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feat: add solutions to lc problem: No.0238
No.0238.Product of Array Except Self
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‎solution/0200-0299/0238.Product of Array Except Self/README.md

Lines changed: 48 additions & 95 deletions
Original file line numberDiff line numberDiff line change
@@ -46,62 +46,15 @@
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<!-- 这里可写通用的实现逻辑 -->
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**暴力：**
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正常计算除自身之外的乘积。
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```txt
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PRODUCT_EXCEPT_SELF(A)
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n = A.length
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let r[0..n]be a new array
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for i = 0 in n
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s = 1
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for j = 0 in n
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if j == i
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continue
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s *= A[j]
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r[i] = s
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return r
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```
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**左右乘积：**
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分别从左至右，从右至左累乘一次即可。
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```txt
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PRODUCT_EXCEPT_SELF(A)
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n = A.length
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let r[0..n]be a new array
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p = 1
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q = 1
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for i = 0 in n
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r[i] = p
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p *= A[i]
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for i = n - 1 in 0 downto
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r[i] *= q
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q *= A[i]
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return r
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```
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**方法一：两次遍历**
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可行性说明：
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我们定义两个变量 `left` 和 `right`，分别表示当前元素左边所有元素的乘积和右边所有元素的乘积。对于数组中的第一个元素，左边没有元素，所以 `left = 1`；对于数组中的最后一个元素，右边没有元素，所以 `right = 1`。用一个长度为 $n$ 的数组 `ans` 来存储最终的答案。
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以 `nums = [1, 2, 3, 4]` 为例。
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我们先从左到右遍历数组，对于遍历到的第 $i$ 个元素，我们用 `left` 更新 `ans[i]` 的值，然后 `left` 乘以 `nums[i]`。
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`r[i]` 的数值由 `nums[0..i - 1]` 的数值乘积所决定。在遍历结束后，最后一个元素得到了最终结果（因为累乘了前方所有数值）。
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接下来，我们从右到左遍历数组，对于遍历到的第 $i$ 个元素，我们将 `ans[i]` 乘以 `right`，然后 `right` 乘以 `nums[i]`。
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```txt
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nums: [1, 2, 3, 4]
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r: [1, 1, 2, 6]
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p: [1, 2, 6, 24]
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```
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而其他位置的数值，距离结果还差什么呢，那就是相对自身，后方所有数值的乘积，于是就有了第二次，从后往前的过程。
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```txt
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nums: [1, 2, 3, 4]
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r: [24, 12, 8, 6]
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p: [24, 24, 12, 4]
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```
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时间复杂度 $O(n)$，忽略答案的空间消耗，空间复杂度 $O(1)$。其中 $n$ 是数组的长度。
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<!-- tabs:start -->
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@@ -113,11 +66,11 @@ nums: [1, 2, 3, 4]
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class Solution:
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def productExceptSelf(self, nums: List[int]) -> List[int]:
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n = len(nums)
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ans = [1] * n
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ans = [0] * n
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left = right = 1
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for i in range(n):
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for i, v in enumerate(nums):
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ans[i] = left
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left *= nums[i]
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left *= v
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for i in range(n - 1, -1, -1):
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ans[i] *= right
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right *= nums[i]
@@ -146,6 +99,46 @@ class Solution {
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}
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```
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### **C++**
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```cpp
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class Solution {
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public:
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vector<int> productExceptSelf(vector<int>& nums) {
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int n = nums.size();
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vector<int> ans(n);
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for (int i = 0, left = 1; i < n; ++i) {
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ans[i] = left;
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left *= nums[i];
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}
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for (int i = n - 1, right = 1; i >= 0; --i) {
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ans[i] *= right;
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right *= nums[i];
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}
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return ans;
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}
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};
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```
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### **Go**
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```go
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func productExceptSelf(nums []int) []int {
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n := len(nums)
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ans := make([]int, n)
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left, right := 1, 1
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for i, v := range nums {
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ans[i] = left
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left *= v
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}
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for i := n - 1; i >= 0; i-- {
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ans[i] *= right
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right *= nums[i]
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}
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return ans
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}
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```
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### **JavaScript**
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```js
@@ -194,46 +187,6 @@ function productExceptSelf(nums: number[]): number[] {
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}
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```
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### **Go**
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```go
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func productExceptSelf(nums []int) []int {
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n := len(nums)
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ans := make([]int, n)
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left, right := 1, 1
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for i := 0; i < n; i++ {
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ans[i] = left
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left *= nums[i]
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}
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for i := n - 1; i >= 0; i-- {
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ans[i] *= right
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right *= nums[i]
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}
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return ans
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}
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```
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### **C++**
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```cpp
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class Solution {
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public:
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vector<int> productExceptSelf(vector<int>& nums) {
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int n = nums.size();
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vector<int> ans(n);
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for (int i = 0, left = 1; i < n; ++i) {
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ans[i] = left;
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left *= nums[i];
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}
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for (int i = n - 1, right = 1; i >= 0; --i) {
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ans[i] *= right;
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right *= nums[i];
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}
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return ans;
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}
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};
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```
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### **Rust**
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```rust

