# Lossy Run-Length Encoding - Microsoft Top Interview Questions

### Problem Statement :

```You are given a lowercase alphabet string s and an integer k.

Consider an operation where we perform a run-length encoding on a string by representing repeated successive characters as a count and character.

For example, the string "aabbbc" would be encoded as "2a3bc". Note that we don't put "1c" for "c" since it only appears once successively.

Given that you can first remove any k consecutive characters in s, return the minimum length possible of the resulting run-length encoding.

Constraints

k ≤ n ≤ 100,000 where n is the length of s.

Example 1

Input

s = "aaaaabbaaaaaccaaa"

k = 2

Output

6

Explanation

The two obvious choices are to remove the "bb"s or the "cc"s.

If we remove the "bb"s, then we'd get "10a2c3a" which has length of 7.

If we remove the "cc"s, then we'd get "5a2b8a" which has length of 6.```

### Solution :

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

struct state {
int lhs, rhs;
int total;
state() {
}
state(int a, int b) {
lhs = a;
rhs = b;
total = 0;
}
};
int lenof(int x) {
if (x == 1) return 0;
}
void update(state& prev, state& curr) {
curr.total = prev.total + lenof(curr.rhs - curr.lhs + 1) + 1;
}
class Solution {
public:
int solve(string s, int k) {
int n = s.size();
if (n == k) return 0;
vector<state> lhs;
lhs.emplace_back(-1, -1);
for (int i = 0; i < n - k; i++) {
if (i == 0 || s[i] != s[i - 1]) {
lhs.emplace_back(i, i);
} else {
lhs.back().rhs++;
}
update(lhs[lhs.size() - 2], lhs.back());
}
// initial estimate - delete the entire suffix
int ret = lhs.back().total;
vector<state> rhs;
rhs.emplace_back(n, n);
for (int i = n - k - 1; i >= 0; i--) {
int add = i + k;
} else {
rhs.back().lhs--;
}
update(rhs[rhs.size() - 2], rhs.back());
// remove the rightmost added character from the left
if (lhs.back().lhs == lhs.back().rhs) {
lhs.pop_back();
} else {
lhs.back().rhs--;
}
if (lhs.size() > 1) {
update(lhs[lhs.size() - 2], lhs.back());
}
// new naive estimate, just stick the two together
ret = min(ret, lhs.back().total + rhs.back().total);
// is it possible that the two ends can be stuck together?
if (lhs.size() > 1 && rhs.size() > 1 && s[lhs.back().rhs] == s[rhs.back().lhs]) {
// add together all the components that are not involved in the merge
int cand = lhs[lhs.size() - 2].total + rhs[rhs.size() - 2].total;
// recompute the compressed length
int tot = rhs.back().rhs - rhs.back().lhs + 1;
tot += lhs.back().rhs - lhs.back().lhs + 1;
cand += lenof(tot) + 1;
ret = min(ret, cand);
}
}
return ret;
}
};

int solve(string s, int k) {
return (new Solution())->solve(s, k);
}```
```

```                        ```Solution in Python :

class Solution:
def solve(self, S, K):
N = len(S)
if N == K:
return 0

left =  * N
for i in range(N - 1):
if S[i] == S[i + 1]:
left[i + 1] = left[i] + 1

right =  * N
for i in reversed(range(N - 1)):
if S[i] == S[i + 1]:
right[i] = right[i + 1] + 1

def rle(x):
return x if x <= 1 else len(str(x)) + 1

R = [len(list(g)) for _, g in groupby(S)]

prefix =  * N
prev = 0
i = 0
for x in R:
for j in range(1, 1 + x):
prefix[i] = prev + rle(j)
i += 1
prev += rle(x)

suffix =  * N
prev = 0
i = N - 1
for x in reversed(R):
for j in range(1, 1 + x):
suffix[i] = prev + rle(j)
i -= 1
prev += rle(x)

ans = min(prefix[~K], suffix[K])
for i in range(len(S) - K - 1):
cand = prefix[i] + suffix[i + K + 1]
lv = left[i]
rv = right[i + K + 1]
if S[i] == S[i + K + 1]:
cand -= rle(lv) + rle(rv)
cand += rle(lv + rv)
ans = min(ans, cand)
return ans```
```

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