There is a robot starting at position (0, 0), the origin, on a 2D plane. Given a sequence of its moves, judge if this robot ends up at (0, 0) after it completes its moves.

The move sequence is represented by a string, and the character moves[i] represents its ith move. Valid moves are R (right), L (left), U (up), and D (down). If the robot returns to the origin after it finishes all of its moves, return true. Otherwise, return false.

Note: The way that the robot is “facing” is irrelevant. “R” will always make the robot move to the right once, “L” will always make it move left, etc. Also, assume that the magnitude of the robot’s movement is the same for each move.

Input: “UD”

Output: true

Explanation: The robot moves up once, and then down once. All moves have the same magnitude, so it ended up at the origin where it started. Therefore, we return true.

Input: “LL”

Output: false

Explanation: The robot moves left twice. It ends up two “moves” to the left of the origin. We return false because it is not at the origin at the end of its moves.

```public class Program {

public static void Main(string[] args) {
var moves = "UD";
var res = JudgeCircle(moves);
Console.WriteLine(res);

moves = "LL";
res = JudgeCircle2(moves);
Console.WriteLine(res);

moves = "ULDR";
res = JudgeCircle3(moves);
Console.WriteLine(res);

moves = "LDURD";
res = JudgeCircle4(moves);
Console.WriteLine(res);

}

private static bool JudgeCircle(string moves) {
//扫描计数法
var countL = 0;
var countR = 0;
var countU = 0;
var countD = 0;
foreach(var move in moves) {
if(move == 'L') countL++;
else if(move == 'R') countR++;
else if(move == 'U') countU++;
else if(move == 'D') countD++;
}
return countL == countR && countU == countD;
}

private static bool JudgeCircle2(string moves) {
//哈希计数法
var dic = new Dictionary<char, int>() {
{'L',0},
{'R',0},
{'U',0},
{'D',0}
};
foreach(var move in moves) {
dic[move]++;
}
return dic['L'] == dic['R'] && dic['U'] == dic['D'];
}

private static bool JudgeCircle3(string moves) {
//差值计数法
var diffL = moves.Length - moves.Replace("L", "").Length;
var diffR = moves.Length - moves.Replace("R", "").Length;
if(diffL != diffR) return false;
var diffU = moves.Length - moves.Replace("U", "").Length;
var diffD = moves.Length - moves.Replace("D", "").Length;
if(diffU != diffD) return false;
return true;
}

private static bool JudgeCircle4(string moves) {
//正则计数法
//若想AC，请手动在 public class Solution { 的上一行
//添加 using System.Text.RegularExpressions;
var countL = Regex.Matches(moves, "L").Count;
var countR = Regex.Matches(moves, "R").Count;
var countU = Regex.Matches(moves, "U").Count;
var countD = Regex.Matches(moves, "D").Count;
return countL == countR && countU == countD;
}

}```

```True
False
True
False```

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