# ---
# title: 87. Scramble String
# id: problem87
# author: Tian Jun
# date: 2020-10-31
# difficulty: Hard
# categories: String, Dynamic Programming
# link: <https://leetcode.com/problems/scramble-string/description/>
# hidden: true
# ---
# 
# We can scramble a string s to get a string t using the following algorithm:
# 
#   1. If the length of the string is 1, stop.
#   2. If the length of the string is > 1, do the following: 
#     * Split the string into two non-empty substrings at a random index, i.e., if the string is `s`, divide it to `x` and `y` where `s = x + y`.
#     * **Randomly**  decide to swap the two substrings or to keep them in the same order. i.e., after this step, `s` may become `s = x + y` or `s = y + x`.
#     * Apply step 1 recursively on each of the two substrings `x` and `y`.
# 
# Given two strings `s1` and `s2` of **the same length** , return `true` if `s2`
# is a scrambled string of `s1`, otherwise, return `false`.
# 
# 
# 
# **Example 1:**
# 
#     
#     
#     Input: s1 = "great", s2 = "rgeat"
#     Output: true
#     Explanation: One possible scenario applied on s1 is:
#     "great" --> "gr/eat" // divide at random index.
#     "gr/eat" --> "gr/eat" // random decision is not to swap the two substrings and keep them in order.
#     "gr/eat" --> "g/r / e/at" // apply the same algorithm recursively on both substrings. divide at ranom index each of them.
#     "g/r / e/at" --> "r/g / e/at" // random decision was to swap the first substring and to keep the second substring in the same order.
#     "r/g / e/at" --> "r/g / e/ a/t" // again apply the algorithm recursively, divide "at" to "a/t".
#     "r/g / e/ a/t" --> "r/g / e/ a/t" // random decision is to keep both substrings in the same order.
#     The algorithm stops now and the result string is "rgeat" which is s2.
#     As there is one possible scenario that led s1 to be scrambled to s2, we return true.
#     
# 
# **Example 2:**
# 
#     
#     
#     Input: s1 = "abcde", s2 = "caebd"
#     Output: false
#     
# 
# **Example 3:**
# 
#     
#     
#     Input: s1 = "a", s2 = "a"
#     Output: true
#     
# 
# 
# 
# **Constraints:**
# 
#   * `s1.length == s2.length`
#   * `1 <= s1.length <= 30`
#   * `s1` and `s2` consist of lower-case English letters.
# 
# 
## @lc code=start
using LeetCode

## add your code here:
## @lc code=end
