{ "data": { "question": { "questionId": "4146", "questionFrontendId": "3771", "categoryTitle": "Algorithms", "boundTopicId": 3850504, "title": "Total Score of Dungeon Runs", "titleSlug": "total-score-of-dungeon-runs", "content": "
You are given a positive integer hp and two positive 1-indexed integer arrays damage and requirement.
There is a dungeon with n trap rooms numbered from 1 to n. Entering room i reduces your health points by damage[i]. After that reduction, if your remaining health points are at least requirement[i], you earn 1 point for that room.
Let score(j) be the number of points you get if you start with hp health points and enter the rooms j, j + 1, ..., n in this order.
Return the integer score(1) + score(2) + ... + score(n), the sum of scores over all starting rooms.
Note: You cannot skip rooms. You can finish your journey even if your health points become non-positive.
\n\n\n
Example 1:
\n\nInput: hp = 11, damage = [3,6,7], requirement = [4,2,5]
\n\nOutput: 3
\n\nExplanation:
\n\nscore(1) = 2, score(2) = 1, score(3) = 0. The total score is 2 + 1 + 0 = 3.
As an example, score(1) = 2 because you get 2 points if you start from room 1.
11 - 3 = 8. You get 1 point because 8 >= 4.8 - 6 = 2. You get 1 point because 2 >= 2.2 - 7 = -5. You do not get any points because -5 < 5.Example 2:
\n\nInput: hp = 2, damage = [10000,1], requirement = [1,1]
\n\nOutput: 1
\n\nExplanation:
\n\nscore(1) = 0, score(2) = 1. The total score is 0 + 1 = 1.
score(1) = 0 because you do not get any points if you start from room 1.
2 - 10000 = -9998. You do not get any points because -9998 < 1.-9998 - 1 = -9999. You do not get any points because -9999 < 1.score(2) = 1 because you get 1 point if you start from room 2.
2 - 1 = 1. You get 1 point because 1 >= 1.\n
Constraints:
\n\n1 <= hp <= 1091 <= n == damage.length == requirement.length <= 1051 <= damage[i], requirement[i] <= 104给你一个 正整数 hp 和两个 正整数 数组 damage 和 requirement,数组下标从 1 开始。
有一个地牢,里面有 n 个陷阱房间,编号从 1 到 n。进入编号为 i 的房间会使你的生命值减少 damage[i]。减少后,如果你的剩余生命值至少为 requirement[i],你可以从该房间获得 1 分。
定义 score(j) 为从房间 j 开始,依次进入房间 j, j + 1, ..., n 时可以获得的总分。
返回整数 score(1) + score(2) + ... + score(n),即从所有起始房间计算的分数总和。
注意: 你不能跳过房间。即使你的生命值降为非正数,你仍然可以继续进入房间。
\n\n\n\n
示例 1:
\n\n输入: hp = 11, damage = [3,6,7], requirement = [4,2,5]
\n\n输出: 3
\n\n解释:
\n\nscore(1) = 2, score(2) = 1, score(3) = 0。总分为 2 + 1 + 0 = 3。
例如,score(1) = 2,因为从房间 1 开始可以获得 2 分:
11 - 3 = 8。因为 8 >= 4,你获得 1 分。8 - 6 = 2。因为 2 >= 2,你获得 1 分。2 - 7 = -5。因为 -5 < 5,你没有获得分数。示例 2:
\n\n输入: hp = 2, damage = [10000,1], requirement = [1,1]
\n\n输出: 1
\n\n解释:
\n\nscore(1) = 0, score(2) = 1。总分为 0 + 1 = 1。
score(1) = 0,因为从房间 1 开始无法获得任何分数:
2 - 10000 = -9998。因为 -9998 < 1,你没有获得分数。-9998 - 1 = -9999。因为 -9999 < 1,你没有获得分数。score(2) = 1,因为从房间 2 开始可以获得 1 分:
2 - 1 = 1。因为 1 >= 1,你获得 1 分。\n\n
提示:
\n\n1 <= hp <= 1091 <= n == damage.length == requirement.length <= 1051 <= damage[i], requirement[i] <= 104pref with the prefix sums.",
"Initially, the total points/score is the total number of subarrays n * (n + 1) / 2.",
"We need to subtract subarrays [i, j] that do not satisfy hp - (pref[j] - pref[i-1]) >= requirement[j]. The inequality is equivalent to pref[i-1] >= requirement[j] - hp + pref[j].",
"For each j, count the previous is with pref[i-1] < requirement[j] - hp + pref[j] using binary search or an ordered data structure."
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