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1320. Minimum Distance to Type a Word Using Two Fingers 👍

  • Time: $O(27^2n) = O(n)$
  • Space: $O(27^2n) = O(n)$
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class Solution {
 public:
  int minimumDistance(string word) {
    // dp[i][j][k] := the minimum distance to type the `word`, where the left
    // finger is on the i-th letter, the right finger is on the j-th letter, and
    // the words[0..k) have been written
    dp.resize(27, vector<vector<int>>(27, vector<int>(word.length(), -1)));
    return minimumDistance(word, 26, 26, 0);
  }

 private:
  vector<vector<vector<int>>> dp;

  int minimumDistance(const string& word, int i, int j, int k) {
    if (k == word.length())
      return 0;
    if (dp[i][j][k] != -1)
      return dp[i][j][k];
    const int next = word[k] - 'A';
    const int moveLeft = dist(i, next) + minimumDistance(word, next, j, k + 1);
    const int moveRight = dist(j, next) + minimumDistance(word, i, next, k + 1);
    return dp[i][j][k] = min(moveLeft, moveRight);
  }

  int dist(int a, int b) {
    if (a == 26)  // the first hovering state
      return 0;
    const int x1 = a / 6;
    const int y1 = a % 6;
    const int x2 = b / 6;
    const int y2 = b % 6;
    return abs(x1 - x2) + abs(y1 - y2);
  }
};

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class Solution {
  public int minimumDistance(String word) {
    // dp[i][j][k] := the minimum distance to type the `word`, where the left
    // finger is on the i-th letter, the right finger is on the j-th letter, and
    // the words[0..k) have been written
    dp = new Integer[27][27][word.length()];
    return minimumDistance(word, 26, 26, 0);
  }

  private Integer[][][] dp;

  private int minimumDistance(final String word, int i, int j, int k) {
    if (k == word.length())
      return 0;
    if (dp[i][j][k] != null)
      return dp[i][j][k];
    final int next = word.charAt(k) - 'A';
    final int moveLeft = dist(i, next) + minimumDistance(word, next, j, k + 1);
    final int moveRight = dist(j, next) + minimumDistance(word, i, next, k + 1);
    return dp[i][j][k] = Math.min(moveLeft, moveRight);
  }

  private int dist(int a, int b) {
    if (a == 26) // the first hovering state
      return 0;
    final int x1 = a / 6;
    final int y1 = a % 6;
    final int x2 = b / 6;
    final int y2 = b % 6;
    return Math.abs(x1 - x2) + Math.abs(y1 - y2);
  }
}

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class Solution:
  def minimumDistance(self, word: str) -> int:
    def dist(a: int, b: int) -> int:
      if a == 26:  # the first hovering state
        return 0
      x1, y1 = a // 6, a % 6
      x2, y2 = b // 6, b % 6
      return abs(x1 - x2) + abs(y1 - y2)

    # dp(i, j, k) := the minimum distance to type the `word`, where the left
    # finger is on the i-th letter, the right finger is on the j-th letter, and
    # the words[0..k) have been written
    @functools.lru_cache(None)
    def dp(i: int, j: int, k: int) -> int:
      if k == len(word):
        return 0
      nxt = ord(word[k]) - ord('A')
      moveLeft = dist(i, nxt) + dp(nxt, j, k + 1)
      moveRight = dist(j, nxt) + dp(i, nxt, k + 1)
      return min(moveLeft, moveRight)

    return dp(26, 26, 0)