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
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
#include <iostream>
#include <vector>

using namespace std;

int** vals;

int getNum(int a) {
	int out = 1;
	out += a;
	out *= a;
	out /= 2;
	return out;
}

pair<int, int> getVal(int s, int n, string& naw, int ss, int d = 0, int cs = 0) {
	int count = 0;
	int poss = 0;
	vals[ss][s] = cs;
	pair<int, int> tmp;
	for (int i = s; i < n; i++) {
		if (i == 25) {
			poss = poss;
		}
		if (naw[i] == '(') {
			vals[ss][i] = poss + cs;
			tmp = getVal(i + 1, n, naw, ss, d + 1, poss + cs);

			count++;
			i = tmp.second;
			poss += tmp.first;
			poss -= getNum(count - 1);
			poss += getNum(count);
			vals[ss][i] = poss + cs;
			continue;

		}
		if (naw[i] == ')' && d > 0) {
			return { poss, i };
		}
		if (naw[i] == ')' && d == 0) {
			count = 0;
			vals[ss][i] = poss + cs;
		}
	}

	return { poss, n };
}

int main() {
	int n, k;
	cin >> n >> k;

	string naw;
	cin >> naw;

	vals = new int* [n+1];

	for (int i = 0; i < n; i++) {
		vals[i] = new int[n+1] {0};
		getVal(i, n, naw, i);
	}

	/*for (int i = 0; i < n; i++) {
		for (int j = 0; j < n; j++) {
			cout << vals[i][j] << " ";
		}
		cout << endl;
	}*/

	int** dp = new int* [n];

	for (int i = 0; i < n; i++) {
		dp[i] = new int[n];
		for (int j = 0; j < n; j++) {
			dp[i][j] = 1e7;
		}
	}

	for (int i = 0; i < n; i++) {
		dp[i][0] = vals[0][i];
	}

	int tmp, tmp2;

	for (int i = 1; i < n; i++) {
		for (int j = i; j < n; j++) {
			for (int l = 1; l < k && l <= i; l++) {
				tmp = dp[i - 1][l - 1];
				tmp2 = vals[i][j];
				if (tmp + tmp2 < dp[j][l]) {
					dp[j][l] = tmp + tmp2;
				}
			}
		}
	}

	cout << dp[n - 1][k - 1];
}