or heuristics

**Why:** It tells you which search to abandon. Real instances are routinely solved by approximation, branch-and-bound, or exploiting structure the general problem lacks, so the classification redirects rather than closes the work, and knowing it early saves months of looking for something almost certainly not there.

Page: https://tryals.app/practice/computer-science-i/integrated-algorithm-design-practice/a-problem-is-shown-to-be-np-complete-why-is-that-useful-news-rather

### 2. For 'find the k most frequent words in a huge text', select every design decision the lesson endorses.

A. Use dynamic programming to count the words
B. Fully sort all distinct words to get the top k
C. Select the top k with a heap of size k
D. Count frequencies with a hash table
E. Justify the design by analysing its complexity

**Answer:** C. Select the top k with a heap of size k; D. Count frequencies with a hash table; E. Justify the design by analysing its complexity

**Why:** Hash-table counting, size-k heap selection, and complexity justification are the endorsed decisions. A full sort is what the heap avoids, and counting words is a simple pass, not a DP problem.

Page: https://tryals.app/practice/computer-science-i/integrated-algorithm-design-practice/for-find-the-k-most-frequent-words-in-a-huge-text-select-every

### 3. Given a new problem, an experienced programmer often recognises it as a variant of something known - shortest path, or a scheduling problem - rather than inventing an algorithm. Why is recognition so much more productive than invention?

A. Because inventing algorithms is forbidden in professional practice.
B. Because recognised problems are always easier than novel ones.
C. Because a recognised problem brings a proved algorithm with known limits.
D. Because all problems are equivalent to a small number of standard ones, so invention is never necessary.

**Answer:** C. Because a recognised problem brings a proved algorithm with known limits.

**Why:** Recognition brings a proved-correct algorithm, a known complexity, known edge cases and usually a tested implementation; invention means taking all of that on yourself. The mapping step is worth practising, 'assign staff to shifts' is bipartite matching, 'order tasks with dependencies' is topological sort. Recognising a problem as NP-complete is valuable too: it tells you to stop looking.

Page: https://tryals.app/practice/computer-science-i/integrated-algorithm-design-practice/given-a-new-problem-an-experienced-programmer-often-recognises-it-as

### 4. The fastest algorithm for a problem in the abstract is the right choice regardless of the data and constraints in front of you.

**Answer:** False

**Why:** False. Insertion sort beats quicksort on nearly-sorted input; an in-place algorithm beats a faster one that needs O(n) extra memory on a device that has none; a simpler algorithm beats a faster one nobody on the team can maintain. The problem, the data and the constraints together decide.

Page: https://tryals.app/practice/computer-science-i/integrated-algorithm-design-practice/the-fastest-algorithm-for-a-problem-in-the-abstract-is-the-right

### 5. Order the first five steps of the design workflow the lesson recommends.

**Answer:**

1. Understand the problem: inputs, output, constraints, and edge cases
2. Choose an algorithmic strategy
3. Pick data structures that make the hot operations fast
4. Argue correctness
5. Analyze time and space complexity

**Why:** Understand, choose a strategy, pick supporting data structures, argue correctness, then analyze complexity (and finally test). Jumping to a strategy before understanding the problem is a classic misstep.

Page: https://tryals.app/practice/computer-science-i/integrated-algorithm-design-practice/order-the-first-five-steps-of-the-design-workflow-the-lesson

### 6. Match each data structure to the hot operation it makes fast.

**Answer:**

- Heap → Repeatedly taking the extreme element
- Hash table → Fast lookup by key
- Sorted array → Binary search
- Queue → First-in, first-out processing

**Why:** A heap for repeated extremes, a hash table for keyed lookup, a sorted array for binary search, a queue for FIFO order. The design rule is to make the strategy's hot operation the structure's fast one.

Page: https://tryals.app/practice/computer-science-i/integrated-algorithm-design-practice/match-each-data-structure-to-the-hot-operation-it-makes-fast