Two Rooms

AtCoder

IDarc212_d

Time2000ms

Memory256MB

Difficulty—

There are $N$ people numbered $1,2,\ldots,N$. For $i\neq j$, the intimacy between persons $i$ and $j$ is $A_{i,j}$. For each of the $N$ people, assign room $X$ or room $Y$. Each of the $N$ people moves to their assigned room. It is acceptable if there is an empty room. Person $i$ is in a **good state** if the following is satisfied: > (Sum of intimacy with person $i$ of all people in the same room as person $i$) $\geq$ (Sum of intimacy with person $i$ of all people in a different room from person $i$). Output one assignment of rooms such that all $N$ people are in a good state. It can be proved that such an assignment always exists. ## Constraints * $2 \leq N \leq 50$ * $-50 \leq A_{i,j} \leq 50$ * $A_{i,j} = A_{j,i}$ * $A_{i,i}=0$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $A_{1,1}$ $A_{1,2}$ $\cdots$ $A_{1,N}$ $A_{2,1}$ $A_{2,2}$ $\cdots$ $A_{2,N}$ $\vdots$ $A_{N,1}$ $A_{N,2}$ $\cdots$ $A_{N,N}$ [samples]

Samples

Input #1

Output #1

XXYY

Suppose persons $1,2$ are assigned to room $X$ and persons $3,4$ are assigned to room $Y$.
For person $1$, the sum of intimacy with people in the same room (person $2$) is $4$, and the sum of intimacy with people in different rooms (persons $3$ and $4$) is $(-2)+(-1)=-3$, so they are in a good state.
All other people are also in a good state, so this assignment satisfies the condition.
Outputting `YYXX` is also correct.

Input #2

Output #2

XXX

It is acceptable if there is an empty room.

API Response (JSON)

{
  "problem": {
    "name": "Two Rooms",
    "description": {
      "content": "There are $N$ people numbered $1,2,\\ldots,N$. For $i\\neq j$, the intimacy between persons $i$ and $j$ is $A_{i,j}$. For each of the $N$ people, assign room $X$ or room $Y$. Each of the $N$ people move",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc212_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ people numbered $1,2,\\ldots,N$. For $i\\neq j$, the intimacy between persons $i$ and $j$ is $A_{i,j}$.\nFor each of the $N$ people, assign room $X$ or room $Y$. Each of the $N$ people move...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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