How do you solve Maximum Total Damage With Spell Casting on LeetCode?

Maximum Total Damage With Spell Casting (LeetCode #3186) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n + k) time complexity and O(k) space complexity. Key insight: Casting spells with the same damage maximizes total damage.

What is the brute force solution for Maximum Total Damage With Spell Casting?

The brute force approach for Maximum Total Damage With Spell Casting is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach checks all possible combinations of spells to find the maximum total damage. This is simple but inefficient, as it considers every possible subset of spells. The optimal Optimal Solution approach improves this to O(n + k).

What are the interview tips for Maximum Total Damage With Spell Casting?

Explain your thought process clearly before coding. Discuss edge cases, such as all spells having the same damage. Practice dynamic programming problems to build intuition.

What are common mistakes when solving Maximum Total Damage With Spell Casting?

Not considering the frequency of spells with the same damage. Overlooking the constraints when updating the dp array.

#3186

Maximum Total Damage With Spell Casting

Medium

ArrayHash TableTwo PointersBinary SearchDynamic ProgrammingSortingCountingHash MapDynamic Programming

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n + k)
Space	O(1)	O(k)

💡

Intuition

Time O(n + k)Space O(k)

The optimal solution uses dynamic programming to build up the maximum damage possible by considering each spell's damage and the constraints on casting. This avoids the combinatorial explosion of subsets.

⚙️

Algorithm

3 steps

1Step 1: Count the frequency of each damage value in the power array.
2Step 2: Use a dynamic programming array where dp[i] represents the maximum damage possible using spells up to damage i.
3Step 3: For each unique damage value, update the dp array based on whether we include that damage or not, considering the constraints.

solution.py12 lines

1from collections import Counter
2
3def max_damage_optimal(power):
4    count = Counter(power)
5    max_damage = 0
6    dp = [0] * (max(count.keys()) + 1)
7    for damage in range(len(dp)):
8        if damage in count:
9            dp[damage] = max(dp[damage - 1], (dp[damage - 2] if damage >= 2 else 0) + damage * count[damage])
10        else:
11            dp[damage] = dp[damage - 1]
12    return dp[-1]

ℹ

Complexity note: The time complexity is O(n + k), where n is the number of spells and k is the range of unique damage values. The space complexity is O(k) for the dp array and the count map.

1Casting spells with the same damage maximizes total damage.
2Avoiding adjacent damage values is crucial for optimal casting.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.