Practice
i < j < k such that nums[i] < nums[k] < nums[j]. Which approach guarantees an optimal solution with linear time complexity?Solution
Step 1: Understand the 132 pattern condition
The problem requires finding a subsequencei < j < kwithnums[i] < nums[k] < nums[j], which is the 132 pattern.Step 2: Identify the approach that achieves O(n) time
The monotonic stack approach iterates from right to left, maintaining candidates for the '3' and '2' elements efficiently, achieving linear time complexity.Final Answer:
Option C -> Option CQuick Check:
Monotonic stack approach is known optimal for 132 pattern detection [OK]
- Thinking brute force is acceptable for large inputs
- Confusing greedy with monotonic stack
- Assuming DP is needed
class Solution:
def evalRPN(self, tokens):
import operator
ops = {
'+': operator.add,
'-': operator.sub,
'*': operator.mul,
'/': lambda x, y: int(x / y),
}
stack = []
for token in tokens:
if token in ops:
right = stack.pop()
left = stack.pop()
stack.append(ops[token](left, right))
else:
stack.append(int(token))
return stack.pop()
sol = Solution()
print(sol.evalRPN(["4", "13", "5", "/", "+"]))
Solution
Step 1: Trace stack operations
Push 4, push 13, push 5; then '/' operator pops 5 and 13, computes int(13/5) = 2, push 2; then '+' operator pops 2 and 4, computes 4+2=6, push 6.Step 2: Final stack pop
Pop the last element 6 as the result.Final Answer:
Option B -> Option BQuick Check:
Stack correctly reflects intermediate results [OK]
- Swapping left and right operands
- Using float division instead of int
- Off-by-one in stack pops
q = MyQueue()
q.push(10)
q.push(20)
print(q.pop())
q.push(30)
print(q.peek())
Solution
Step 1: Trace pop() after pushing 10 and 20
pop_stack is empty, transfer push_stack [10,20] reversed to pop_stack [20,10], pop() returns 10.Step 2: After pushing 30, peek() checks pop_stack which has [20], so peek returns 20
After pop(), pop_stack has [20], push_stack has [30]. peek() does not transfer because pop_stack is not empty, so peek returns 20.Final Answer:
Option B -> Option BQuick Check:
pop() returns 10, peek() returns 20 [OK]
- Assuming peek returns 10 after pop
- Forgetting transfer only when pop_stack empty
Solution
Step 1: Analyze iteration over asteroids
The algorithm iterates over each asteroid once.Step 2: Analyze stack operations
Each asteroid can be pushed once and popped once, so total stack operations are O(n).Final Answer:
Option A -> Option AQuick Check:
Each asteroid processed at most twice (push/pop) [OK]
- Assuming nested while loop causes O(n^2)
- Confusing stack operations with sorting
- Ignoring amortized analysis of stack pops
Solution
Step 1: Understand operator precedence
Multiplication and division have higher precedence than addition and subtraction, so evaluation order matters.Step 2: Modify stack approach
Using two stacks (numbers and operators) allows applying higher precedence operators immediately, preserving correct order.Step 3: Why other options fail
Single stack ignoring precedence leads to wrong results; postfix conversion is valid but more complex; relying on eval() is unsafe and not interview-appropriate.Final Answer:
Option A -> Option AQuick Check:
Two-stack approach is standard for precedence and parentheses [OK]
- Ignoring precedence or relying on single stack only
