1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
#include "bits/stdc++.h" // Tomasz Nowak
using namespace std;     // University of Warsaw
using LL = long long;
#define FOR(i, l, r) for(int i = (l); i <= (r); ++i)
#define REP(i, n) FOR(i, 0, (n) - 1)
#define ssize(x) int(x.size())
template<class A, class B> auto& operator<<(ostream &o, pair<A, B> p) {
	return o << '(' << p.first << ", " << p.second << ')';
}
template<class T> auto operator<<(ostream &o, T x) -> decltype(x.end(), o) {
	o << '{'; int i = 0; for(auto e : x) o << (", ")+2*!i++ << e; return o << '}';
}
#ifdef DEBUG
#define debug(x...) cerr << "[" #x "]: ", [](auto... $) {((cerr << $ << "; "), ...); }(x), cerr << '\n'
#else
#define debug(...) {}
#endif

int main() {
	cin.tie(0)->sync_with_stdio(0);

	int n, k;
	cin >> n >> k;
	vector<int> in(n);
	REP(i, n) {
		char c;
		cin >> c;
		in[i] = c == '(' ? +1 : -1;
	}
	debug(n, k, in);

	vector in_interval(n, vector<LL>(n));
	REP(l, n) {
		int sum = 0;
		FOR(r, l, n - 1) {
			sum += in[r];
			if(sum < 0)
				break;
			if(sum == 0)
				++in_interval[l][r];
		}
	}
	debug(in_interval);
	FOR(len, 2, n)
		REP(l, n - len + 1) {
			int r = l + len - 1;
			in_interval[l][r] += in_interval[l + 1][r] + in_interval[l][r - 1] - in_interval[l + 1][r - 1];
		}
	debug(in_interval);

	vector dp(n, vector<LL>(k));
	REP(r, n)
		dp[r][0] = in_interval[0][r];
	FOR(used_k, 1, k - 1) {
		REP(r, n)
			dp[r][used_k] = dp[r][used_k - 1];
		REP(r, n) {
			FOR(l, 0, r)
				dp[r][used_k] = min(dp[r][used_k], (l == 0 ? 0 : dp[l - 1][used_k - 1]) + in_interval[l][r]);
			debug(used_k, r, dp[r][used_k]);
		}
	}
	cout << dp[n - 1][k - 1] << '\n';
}