Formatted question description: https://leetcode.ca/all/1320.html
1320. Minimum Distance to Type a Word Using Two Fingers (Hard)
You have a keyboard layout as shown above in the XY plane, where each English uppercase letter is located at some coordinate, for example, the letter A is located at coordinate (0,0), the letter B is located at coordinate (0,1), the letter P is located at coordinate (2,3) and the letter Z is located at coordinate (4,1).
Given the string word
, return the minimum total distance to type such string using only two fingers. The distance between coordinates (x_{1},y_{1}) and (x_{2},y_{2}) is x_{1}  x_{2} + y_{1}  y_{2}.
Note that the initial positions of your two fingers are considered free so don't count towards your total distance, also your two fingers do not have to start at the first letter or the first two letters.
Example 1:
Input: word = "CAKE" Output: 3 Explanation: Using two fingers, one optimal way to type "CAKE" is: Finger 1 on letter 'C' > cost = 0 Finger 1 on letter 'A' > cost = Distance from letter 'C' to letter 'A' = 2 Finger 2 on letter 'K' > cost = 0 Finger 2 on letter 'E' > cost = Distance from letter 'K' to letter 'E' = 1 Total distance = 3
Example 2:
Input: word = "HAPPY" Output: 6 Explanation: Using two fingers, one optimal way to type "HAPPY" is: Finger 1 on letter 'H' > cost = 0 Finger 1 on letter 'A' > cost = Distance from letter 'H' to letter 'A' = 2 Finger 2 on letter 'P' > cost = 0 Finger 2 on letter 'P' > cost = Distance from letter 'P' to letter 'P' = 0 Finger 1 on letter 'Y' > cost = Distance from letter 'A' to letter 'Y' = 4 Total distance = 6
Example 3:
Input: word = "NEW" Output: 3
Example 4:
Input: word = "YEAR" Output: 7
Constraints:
2 <= word.length <= 300
 Each
word[i]
is an English uppercase letter.
Related Topics:
Dynamic Programming
Solution 1. DP
// OJ: https://leetcode.com/problems/minimumdistancetotypeawordusingtwofingers/
// Time: O(N)
// Space: O(1)
// Ref: https://leetcode.com/problems/minimumdistancetotypeawordusingtwofingers/discuss/477652/JavaC%2B%2BPython1DDPO(1)Space
class Solution {
int d(int a, int b) {
return abs(a / 6  b / 6) + abs(a % 6  b % 6);
}
public:
int minimumDistance(string word) {
vector<int> dp(26);
int res = 0, save = 0, n = word.size();
for (int i = 0; i < n  1; ++i) {
int b = word[i]  'A', c = word[i + 1]  'A';
for (int a = 0; a < 26; ++a)
dp[b] = max(dp[b], dp[a] + d(b, c)  d(a, c));
save = max(save, dp[b]);
res += d(b, c);
}
return res  save;
}
};
Java

class Solution { public int minimumDistance(String word) { int length = word.length(); int[][] dp = new int[length][length]; int[][] distances = new int[length][length]; for (int i = 0; i < length; i++) { for (int j = i + 1; j < length; j++) distances[i][j] = distance(word.charAt(i)  'A', word.charAt(j)  'A'); } for (int i = 1; i < length; i++) { for (int j = 0; j < length; j++) dp[i][j] = Integer.MAX_VALUE; for (int j = 0; j < i  1; j++) { dp[i][j] = Math.min(dp[i][j], dp[i  1][j] + distances[i  1][i]); dp[i][i  1] = Math.min(dp[i][i  1], dp[i  1][j] + distances[j][i]); } dp[i][i  1] = Math.min(dp[i][i  1], dp[i  1][i  1]); dp[i][i] = dp[i  1][i  1] + distances[i  1][i]; } int minDistance = Integer.MAX_VALUE; for (int i = 0; i < length  1; i++) minDistance = Math.min(minDistance, dp[length  1][i]); return minDistance; } public int distance(int position1, int position2) { int x1 = position1 / 6, y1 = position1 % 6; int x2 = position2 / 6, y2 = position2 % 6; return Math.abs(x2  x1) + Math.abs(y2  y1); } }

// OJ: https://leetcode.com/problems/minimumdistancetotypeawordusingtwofingers/ // Time: O(N) // Space: O(1) // Ref: https://leetcode.com/problems/minimumdistancetotypeawordusingtwofingers/discuss/477652/JavaC%2B%2BPython1DDPO(1)Space class Solution { int d(int a, int b) { return abs(a / 6  b / 6) + abs(a % 6  b % 6); } public: int minimumDistance(string word) { vector<int> dp(26); int res = 0, save = 0, n = word.size(); for (int i = 0; i < n  1; ++i) { int b = word[i]  'A', c = word[i + 1]  'A'; for (int a = 0; a < 26; ++a) dp[b] = max(dp[b], dp[a] + d(b, c)  d(a, c)); save = max(save, dp[b]); res += d(b, c); } return res  save; } };

print("Todo!")