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83 lines
2.5 KiB
Markdown
Executable File
83 lines
2.5 KiB
Markdown
Executable File
# [898. Bitwise ORs of Subarrays](https://leetcode.com/problems/bitwise-ors-of-subarrays/)
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## 题目
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We have an array `A` of non-negative integers.
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For every (contiguous) subarray `B = [A[i], A[i+1], ..., A[j]]` (with `i <= j`), we take the bitwise OR of all the elements in `B`, obtaining a result `A[i] | A[i+1] | ... | A[j]`.
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Return the number of possible results. (Results that occur more than once are only counted once in the final answer.)
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**Example 1:**
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Input: [0]
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Output: 1
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Explanation:
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There is only one possible result: 0.
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**Example 2:**
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Input: [1,1,2]
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Output: 3
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Explanation:
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The possible subarrays are [1], [1], [2], [1, 1], [1, 2], [1, 1, 2].
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These yield the results 1, 1, 2, 1, 3, 3.
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There are 3 unique values, so the answer is 3.
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**Example 3:**
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Input: [1,2,4]
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Output: 6
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Explanation:
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The possible results are 1, 2, 3, 4, 6, and 7.
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**Note:**
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1. `1 <= A.length <= 50000`
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2. `0 <= A[i] <= 10^9`
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## 题目大意
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我们有一个非负整数数组 A。对于每个（连续的）子数组 B = [A[i], A[i+1], ..., A[j]] （ i <= j），我们对 B 中的每个元素进行按位或操作，获得结果 A[i] | A[i+1] | ... | A[j]。返回可能结果的数量。（多次出现的结果在最终答案中仅计算一次。）
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## 解题思路
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- 给出一个数组，要求求出这个数组所有的子数组中，每个集合内所有数字取 `|` 运算以后，不同结果的种类数。
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- 这道题可以这样考虑，第一步，先考虑所有的子数组如何得到，以 `[001, 011, 100, 110, 101]` 为例，所有的子数组集合如下：
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```c
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[001]
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[001 011] [011]
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[001 011 100] [011 100] [100]
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[001 011 100 110] [011 100 110] [100 110] [110]
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[001 011 100 110 101] [011 100 110 101] [100 110 101] [110 101] [101]
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```
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可以发现，从左往右遍历原数组，每次新来的一个元素，依次加入到之前已经生成过的集合中，再以自己为单独集合。这样就可以生成原数组的所有子集。
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- 第二步，将每一行的子集内的所有元素都进行 `|` 运算，得到：
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```c
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001
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011 011
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111 111 100
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111 111 110 110
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111 111 111 111 101
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```
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- 第三步，去重：
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```c
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001
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011
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111 100
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111 110
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111 101
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```
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由于二进制位不超过 32 位，所以这里每一行最多不会超过 32 个数。所以最终时间复杂度不会超过 O(32 N)，即 O(K * N)。最后将这每一行的数字都放入最终的 map 中去重即可。
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