Start by mapping each unique spell power to its total damage using a hash table, then scan through powers in order. Apply dynamic programming to decide for each power whether including it maximizes total damage without breaking adjacency rules. This approach efficiently handles large arrays by combining scanning, counting, and smart selection to reach the optimal total damage.
Problem Statement
You are given an array power where each element represents the damage of a spell a magician can cast. Multiple spells can have the same damage value, and the magician wants to maximize total damage through careful selection.
The magician cannot cast any spell whose damage is within 2 of another chosen spell. That is, if a spell with power[i] is cast, spells with power[i]-2, power[i]-1, power[i]+1, and power[i]+2 cannot be used. Compute the maximum total damage achievable under these constraints.
Examples
Example 1
Input: power = [1,1,3,4]
Output: 6
The maximum possible damage of 6 is produced by casting spells 0, 1, 3 with damage 1, 1, 4.
Example 2
Input: power = [7,1,6,6]
Output: 13
The maximum possible damage of 13 is produced by casting spells 1, 2, 3 with damage 1, 6, 6.
Constraints
- 1 <= power.length <= 105
- 1 <= power[i] <= 109
Solution Approach
Map Power to Total Damage
Create a hash table to sum all occurrences of each unique power. This allows quick lookup of total damage contribution for any chosen power and sets up for dynamic programming decisions.
Dynamic Programming Over Sorted Powers
Sort the unique powers and iterate through them. For each power, calculate two options: include the total damage from this power plus the best damage from non-conflicting previous powers, or skip this power and carry forward the previous maximum. Select the higher of the two.
Final Damage Selection
After processing all powers, the maximum stored in the dynamic programming array represents the optimal total damage. Return this value as the answer, ensuring the adjacency rules are maintained throughout.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
Time complexity is O(n + m log m), where n is the length of power and m is the number of unique powers, due to counting and sorting. Space complexity is O(m) for the hash table and dynamic programming array.
What Interviewers Usually Probe
- They may emphasize using all spells of the same power when choosing to cast it.
- Expect hints toward array scanning combined with hash lookup for efficiency.
- Watch for discussions about handling large power values within the adjacency constraints.
Common Pitfalls or Variants
Common pitfalls
- Failing to sum all duplicates of a power before dynamic programming.
- Not properly skipping conflicting powers within the +-2 range.
- Assuming sequential indices matter instead of actual power values.
Follow-up variants
- Allowing conflicts within a range k instead of 2.
- Casting each spell at most once instead of summing duplicates.
- Maximizing damage under additional cooldown constraints between casts.
How GhostInterview Helps
- Highlights the exact array scanning plus hash lookup pattern to simplify decision making.
- Shows step-by-step dynamic programming logic for selecting non-conflicting powers.
- Illustrates how to combine counting, sorting, and scanning efficiently to reach the optimal damage.
Topic Pages
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- LeetCode Interview Copilot - Use GhostInterview as a live solver when you want direct help with LeetCode-style coding questions.
- Coding Interview Assistant - See how GhostInterview supports array, string, linked list, graph, and tree interview workflows.
- How GhostInterview Works - Review the screenshot, reasoning, and answer flow before using the solver in a live interview.
FAQ
What is the best way to handle duplicate spell powers in Maximum Total Damage With Spell Casting?
Sum all duplicates of each power first in a hash table to consider their total contribution before applying dynamic programming.
Why do we sort unique powers instead of the original array?
Sorting unique powers ensures adjacency checks are based on power values, not indices, enabling correct dynamic programming decisions.
Can this method handle very large power values efficiently?
Yes, using a hash table avoids iterating through unused power values and keeps computation limited to actual unique powers.
How does the +-2 conflict rule affect dynamic programming?
It defines which previous powers are safe to combine with the current power, guiding the choice between including or skipping each power.
Is array scanning plus hash lookup essential for this problem?
Yes, this pattern efficiently aggregates spell damage and enables conflict-aware selection for maximum total damage.
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This problem involves minimizing the length of a sorted array by repeatedly removing adjacent pairs of equal elements.
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