# Half Monotonous String - Google Top Interview Questions

### Problem Statement :

```You are given a lowercase alphabet string s of even length consisting of lowercase alphabet letters.

Return the minimum number of characters that need to be updated such that one of the following three conditions is true for all 0 ≤ i < n/2 and n/2 ≤ j < n:

s[i] > s[j] or
s[i] < s[j] or
s[i] == s[j]
Constraints

0 ≤ n ≤ 100,000 where n is the length of s

Example 1

Input

s = "aa"

Output

0

Explanation

This string already meets the s[i] == s[j] condition

Example 2

Input

s = "aaabba"

Output

1

Explanation

If we change the last "a" to "b", then we can satisfy the s[i] < s[j] condition.

Example 3

Input

s = "bccbba"

Output

1

Explanation

If we change the first "b" to "c", then we can satisfy the s[i] > s[j] condition.```

### Solution :

```                        ```Solution in C++ :

int solve(string s) {
int len = s.length(), maxCnt = 0;
vector<int> cnt(26, 0);
for (int i = 0; i < len; i++) {
cnt[s[i] - 'a']++;
maxCnt = max(maxCnt, cnt[s[i] - 'a']);
}
int res = len - maxCnt;
for (char ch = 'b'; ch < 'z'; ch++) {
int cnt1 = 0, cnt2 = 0, cnt3 = 0, cnt4 = 0;
for (int i = 0; i < len / 2; i++) {
if (s[i] >= ch) {
cnt1++;
} else if (s[i] <= ch - 1) {
cnt2++;
}
}
for (int i = len / 2; i < len; i++) {
if (s[i] >= ch) {
cnt3++;
}
if (s[i] <= ch - 1) {
cnt4++;
}
}
res = min({res, cnt1 + cnt4, cnt2 + cnt3});
}
return res;
}```
```

```                        ```Solution in Java :

import java.util.*;

class Solution {
public int solve(String s) {
int N = s.length();
int[] A = new int[26];
int[] B = new int[26];
for (int i = 0; i < N; i++) {
int c = s.charAt(i) - 'a';
if (i < N / 2)
A[c] += 1;
else
B[c] += 1;
}
int ans = Integer.MAX_VALUE;

// fix all characters in A to be greater than i and all the characters in B to be less than
// or equal to i.
for (int i = 0; i < 26; i++) {
int fix = 0;
for (int j = 0; j <= i; j++) fix += A[j];
for (int j = i + 1; j < 26; j++) fix += B[j];
ans = Math.min(ans, fix);
}

// fix all characters in A to be less than i and all the characters in B to be greater than
// or equal to i.
for (int i = 0; i < 26; i++) {
int fix = 0;
for (int j = i; j < 26; j++) fix += A[j];
for (int j = 0; j < i; j++) fix += B[j];
ans = Math.min(ans, fix);
}

// fix all characters in A and B to equal i.
for (int i = 0; i < 26; i++) {
int fix = N - (A[i] + B[i]);
ans = Math.min(ans, fix);
}

return ans;
}
}```
```

```                        ```Solution in Python :

class Solution:
def solve(self, s):
n = len(s)
left = Counter(s[: n >> 1])
right = Counter(s[n >> 1 :])

ans = n
for pivot in ascii_lowercase:
# All same
ans = min(ans, n - left[pivot] - right[pivot])

# left <= pivot < right
good = sum(left[c] for c in left if c <= pivot)
good += sum(right[c] for c in right if c > pivot)
ans = min(ans, n - good)

# right <= pivot < left
good = sum(left[c] for c in left if c > pivot)
good += sum(right[c] for c in right if c <= pivot)
ans = min(ans, n - good)

return ans```
```

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