leetcode 514 freedom trail
In the video game Fallout 4, the quest "Road to Freedom" requires players to reach a metal dial called the "Freedom Trail Ring", and use the dial to spell a specific keyword in order to open the door.
Given a string ring, which represents the code engraved on the outer ring and another string key, which represents the keyword needs to be spelled. You need to find the minimum number of steps in order to spell all the characters in the keyword.
Initially, the first character of theringis aligned at 12:00 direction. You need to spell all the characters in the stringkeyone by one by rotating the ring clockwise or anticlockwise to make each character of the stringkeyaligned at 12:00 direction and then by pressing the center button.At the stage of rotating the ring to spell the key characterkey[i]:
- You can rotate the ring clockwise or anticlockwise one place, which counts as 1 step. The final purpose of the rotation is to align one of the string ring's characters at the 12:00 direction, where this character must equal to the character key[i].
- If the character key[i] has been aligned at the 12:00 direction, you need to press the center button to spell, which also counts as 1 step. After the pressing, you could begin to spell the next character in the key (next stage), otherwise, you've finished all the spelling.
Example:
Input: ring = "godding", key = "gd" Output: 4 Explanation:
For the first key character 'g', since it is already in place, we just need 1 step to spell this character.
For the second key character 'd', we need to rotate the ring "godding" anticlockwise by two steps to make it become "ddinggo".
Also, we need 1 more step for spelling.
So the final output is 4.
题目的意思大概是说旋转ring逐个拼出key字符串的字符（可以顺时针，逆时针旋转，旋转每经过 一个字符，所走的步数就要加1，最后按button确定时步数再加1），求最小步数。
刚看到这个题的时候，就考虑用动态规划来解，所以一直去思考它的状态转移过程。如果key中的某个字符在ring中多次出现，则所有这些字符对应key中的字符都表示一个状态，不能确定哪个状态是最优的，（因为最后优化的步数是累积的，所以可能当前走的步数较大，后面却很小），很难写出其状态转移公式，所以最后考虑用带记忆的dfs求解，用一个数组dp[ring.length()][key.length()],dp[i][j]表示ring中第i个字符（从0开始）在12点方向，要得到key中j以后所有字符（包含j）所需要的步数。