{ "data": { "question": { "questionId": "3411", "questionFrontendId": "3145", "categoryTitle": "Algorithms", "boundTopicId": 2772487, "title": "Find Products of Elements of Big Array", "titleSlug": "find-products-of-elements-of-big-array", "content": "

The powerful array of a non-negative integer x is defined as the shortest sorted array of powers of two that sum up to x. The table below illustrates examples of how the powerful array is determined. It can be proven that the powerful array of x is unique.

\n\n\n\t\n\t\t\n\t\t\t\n\t\t\t\n\t\t\t\n\t\t\n\t\t\n\t\t\t\n\t\t\t\n\t\t\t\n\t\t\n\t\t\n\t\t\t\n\t\t\t\n\t\t\t\n\t\t\n\t\t\n\t\t\t\n\t\t\t\n\t\t\t\n\t\t\n\t\t\n\t\t\t\n\t\t\t\n\t\t\t\n\t\t\n\t\t\n\t\t\t\n\t\t\t\n\t\t\t\n\t\t\n\t\n
numBinary Representationpowerful array
100001[1]
801000[8]
1001010[2, 8]
1301101[1, 4, 8]
2310111[1, 2, 4, 16]
\n\n

The array big_nums is created by concatenating the powerful arrays for every positive integer i in ascending order: 1, 2, 3, and so on. Thus, big_nums begins as [1, 2, 1, 2, 4, 1, 4, 2, 4, 1, 2, 4, 8, ...].

\n\n

You are given a 2D integer matrix queries, where for queries[i] = [fromi, toi, modi] you should calculate (big_nums[fromi] * big_nums[fromi + 1] * ... * big_nums[toi]) % modi.

\n\n

Return an integer array answer such that answer[i] is the answer to the ith query.

\n\n

 

\n

Example 1:

\n\n
\n

Input: queries = [[1,3,7]]

\n\n

Output: [4]

\n\n

Explanation:

\n\n

There is one query.

\n\n

big_nums[1..3] = [2,1,2]. The product of them is 4. The result is 4 % 7 = 4.

\n
\n\n

Example 2:

\n\n
\n

Input: queries = [[2,5,3],[7,7,4]]

\n\n

Output: [2,2]

\n\n

Explanation:

\n\n

There are two queries.

\n\n

First query: big_nums[2..5] = [1,2,4,1]. The product of them is 8. The result is 8 % 3 = 2.

\n\n

Second query: big_nums[7] = 2. The result is 2 % 4 = 2.

\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "大数组元素的乘积", "translatedContent": "

一个非负整数 x 的 强数组 指的是满足元素为 2 的幂且元素总和为 x 的最短有序数组。下表说明了如何确定 强数组 的示例。可以证明，x 对应的强数组是独一无二的。

\n\n\n\t\n\t\t\n\t\t\t\n\t\t\t\n\t\t\t\n\t\t\n\t\t\n\t\t\t\n\t\t\t\n\t\t\t\n\t\t\n\t\t\n\t\t\t\n\t\t\t\n\t\t\t\n\t\t\n\t\t\n\t\t\t\n\t\t\t\n\t\t\t\n\t\t\n\t\t\n\t\t\t\n\t\t\t\n\t\t\t\n\t\t\n\t\t\n\t\t\t\n\t\t\t\n\t\t\t\n\t\t\n\t\n
数字二进制表示强数组
100001[1]
801000[8]
1001010[2, 8]
1301101[1, 4, 8]
2310111[1, 2, 4, 16]
\n\n

 

\n\n

我们将每一个升序的正整数 i （即1，2，3等等）的 强数组 连接得到数组 big_nums ，big_nums 开始部分为 [1, 2, 1, 2, 4, 1, 4, 2, 4, 1, 2, 4, 8, ...] 。

\n\n

给你一个二维整数数组 queries ，其中 queries[i] = [fromi, toi, modi] ，你需要计算 (big_nums[fromi] * big_nums[fromi + 1] * ... * big_nums[toi]) % modi 。

\n\n

请你返回一个整数数组 answer ，其中 answer[i] 是第 i 个查询的答案。

\n\n

 

\n\n

示例 1：

\n\n

输入：queries = [[1,3,7]]

\n\n

输出：[4]

\n\n

解释：

\n\n

只有一个查询。

\n\n

big_nums[1..3] = [2,1,2] 。它们的乘积为 4。结果为 4 % 7 = 4。

\n\n

示例 2：

\n\n

输入：queries = [[2,5,3],[7,7,4]]

\n\n

输出：[2,2]

\n\n

解释：

\n\n

有两个查询。

\n\n

第一个查询：big_nums[2..5] = [1,2,4,1] 。它们的乘积为 8 。结果为  8 % 3 = 2。

\n\n

第二个查询：big_nums[7] = 2 。结果为 2 % 4 = 2。

\n\n

 

\n\n

提示：

\n\n\n\n

 

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Racket CS<\\/a> v8.15<\\/p>\\r\\n\\r\\n
\\u4f7f\\u7528 #lang racket<\\/p>\\r\\n\\r\\n
\\u5df2\\u9884\\u5148 (require data\\/gvector data\\/queue data\\/order data\\/heap). \\u82e5\\u9700\\u4f7f\\u7528\\u5176\\u5b83\\u6570\\u636e\\u7ed3\\u6784\\uff0c\\u53ef\\u81ea\\u884c require\\u3002<\\/p>\"],\"erlang\":[\"Erlang\",\"Erlang\\/OTP 26\"],\"elixir\":[\"Elixir\",\"Elixir 1.17 with Erlang\\/OTP 26\"],\"dart\":[\"Dart\",\"
Dart 3.2\\u3002\\u60a8\\u53ef\\u4ee5\\u4f7f\\u7528 collection<\\/a> \\u5305<\\/p>\\r\\n\\r\\n
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\\u7248\\u672c\\uff1a0.53.11 (cjnative)<\\/p>\\r\\n\\r\\n
\\u7f16\\u8bd1\\u53c2\\u6570\\uff1a-O2 --disable-reflection<\\/code><\\/p>\\r\\n\\r\\n
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