Which approach best balances time and space by using a compact representation of visited elements and avoids redundant recomputation?
easy🔍 Pattern Recognition Q11 of Q15
Bit Manipulation - Generate All Permutations Using Bitmask DP
You need to generate all permutations of n distinct elements efficiently. Which approach best balances time and space by using a compact representation of visited elements and avoids redundant recomputation?
ABacktracking with a boolean visited array and recursion without memoization
BGreedy algorithm that picks the next smallest unused element at each step
CBitmask DP with iterative tabulation that uses bitmasks to track visited elements and builds permutations bottom-up
DDynamic programming on subsets without bitmasking, using nested loops over all permutations
Step-by-Step Solution
Step 1: Understand the problem constraints
Generating all permutations requires enumerating all orderings of n elements, which is factorial in size. Efficient tracking of visited elements is crucial.
Step 2: Identify the approach that uses bitmasking
Bitmask DP uses an integer to represent visited elements compactly, enabling memoization and iterative building of permutations without redundant recomputation.
Final Answer:
Option C -> Option C
Quick Check:
Bitmask DP with iterative tabulation is the known optimal approach for this problem [OK]
Quick Trick:Bitmask DP uses bits to track visited elements efficiently [OK]
Common Mistakes:
MISTAKES
Assuming greedy can generate all permutations correctly
Using DP without bitmasking leads to inefficient state tracking
Trap Explanation:
PITFALL
Greedy and naive DP approaches seem simpler but fail to generate all permutations or avoid recomputation.
Interviewer Note:
CONTEXT
Tests if candidate recognizes bitmask DP pattern for permutation generation.
Master "Generate All Permutations Using Bitmask DP" in Bit Manipulation
3 interactive learning modes - each teaches the same concept differently
