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Commit 01b8a10

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feat: add solutions to lc problem: No.2657 (doocs#4338)
No.2657.Find the Prefix Common Array of Two Arrays close doocs#3952 
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‎solution/2600-2699/2657.Find the Prefix Common Array of Two Arrays/README.md‎

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<!-- solution:end -->
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<!-- solution:start -->
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### 方法三:位运算(空间优化)
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由于题目中给定的数组 $A$ 和 $B$ 的元素范围是 $[1,n],ドル且不超过 50ドル,ドル我们可以使用一个整数 $x$ 和一个整数 $y$ 来分别表示数组 $A$ 和 $B$ 中每个元素的出现情况。具体地,我们用整数 $x$ 的第 $i$ 位表示元素 $i$ 是否在数组 $A$ 中出现过,用整数 $y$ 的第 $i$ 位表示元素 $i$ 是否在数组 $B$ 中出现过。
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时间复杂度 $O(n),ドル其中 $n$ 是数组 $A$ 和 $B$ 的长度。空间复杂度 $O(1)$。
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<!-- tabs:start -->
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#### Python3
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```python
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class Solution:
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def findThePrefixCommonArray(self, A: List[int], B: List[int]) -> List[int]:
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ans = []
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x = y = 0
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for a, b in zip(A, B):
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x |= 1 << a
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y |= 1 << b
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ans.append((x & y).bit_count())
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return ans
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```
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#### Java
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```java
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class Solution {
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public int[] findThePrefixCommonArray(int[] A, int[] B) {
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int n = A.length;
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int[] ans = new int[n];
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long x = 0, y = 0;
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for (int i = 0; i < n; i++) {
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x |= 1L << A[i];
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y |= 1L << B[i];
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ans[i] = Long.bitCount(x & y);
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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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#### C++
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```cpp
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class Solution {
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public:
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vector<int> findThePrefixCommonArray(vector<int>& A, vector<int>& B) {
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int n = A.size();
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vector<int> ans(n);
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long long x = 0, y = 0;
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for (int i = 0; i < n; ++i) {
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x |= (1LL << A[i]);
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y |= (1LL << B[i]);
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ans[i] = __builtin_popcountll(x & y);
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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 findThePrefixCommonArray(A []int, B []int) []int {
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n := len(A)
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ans := make([]int, n)
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var x, y int
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for i := 0; i < n; i++ {
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x |= 1 << A[i]
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y |= 1 << B[i]
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ans[i] = bits.OnesCount(uint(x & y))
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}
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return ans
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}
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```
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#### TypeScript
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```ts
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function findThePrefixCommonArray(A: number[], B: number[]): number[] {
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const n = A.length;
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const ans: number[] = [];
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let [x, y] = [0n, 0n];
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for (let i = 0; i < n; i++) {
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x |= 1n << BigInt(A[i]);
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y |= 1n << BigInt(B[i]);
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ans.push(bitCount64(x & y));
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}
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return ans;
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}
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function bitCount64(i: bigint): number {
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i = i - ((i >> 1n) & 0x5555555555555555n);
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i = (i & 0x3333333333333333n) + ((i >> 2n) & 0x3333333333333333n);
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i = (i + (i >> 4n)) & 0x0f0f0f0f0f0f0f0fn;
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i = i + (i >> 8n);
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i = i + (i >> 16n);
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i = i + (i >> 32n);
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return Number(i & 0x7fn);
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}
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```
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<!-- tabs:end -->
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<!-- solution:end -->
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<!-- problem:end -->

‎solution/2600-2699/2657.Find the Prefix Common Array of Two Arrays/README_EN.md‎

