oj.uz

Submission #790685

# Submission time Handle Problem Language Result Execution time Memory
790685 2023-07-23T05:46:13 Z qwerasdfzxcl Chorus (JOI23_chorus) C++17
100 / 100
 4046 ms 59124 KB 
#include <bits/stdc++.h>
#pragma GCC optimize("O3")
#pragma GCC target("avx2")

using namespace std;
typedef long long ll;
constexpr ll INF = 4e18;
char s[2002000];
int a[1001000], b[1001000], nxt[2002000], prv[2002000], r2[1001000];
ll cst[505][505], dp_naive[505][505], sum[1001000];

inline ll cost(int l, int r){ // O(1)
	if (r2[r] < l) return 0;

	return (ll)(r+1) * (r2[r]-l+1) - (sum[r2[r]] - sum[l-1]);
}

ll naive(int n, int k){
	for (int i=1;i<=n;i++){
		for (int j=i;j<=n;j++){
			for (int k=i;k<=j;k++){
				cst[i][j] += max(j-nxt[b[k]]+1, 0);
			}
		}
	}

	for (int i=0;i<=n;i++){
		fill(dp_naive[i], dp_naive[i]+k+1, INF);
	}
	dp_naive[0][0] = 0;

	for (int i=1;i<=n;i++){
		for (int j=1;j<=k;j++){
			for (int p=0;p<i;p++) dp_naive[i][j] = min(dp_naive[i][j], dp_naive[p][j-1] + cst[p+1][i]);
		}
	}

	return dp_naive[n][k];
}

ll dp[1001000];
int dp2[1001000];

struct Hull{
	vector<int> st, st2;
	int pt, cap;
	ll lambda;

	void init(int n, ll _lambda){
		st.clear();
		st2.clear();
		pt = 0;
		cap = n;
		lambda = _lambda;
	}

	inline ll calc(int f, int x){
		assert(f < x);
		return dp[f] + cost(f+1, x) * 2 + lambda;
	}

	int cross(int f, int g){
		int l = g+1, r = cap, ret = cap+1;
		while(l<=r){
			int mid = (l+r)>>1;
			if (calc(f, mid) > calc(g, mid)) ret = mid, r = mid-1;
			else l = mid+1;
		}

		return ret;

	}

	void push(int x){
		if (x==cap) return;

		while(st.size() >= 2 && st2.back() >= x+1 && calc(st.back(), st2.back()) >= calc(x, st2.back())){
			st.pop_back();
			st2.pop_back();
		}

		if (st.size() >= 1 && calc(st.back(), cap) <= calc(x, cap)) return;

		if (st.size() >= 1) st2.push_back(cross(st.back(), x));
		st.push_back(x);

		assert(st2.empty() || st2.back() <= cap);
	}

	pair<ll, int> query(int x){
		pt = min(pt, (int)st.size()-1);
		while(pt+1<(int)st.size() && st2[pt] <= x) pt++;
		return {calc(st[pt], x), dp2[st[pt]]+1};
	}


}hull;

int alien(int n, ll lambda){ // y + \lambda x min
	hull.init(n, lambda);
	hull.push(0);

	for (int i=1;i<=n;i++){
		auto [val, cnt] = hull.query(i);
		dp[i] = val;
		dp2[i] = cnt;

		hull.push(i);
	}

	return dp2[n];
}

ll solve(int n, int k){
	ll l = 0, r = 1e12 + 100, opt = -1;
	while(l<=r){
		ll mid = (l+r) / 2;
		int val = alien(n, mid*2-1);
		if (val==k){
			return (dp[n] - (mid*2-1) * val) / 2;
		}

		if (val >= k) opt = mid, l = mid+1;
		else r = mid-1;
	}

	assert(opt >= 0);
	int cnt = alien(n, opt*2-1);
	ll val = (dp[n] - (opt*2-1) * cnt) / 2;

	if (cnt==k){
		return val;
	}

	int cnt2 = alien(n, opt*2+1);
	ll val2 = (dp[n] - (opt*2+1) * cnt2) / 2;
	assert(cnt2 < k);

	return val2 - opt * (k-cnt2);
}

int main(){
	int n, k;
	scanf("%d %d", &n, &k);

	hull.st.reserve(n+100);
	hull.st2.reserve(n+100);

