Project Notes

Product of Array Except Self

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Description

tab: English
 
<p>Given an integer array <code>nums</code>, return <em>an array</em> <code>answer</code> <em>such that</em> <code>answer[i]</code> <em>is equal to the product of all the elements of</em> <code>nums</code> <em>except</em> <code>nums[i]</code>.</p>
 
<p>The product of any prefix or suffix of <code>nums</code> is <strong>guaranteed</strong> to fit in a <strong>32-bit</strong> integer.</p>
 
<p>You must write an algorithm that runs in&nbsp;<code>O(n)</code>&nbsp;time and without using the division operation.</p>
 
<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<pre><strong>Input:</strong> nums = [1,2,3,4]
<strong>Output:</strong> [24,12,8,6]
</pre><p><strong class="example">Example 2:</strong></p>
<pre><strong>Input:</strong> nums = [-1,1,0,-3,3]
<strong>Output:</strong> [0,0,9,0,0]
</pre>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>
 
<ul>
	<li><code>2 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>-30 &lt;= nums[i] &lt;= 30</code></li>
	<li>The input is generated such that <code>answer[i]</code> is <strong>guaranteed</strong> to fit in a <strong>32-bit</strong> integer.</li>
</ul>
 
<p>&nbsp;</p>
<p><strong>Follow up:</strong>&nbsp;Can you solve the problem in <code>O(1)</code>&nbsp;extra&nbsp;space complexity? (The output array <strong>does not</strong> count as extra space for space complexity analysis.)</p>
 
 
 
> [!tip]- Hint 1
> 
> Think how you can efficiently utilize prefix and suffix products to calculate the product of all elements except self for each index. Can you pre-compute the prefix and suffix products in linear time to avoid redundant calculations?
 
> [!tip]- Hint 2
> 
> Can you minimize additional space usage by reusing memory or modifying the input array to store intermediate results?
 
 
---
 
[submissions](https://leetcode.com/problems/product-of-array-except-self/submissions/) | [solutions](https://leetcode.com/problems/product-of-array-except-self/solutions/)
 
 
tab: 中文
 
<p>给你一个整数数组&nbsp;<code>nums</code>，返回 数组&nbsp;<code>answer</code>&nbsp;，其中&nbsp;<code>answer[i]</code>&nbsp;等于&nbsp;<code>nums</code>&nbsp;中除&nbsp;<code>nums[i]</code>&nbsp;之外其余各元素的乘积&nbsp;。</p>
 
<p>题目数据 <strong>保证</strong> 数组&nbsp;<code>nums</code>之中任意元素的全部前缀元素和后缀的乘积都在&nbsp; <strong>32 位</strong> 整数范围内。</p>
 
<p>请&nbsp;<strong>不要使用除法，</strong>且在&nbsp;<code>O(n)</code> 时间复杂度内完成此题。</p>
 
<p>&nbsp;</p>
 
<p><strong>示例 1:</strong></p>
 
<pre>
<strong>输入:</strong> nums = <code>[1,2,3,4]</code>
<strong>输出:</strong> <code>[24,12,8,6]</code>
</pre>
 
<p><strong>示例 2:</strong></p>
 
<pre>
<strong>输入:</strong> nums = [-1,1,0,-3,3]
<strong>输出:</strong> [0,0,9,0,0]
</pre>
 
<p>&nbsp;</p>
 
<p><strong>提示：</strong></p>
 
<ul>
	<li><code>2 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>-30 &lt;= nums[i] &lt;= 30</code></li>
	<li>输入&nbsp;<strong>保证</strong> 数组&nbsp;<code>answer[i]</code>&nbsp;在&nbsp; <strong>32 位</strong> 整数范围内</li>
</ul>
 
<p>&nbsp;</p>
 
<p><strong>进阶：</strong>你可以在 <code>O(1)</code>&nbsp;的额外空间复杂度内完成这个题目吗？（ 出于对空间复杂度分析的目的，输出数组&nbsp;<strong>不被视为&nbsp;</strong>额外空间。）</p>
 
 
 
> [!tip]- 提示 1
> 
> Think how you can efficiently utilize prefix and suffix products to calculate the product of all elements except self for each index. Can you pre-compute the prefix and suffix products in linear time to avoid redundant calculations?
 
> [!tip]- 提示 2
> 
> Can you minimize additional space usage by reusing memory or modifying the input array to store intermediate results?
 
 
---
 
[提交记录](https://leetcode.cn/problems/product-of-array-except-self/submissions/) | [题解](https://leetcode.cn/problems/product-of-array-except-self/solution/)

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