# 1138. Alphabet Board Path

## Description

On an alphabet board, we start at position (0, 0), corresponding to character board[0][0].

Here, board = ["abcde", "fghij", "klmno", "pqrst", "uvwxy", "z"], as shown in the diagram below.

We may make the following moves:

• 'U' moves our position up one row, if the position exists on the board;
• 'D' moves our position down one row, if the position exists on the board;
• 'L' moves our position left one column, if the position exists on the board;
• 'R' moves our position right one column, if the position exists on the board;
• '!' adds the character board[r][c] at our current position (r, c) to the answer.

(Here, the only positions that exist on the board are positions with letters on them.)

Return a sequence of moves that makes our answer equal to target in the minimum number of moves.  You may return any path that does so.

Example 1:

Input: target = "leet"
Output: "DDR!UURRR!!DDD!"


Example 2:

Input: target = "code"
Output: "RR!DDRR!UUL!R!"


Constraints:

• 1 <= target.length <= 100
• target consists only of English lowercase letters.

## Solutions

Solution 1: Simulation

Starting from the origin point $(0, 0)$, simulate each step of the movement, appending the result of each step to the answer. Note that the direction of movement follows the order “left, up, right, down”.

The time complexity is $O(n)$, where $n$ is the length of the string target, as each character in the string target needs to be traversed. Ignoring the space consumption of the answer, the space complexity is $O(1)$.

• class Solution {
public String alphabetBoardPath(String target) {
StringBuilder ans = new StringBuilder();
int i = 0, j = 0;
for (int k = 0; k < target.length(); ++k) {
int v = target.charAt(k) - 'a';
int x = v / 5, y = v % 5;
while (j > y) {
--j;
ans.append('L');
}
while (i > x) {
--i;
ans.append('U');
}
while (j < y) {
++j;
ans.append('R');
}
while (i < x) {
++i;
ans.append('D');
}
ans.append("!");
}
return ans.toString();
}
}

• class Solution {
public:
string alphabetBoardPath(string target) {
string ans;
int i = 0, j = 0;
for (char& c : target) {
int v = c - 'a';
int x = v / 5, y = v % 5;
while (j > y) {
--j;
ans += 'L';
}
while (i > x) {
--i;
ans += 'U';
}
while (j < y) {
++j;
ans += 'R';
}
while (i < x) {
++i;
ans += 'D';
}
ans += '!';
}
return ans;
}
};

• class Solution:
def alphabetBoardPath(self, target: str) -> str:
i = j = 0
ans = []
for c in target:
v = ord(c) - ord("a")
x, y = v // 5, v % 5
while j > y:
j -= 1
ans.append("L")
while i > x:
i -= 1
ans.append("U")
while j < y:
j += 1
ans.append("R")
while i < x:
i += 1
ans.append("D")
ans.append("!")
return "".join(ans)


• func alphabetBoardPath(target string) string {
ans := []byte{}
var i, j int
for _, c := range target {
v := int(c - 'a')
x, y := v/5, v%5
for j > y {
j--
ans = append(ans, 'L')
}
for i > x {
i--
ans = append(ans, 'U')
}
for j < y {
j++
ans = append(ans, 'R')
}
for i < x {
i++
ans = append(ans, 'D')
}
ans = append(ans, '!')
}
return string(ans)
}