{ "data": { "question": { "questionId": "3638", "questionFrontendId": "3389", "boundTopicId": null, "title": "Minimum Operations to Make Character Frequencies Equal", "titleSlug": "minimum-operations-to-make-character-frequencies-equal", "content": "
You are given a string s
.
A string t
is called good if all characters of t
occur the same number of times.
You can perform the following operations any number of times:
\n\ns
.s
.s
to its next letter in the alphabet.Note that you cannot change 'z'
to 'a'
using the third operation.
Return the minimum number of operations required to make s
good.
\n
Example 1:
\n\nInput: s = "acab"
\n\nOutput: 1
\n\nExplanation:
\n\nWe can make s
good by deleting one occurrence of character 'a'
.
Example 2:
\n\nInput: s = "wddw"
\n\nOutput: 0
\n\nExplanation:
\n\nWe do not need to perform any operations since s
is initially good.
Example 3:
\n\nInput: s = "aaabc"
\n\nOutput: 2
\n\nExplanation:
\n\nWe can make s
good by applying these operations:
'a'
to 'b'
'c'
into s
\n
Constraints:
\n\n3 <= s.length <= 2 * 104
s
contains only lowercase English letters.occ
where occ[x]
is the number of occurrences of the x
character of the alphabet. How do the described operations change occ
?",
"We have three types of operations: increase any occ[x]
by 1, decrease any occ[x]
by 1, or decrease any occ[x]
by 1 and simultaneously increase occ[x + 1]
by 1 at the same time. To make s
good, we need to make occ
good. occ
is good if and only if every occ[x]
equals either 0 or some constant c
.",
"If you know the value of c
, how can you calculate the minimum operations required to make occ
good?",
"Observation 1: It is never optimal to apply the third type of operation (simultaneous decrease and increase) on two continuous elements occ[x]
and occ[x + 1]
. Instead, we can decrease occ[x]
by 1 then increase occ[x + 2]
by 1 to achieve the same effect.",
"Observation 2: It is never optimal to increase an element of occ
then decrease it, or vice versa.",
"Use dynamic programming where dp[i]
is the minimum number of operations required to make occ[0..i]
good. You will need to use the above observations to come up with the transitions."
],
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