A string S
of lowercase letters is given. We want to partition this string into as many parts as possible so that each letter appears in at most one part, and return a list of integers representing the size of these parts.
Example 1:
Input: S = "ababcbacadefegdehijhklij" Output: [9,7,8] Explanation: The partition is "ababcbaca", "defegde", "hijhklij". This is a partition so that each letter appears in at most one part. A partition like "ababcbacadefegde", "hijhklij" is incorrect, because it splits S into less parts.
Note:
S
will have length in range [1, 500]
.S
will consist of lowercase letters ('a'
to 'z'
) only.Intuition
Let's try to repeatedly choose the smallest left-justified partition.
Consider the first label, say it's 'a'
. The first partition must include it, and also the last occurrence of 'a'
.
However, between those two occurrences of 'a'
, there could be other labels that make the minimum size of this partition bigger. For example, in "abccaddbeffe"
, the minimum first partition is "abccaddb"
.
This gives us the idea for the algorithm: For each letter encountered, process the last occurrence of that letter, extending the current partition [anchor, j]
appropriately.
Algorithm
We need an array last[char] -> index of S where char occurs last
.
Then, let anchor
and j
be the start and end of the current partition.
If we are at a label that occurs last at some index after j
, we'll extend the partition j = last[c]
. If we are at the end of the partition (i == j
) then we'll append a partition size to our answer, and set the start of our new partition to i+1
.
Complexity Analysis
Time Complexity: , where is the length of .
Space Complexity: .
Analysis written by: @awice.