## 657. Judge Route Circle

Initially, there is a Robot at position (0, 0). Given a sequence of its moves, judge if this robot makes a circle, which means it moves back to the original place.

The move sequence is represented by a string. And each move is represent by a character. The valid robot moves are `R` (Right), `L` (Left), `U` (Up) and `D` (down). The output should be true or false representing whether the robot makes a circle.

Example 1:

```Input: "UD"
Output: true
```

Example 2:

```Input: "LL"
Output: false
```

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#### Approach #1: Simulation [Accepted]

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Intuition

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We can simulate the position of the robot after each command.

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Algorithm

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Initially, the robot is at `(x, y) = (0, 0)`. If the move is `\'U\'`, the robot goes to `(x, y-1)`; if the move is `\'R\'`, the robot goes to `(x, y) = (x+1, y)`, and so on.

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Complexity Analysis

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Time Complexity: , where is the length of `moves`. We iterate through the string.

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Space Complexity: . In Java, our character array is .

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Analysis written by: @awice.

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