How do you solve Total Score of Dungeon Runs on LeetCode?

Total Score of Dungeon Runs (LeetCode #3771) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Prefix sums reduce repetitive calculations.

What is the time complexity of Total Score of Dungeon Runs?

The optimal solution for Total Score of Dungeon Runs runs in O(n) time and uses O(n) space. Prefix sums allow us to compute cumulative damage in constant time, leading to linear complexity overall.

What is the brute force solution for Total Score of Dungeon Runs?

The brute force approach for Total Score of Dungeon Runs is Brute Force, with O(n²) time complexity and O(1) space complexity. We can calculate the score for each starting room by iterating through all rooms and checking health points after each room. This method is straightforward but inefficient. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Total Score of Dungeon Runs?

Total Score of Dungeon Runs uses the following concepts: Array, Binary Search, Prefix Sum. The recommended patterns to study are: Prefix Sum, Dynamic Programming.

What are the interview tips for Total Score of Dungeon Runs?

Explain your thought process clearly. Consider edge cases like minimum hp. Optimize your solution before coding.

What are common mistakes when solving Total Score of Dungeon Runs?

Not updating health points correctly after each room. Confusing 0-indexed and 1-indexed arrays.

#3771

Total Score of Dungeon Runs

Medium

ArrayBinary SearchPrefix SumPrefix SumDynamic Programming

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(n)Space O(n)

Using prefix sums allows us to efficiently calculate health reductions and determine scores in linear time.

⚙️

Algorithm

3 steps

1Step 1: Create a prefix sum array for damage to track cumulative damage up to each room.
2Step 2: For each room j, calculate remaining health after entering room j and subsequent rooms using the prefix sum.
3Step 3: Check if remaining health meets requirements and accumulate scores.

solution.py14 lines

1def totalScore(hp, damage, requirement):
2    n = len(damage)
3    prefix = [0] * n
4    prefix[0] = damage[0]
5    for i in range(1, n):
6        prefix[i] = prefix[i-1] + damage[i]
7    total = 0
8    for j in range(n):
9        health = hp - prefix[j]
10        for i in range(j, n):
11            if health >= requirement[i]:
12                total += 1
13            health -= damage[i]
14    return total

ℹ

Complexity note: Prefix sums allow us to compute cumulative damage in constant time, leading to linear complexity overall.

1Prefix sums reduce repetitive calculations.
2Health points can be tracked dynamically as rooms are entered.

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