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<!-- solution:end -->
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<!-- solution:start -->
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### Solution 3: Bit Manipulation (Space Optimization)
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Since the elements of arrays $A$ and $B$ are in the range $[1, n]$ and do not exceed 50ドル,ドル we can use an integer $x$ and an integer $y$ to represent the occurrence of each element in arrays $A$ and $B,ドル respectively. Specifically, we use the $i$-th bit of integer $x$ to indicate whether element $i$ has appeared in array $A,ドル and the $i$-th bit of integer $y$ to indicate whether element $i$ has appeared in array $B$.
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The time complexity of this solution is $O(n),ドル where $n$ is the length of arrays $A$ and $B$. The space complexity is $O(1)$.
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<!-- tabs:start -->
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#### Python3
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```python
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class Solution:
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def findThePrefixCommonArray(self, A: List[int], B: List[int]) -> List[int]:
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ans = []
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x = y = 0
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for a, b in zip(A, B):
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x |= 1 << a
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y |= 1 << b
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ans.append((x & y).bit_count())
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return ans
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```
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#### Java
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```java
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class Solution {
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public int[] findThePrefixCommonArray(int[] A, int[] B) {
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int n = A.length;
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int[] ans = new int[n];
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long x = 0, y = 0;
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for (int i = 0; i < n; i++) {
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x |= 1L << A[i];
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y |= 1L << B[i];
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ans[i] = Long.bitCount(x & y);
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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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#### C++
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```cpp
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class Solution {
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public:
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vector<int> findThePrefixCommonArray(vector<int>& A, vector<int>& B) {
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int n = A.size();
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vector<int> ans(n);
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long long x = 0, y = 0;
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for (int i = 0; i < n; ++i) {
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x |= (1LL << A[i]);
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y |= (1LL << B[i]);
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ans[i] = __builtin_popcountll(x & y);
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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 findThePrefixCommonArray(A []int, B []int) []int {
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n := len(A)
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ans := make([]int, n)
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var x, y int
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for i := 0; i < n; i++ {
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x |= 1 << A[i]
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y |= 1 << B[i]
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ans[i] = bits.OnesCount(uint(x & y))
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}
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return ans
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}
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```
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#### TypeScript
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```ts
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function findThePrefixCommonArray(A: number[], B: number[]): number[] {
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const n = A.length;
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const ans: number[] = [];
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let [x, y] = [0n, 0n];
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for (let i = 0; i < n; i++) {
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x |= 1n << BigInt(A[i]);
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y |= 1n << BigInt(B[i]);
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ans.push(bitCount64(x & y));
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}
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return ans;
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}
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function bitCount64(i: bigint): number {
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i = i - ((i >> 1n) & 0x5555555555555555n);
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i = (i & 0x3333333333333333n) + ((i >> 2n) & 0x3333333333333333n);
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i = (i + (i >> 4n)) & 0x0f0f0f0f0f0f0f0fn;
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i = i + (i >> 8n);
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i = i + (i >> 16n);
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i = i + (i >> 32n);
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return Number(i & 0x7fn);
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}
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```
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<!-- tabs:end -->
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<!-- solution:end -->
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<!-- problem:end -->
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class Solution {
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public:
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vector<int> findThePrefixCommonArray(vector<int>& A, vector<int>& B) {
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int n = A.size();
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vector<int> ans(n);
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long long x = 0, y = 0;
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for (int i = 0; i < n; ++i) {
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x |= (1LL << A[i]);
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y |= (1LL << B[i]);
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ans[i] = __builtin_popcountll(x & y);
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}
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return ans;
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}
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};
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func findThePrefixCommonArray(A []int, B []int) []int {
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n := len(A)
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ans := make([]int, n)
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var x, y int
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for i := 0; i < n; i++ {
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x |= 1 << A[i]
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y |= 1 << B[i]
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ans[i] = bits.OnesCount(uint(x & y))
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}
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return ans
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}
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class Solution {
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public int[] findThePrefixCommonArray(int[] A, int[] B) {
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int n = A.length;
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int[] ans = new int[n];
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long x = 0, y = 0;
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for (int i = 0; i < n; i++) {
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x |= 1L << A[i];
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y |= 1L << B[i];
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ans[i] = Long.bitCount(x & y);
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}
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return ans;
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}
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}
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class Solution:
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def findThePrefixCommonArray(self, A: List[int], B: List[int]) -> List[int]:
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ans = []
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x = y = 0
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for a, b in zip(A, B):
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x |= 1 << a
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y |= 1 << b
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ans.append((x & y).bit_count())
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return ans
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function findThePrefixCommonArray(A: number[], B: number[]): number[] {
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const n = A.length;
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const ans: number[] = [];
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let [x, y] = [0n, 0n];
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for (let i = 0; i < n; i++) {
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x |= 1n << BigInt(A[i]);
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y |= 1n << BigInt(B[i]);
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ans.push(bitCount64(x & y));
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}
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return ans;
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}
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function bitCount64(i: bigint): number {
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i = i - ((i >> 1n) & 0x5555555555555555n);
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i = (i & 0x3333333333333333n) + ((i >> 2n) & 0x3333333333333333n);
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i = (i + (i >> 4n)) & 0x0f0f0f0f0f0f0f0fn;
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i = i + (i >> 8n);
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i = i + (i >> 16n);
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i = i + (i >> 32n);
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return Number(i & 0x7fn);
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}

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