Given the following partial dp table state for n=3 permutations (bitmask keys shown with their stored permutations): { 0: [[]], 1: [[0]], 3: [[0,1],[1,0]], 7: [[0,1,2],[0,2,1],[1,0,2],[1,2,0],[2,0,1],[2,1,0]] } Which element was added last to reach dp[3] from dp[1]?

hard🔄 Reverse Engineer Q9 of Q15

Bit Manipulation - Generate All Permutations Using Bitmask DP

AElement 1

BElement 3

CElement 2

DElement 0

Step-by-Step Solution

Solution:

Step 1: Understand bitmask keys
dp[1] corresponds to mask 001 (element 0 used), dp[3] is 011 (elements 0 and 1 used).
Step 2: Identify added element
Transition from 1 to 3 adds element with bit 2^1 = 2, which is element 1.
Final Answer:
Option A -> Option A
Quick Check:
Bitmask difference shows element 1 added last [OK]

Quick Trick: Bitmask difference reveals last added element [OK]

Common Mistakes:

MISTAKES

Misreading bitmask or confusing element indices

Trap Explanation:

PITFALL

Candidates confuse bit positions with element values.

Interviewer Note:

CONTEXT

Tests deep understanding of bitmask DP state transitions

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Given the following partial dp table state for n=3 permutations (bitmask keys shown with their stored permutations): { 0: [[]], 1: [[0]], 3: [[0,1],[1,0]], 7: [[0,1,2],[0,2,1],[1,0,2],[1,2,0],[2,0,1],[2,1,0]] } Which element was added last to reach dp[3] from dp[1]?

Step 1: Understand bitmask keys

Step 2: Identify added element

Final Answer:

Quick Check:

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