‎solution/0200-0299/0238.Product of Array Except Self/README_EN.md

Lines changed: 43 additions & 43 deletions
Original file line numberDiff line numberDiff line change
@@ -40,11 +40,11 @@
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class Solution:
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def productExceptSelf(self, nums: List[int]) -> List[int]:
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n = len(nums)
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ans = [1] * n
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ans = [0] * n
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left = right = 1
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for i in range(n):
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for i, v in enumerate(nums):
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ans[i] = left
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left *= nums[i]
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left *= v
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for i in range(n - 1, -1, -1):
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ans[i] *= right
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right *= nums[i]
@@ -71,6 +71,46 @@ class Solution {
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}
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```
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### **C++**
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```cpp
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class Solution {
78+
public:
79+
vector<int> productExceptSelf(vector<int>& nums) {
80+
int n = nums.size();
81+
vector<int> ans(n);
82+
for (int i = 0, left = 1; i < n; ++i) {
83+
ans[i] = left;
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left *= nums[i];
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}
86+
for (int i = n - 1, right = 1; i >= 0; --i) {
87+
ans[i] *= right;
88+
right *= nums[i];
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}
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return ans;
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}
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};
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```
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### **Go**
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```go
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func productExceptSelf(nums []int) []int {
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n := len(nums)
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ans := make([]int, n)
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left, right := 1, 1
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for i, v := range nums {
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ans[i] = left
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left *= v
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}
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for i := n - 1; i >= 0; i-- {
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ans[i] *= right
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right *= nums[i]
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}
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return ans
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}
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```
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### **JavaScript**
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```js
@@ -119,46 +159,6 @@ function productExceptSelf(nums: number[]): number[] {
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}
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```
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### **Go**
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```go
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func productExceptSelf(nums []int) []int {
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n := len(nums)
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ans := make([]int, n)
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left, right := 1, 1
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for i := 0; i < n; i++ {
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ans[i] = left
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left *= nums[i]
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}
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for i := n - 1; i >= 0; i-- {
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ans[i] *= right
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right *= nums[i]
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}
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return ans
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}
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```
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### **C++**
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```cpp
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class Solution {
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public:
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vector<int> productExceptSelf(vector<int>& nums) {
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int n = nums.size();
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vector<int> ans(n);
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for (int i = 0, left = 1; i < n; ++i) {
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ans[i] = left;
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left *= nums[i];
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}
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for (int i = n - 1, right = 1; i >= 0; --i) {
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ans[i] *= right;
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right *= nums[i];
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}
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return ans;
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}
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};
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```
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### **Rust**
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```rust

‎solution/0200-0299/0238.Product of Array Except Self/Solution.go

Lines changed: 2 additions & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -2,9 +2,9 @@ func productExceptSelf(nums []int) []int {
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n := len(nums)
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ans := make([]int, n)
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left, right := 1, 1
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for i := 0; i < n; i++ {
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for i, v := range nums {
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ans[i] = left
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left *= nums[i]
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left *= v
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}
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for i := n - 1; i >= 0; i-- {
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ans[i] *= right

‎solution/0200-0299/0238.Product of Array Except Self/Solution.py

Lines changed: 3 additions & 3 deletions
Original file line numberDiff line numberDiff line change
@@ -1,11 +1,11 @@
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class Solution:
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def productExceptSelf(self, nums: List[int]) -> List[int]:
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n = len(nums)
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ans = [1] * n
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ans = [0] * n
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left = right = 1
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for i in range(n):
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for i, v in enumerate(nums):
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ans[i] = left
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left *= nums[i]
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left *= v
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for i in range(n - 1, -1, -1):
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ans[i] *= right
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right *= nums[i]

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