{ "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).

\n\n

There are n + 1 taps located at points [0, 1, ..., n] in the garden.

\n\n

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.

\n\n

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\"\"\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\n\n", "translatedTitle": "灌溉花园的最少水龙头数目", "translatedContent": "

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。

\n\n

花园里总共有 n + 1 个水龙头，分别位于 [0, 1, ..., n] 。

\n\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]] 。

\n\n

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\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：

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