{ "data": { "question": { "questionId": "1451", "questionFrontendId": "1326", "categoryTitle": "Algorithms", "boundTopicId": 74731, "title": "Minimum Number of Taps to Open to Water a Garden", "titleSlug": "minimum-number-of-taps-to-open-to-water-a-garden", "content": "
There is a one-dimensional garden on the x-axis. The garden starts at the point 0
and ends at the point n
. (i.e., the length of the garden is n
).
There are n + 1
taps located at points [0, 1, ..., n]
in the garden.
Given an integer n
and an integer array ranges
of length n + 1
where ranges[i]
(0-indexed) means the i-th
tap can water the area [i - ranges[i], i + ranges[i]]
if it was open.
Return the minimum number of taps that should be open to water the whole garden, If the garden cannot be watered return -1.
\n\n\n
Example 1:
\n\nInput: n = 5, ranges = [3,4,1,1,0,0]\nOutput: 1\nExplanation: The tap at point 0 can cover the interval [-3,3]\nThe tap at point 1 can cover the interval [-3,5]\nThe tap at point 2 can cover the interval [1,3]\nThe tap at point 3 can cover the interval [2,4]\nThe tap at point 4 can cover the interval [4,4]\nThe tap at point 5 can cover the interval [5,5]\nOpening Only the second tap will water the whole garden [0,5]\n\n\n
Example 2:
\n\n\nInput: n = 3, ranges = [0,0,0,0]\nOutput: -1\nExplanation: Even if you activate all the four taps you cannot water the whole garden.\n\n\n
\n
Constraints:
\n\n1 <= n <= 104
ranges.length == n + 1
0 <= ranges[i] <= 100
在 x 轴上有一个一维的花园。花园长度为 n
,从点 0
开始,到点 n
结束。
花园里总共有 n + 1
个水龙头,分别位于 [0, 1, ..., n]
。
给你一个整数 n
和一个长度为 n + 1
的整数数组 ranges
,其中 ranges[i]
(下标从 0 开始)表示:如果打开点 i
处的水龙头,可以灌溉的区域为 [i - ranges[i], i + ranges[i]]
。
请你返回可以灌溉整个花园的 最少水龙头数目 。如果花园始终存在无法灌溉到的地方,请你返回 -1 。
\n\n\n\n
示例 1:
\n\n\n输入:n = 5, ranges = [3,4,1,1,0,0]\n输出:1\n解释:\n点 0 处的水龙头可以灌溉区间 [-3,3]\n点 1 处的水龙头可以灌溉区间 [-3,5]\n点 2 处的水龙头可以灌溉区间 [1,3]\n点 3 处的水龙头可以灌溉区间 [2,4]\n点 4 处的水龙头可以灌溉区间 [4,4]\n点 5 处的水龙头可以灌溉区间 [5,5]\n只需要打开点 1 处的水龙头即可灌溉整个花园 [0,5] 。\n\n\n
示例 2:
\n\n\n输入:n = 3, ranges = [0,0,0,0]\n输出:-1\n解释:即使打开所有水龙头,你也无法灌溉整个花园。\n\n\n
\n\n
提示:
\n\n1 <= n <= 104
ranges.length == n + 1
0 <= ranges[i] <= 100
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