Sum of Min of Xor

AtCoder

IDarc127_d

Time5000ms

Memory256MB

Difficulty—

Given are sequences of $N$ integers each: $(A_1,A_2,\cdots,A_N)$ and $(B_1,B_2,\cdots,B_N)$. Find $\sum_{1 \leq i < j \leq N} \min(A_i \oplus A_j, B_i \oplus B_j)$, where $\oplus$ denotes the bitwise XOR. ## Constraints * $1 \leq N \leq 250000$ * $0 \leq A_i,B_i < 2^{18}$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $\cdots$ $A_N$ $B_1$ $B_2$ $\cdots$ $B_N$ [samples]

Samples

Input #1

3
1 2 3
4 5 6

Output #1

4

*   $\min(1 \oplus 2, 4 \oplus 5)=\min(3,1)=1$
*   $\min(1 \oplus 3, 4 \oplus 6)=\min(2,2)=2$
*   $\min(2 \oplus 3, 5 \oplus 6)=\min(1,3)=1$

Thus, the answer is $1+2+1=4$.

Input #2

4
1 2 3 4
1 2 3 4

Output #2

Input #3

10
195247 210567 149398 9678 23694 46151 187762 17915 176476 249828
68649 128425 249346 62366 194119 117620 26327 161384 207 57656

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Sum of Min of Xor",
    "description": {
      "content": "Given are sequences of $N$ integers each: $(A_1,A_2,\\cdots,A_N)$ and $(B_1,B_2,\\cdots,B_N)$. Find $\\sum_{1 \\leq i < j \\leq N} \\min(A_i \\oplus A_j, B_i \\oplus B_j)$, where $\\oplus$ denotes the bitwise ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 5000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc127_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given are sequences of $N$ integers each: $(A_1,A_2,\\cdots,A_N)$ and $(B_1,B_2,\\cdots,B_N)$.\nFind $\\sum_{1 \\leq i < j \\leq N} \\min(A_i \\oplus A_j, B_i \\oplus B_j)$, where $\\oplus$ denotes the bitwise ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments