Practice
Solution
Step 1: Understand the problem requirements
The problem requires detecting duplicates efficiently in an array.Step 2: Compare approaches based on time complexity
Sorting then scanning is O(n log n), nested loops is O(n²), and dynamic programming is unnecessary here. Using a hash set allows O(n) time with O(n) space by checking membership during one pass.Final Answer:
Option B -> Option BQuick Check:
Hash set membership check is O(1) average, enabling linear time detection [OK]
- Confusing sorting approach as optimal
- Thinking nested loops are efficient enough
- Misapplying DP to a membership problem
isHappy(7)?
def sum_of_squares(num):
return sum(int(d) ** 2 for d in str(num))
UNHAPPY_CYCLE = {4, 16, 37, 58, 89, 145, 42, 20}
def isHappy(n: int) -> bool:
while n != 1 and n not in UNHAPPY_CYCLE:
n = sum_of_squares(n)
return n == 1
print(isHappy(7))
Solution
Step 1: Trace sum_of_squares for n=7
7 -> 7² = 49Step 2: Iterate until n=1 or cycle detected
49 -> 4²+9²=16+81=97 -> 9²+7²=81+49=130 -> 1²+3²+0²=1+9+0=10 -> 1²+0²=1 -> loop ends, returns trueFinal Answer:
Option B -> Option BQuick Check:
7 is a happy number, code returns true [OK]
- Assuming 7 leads to cycle or infinite loop
k elements that appear most frequently. Which algorithmic approach guarantees an optimal solution with linear time complexity?Solution
Step 1: Understand problem constraints
The problem requires finding top k frequent elements efficiently, ideally in linear time.Step 2: Identify approach with linear time complexity
Bucket sort groups elements by frequency, allowing O(n) time retrieval of top k elements by scanning buckets from high to low frequency.Final Answer:
Option A -> Option AQuick Check:
Bucket sort approach is known to run in O(n) time for this problem [OK]
- Sorting entire array is O(n log n), not optimal
- Greedy approach ignores frequency counts
- DP is unrelated to frequency counting here
res just before the function returns when called with nums = [1,2,2,3] and k = 2?Solution
Step 1: Calculate frequency map for nums=[1,2,2,3]
freq = {1:1, 2:2, 3:1}, max_freq = 2Step 2: Fill buckets and collect top k=2 elements
buckets = [[], [1,3], [2]]; iterate from freq=2 down: add 2, then freq=1 add 1; res = [2,1]Final Answer:
Option B -> Option BQuick Check:
Order depends on bucket insertion; here 2 appears before 1 [OK]
- Confusing order of elements in buckets
- Assuming sorted order inside buckets
- Off-by-one in frequency indexing
k problem, given an input array of length n and integer k?Solution
Step 1: Analyze time complexity
The algorithm iterates once over the array (length n), performing O(1) operations per element, so time is O(n).Step 2: Analyze space complexity
We store earliest indices for each remainder modulo k, so space is O(k), independent of n.Final Answer:
Option B -> Option BQuick Check:
Linear time and space proportional to k [OK]
- Confusing nested loops complexity with prefix sum approach
- Assuming space is O(n) due to prefix sums stored
- Thinking time is O(n*k) due to modulo operations