	scanf("%s", s+1);
	int ptA = 1, ptB = 1;
	for (int i=1;i<=n*2;i++){
		if (s[i]=='A'){
			prv[i] = ptB-1;
			a[ptA++] = i;
		} 
		else{
			prv[i] = ptB;
			b[ptB++] = i;
		}
	}

	for (int i=n*2;i;i--){
		if (s[i]=='A') nxt[i] = --ptA;
		else nxt[i] = ptA;
	}

	for (int i=1;i<=n;i++) sum[i] = sum[i-1] + nxt[b[i]], r2[i] = min(i, prv[a[i]]);

	printf("%lld\n", solve(n, k));	
}

Compilation message

chorus.cpp: In function 'int main()':
chorus.cpp:144:7: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
  144 |  scanf("%d %d", &n, &k);
      |  ~~~~~^~~~~~~~~~~~~~~~~
chorus.cpp:149:7: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
  149 |  scanf("%s", s+1);
      |  ~~~~~^~~~~~~~~~~

Subtask #1
16.0 / 16.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 0 ms 308 KB Output is correct
4 Correct 1 ms 312 KB Output is correct
5 Correct 0 ms 340 KB Output is correct
6 Correct 0 ms 340 KB Output is correct
7 Correct 0 ms 340 KB Output is correct
8 Correct 0 ms 340 KB Output is correct
9 Correct 0 ms 308 KB Output is correct
10 Correct 0 ms 340 KB Output is correct
11 Correct 1 ms 340 KB Output is correct
12 Correct 1 ms 340 KB Output is correct
13 Correct 1 ms 340 KB Output is correct
14 Correct 0 ms 340 KB Output is correct
15 Correct 1 ms 340 KB Output is correct
16 Correct 1 ms 340 KB Output is correct

Subtask #2
24.0 / 24.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 0 ms 308 KB Output is correct
4 Correct 1 ms 312 KB Output is correct
5 Correct 0 ms 340 KB Output is correct
6 Correct 0 ms 340 KB Output is correct
7 Correct 0 ms 340 KB Output is correct
8 Correct 0 ms 340 KB Output is correct
9 Correct 0 ms 308 KB Output is correct
10 Correct 0 ms 340 KB Output is correct
11 Correct 1 ms 340 KB Output is correct
12 Correct 1 ms 340 KB Output is correct
13 Correct 1 ms 340 KB Output is correct
14 Correct 0 ms 340 KB Output is correct
15 Correct 1 ms 340 KB Output is correct
16 Correct 1 ms 340 KB Output is correct
17 Correct 1 ms 340 KB Output is correct
18 Correct 1 ms 340 KB Output is correct
19 Correct 1 ms 340 KB Output is correct
20 Correct 1 ms 340 KB Output is correct
21 Correct 1 ms 340 KB Output is correct
22 Correct 1 ms 340 KB Output is correct
23 Correct 1 ms 340 KB Output is correct
24 Correct 1 ms 340 KB Output is correct
25 Correct 1 ms 340 KB Output is correct
26 Correct 1 ms 340 KB Output is correct
27 Correct 1 ms 316 KB Output is correct
28 Correct 1 ms 340 KB Output is correct

Subtask #3
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 0 ms 308 KB Output is correct
4 Correct 1 ms 312 KB Output is correct
5 Correct 0 ms 340 KB Output is correct
6 Correct 0 ms 340 KB Output is correct
7 Correct 0 ms 340 KB Output is correct
8 Correct 0 ms 340 KB Output is correct
9 Correct 0 ms 308 KB Output is correct
10 Correct 0 ms 340 KB Output is correct
11 Correct 1 ms 340 KB Output is correct
12 Correct 1 ms 340 KB Output is correct
13 Correct 1 ms 340 KB Output is correct
14 Correct 0 ms 340 KB Output is correct
15 Correct 1 ms 340 KB Output is correct
16 Correct 1 ms 340 KB Output is correct
17 Correct 1 ms 340 KB Output is correct
18 Correct 1 ms 340 KB Output is correct
19 Correct 1 ms 340 KB Output is correct
20 Correct 1 ms 340 KB Output is correct
21 Correct 1 ms 340 KB Output is correct
22 Correct 1 ms 340 KB Output is correct
23 Correct 1 ms 340 KB Output is correct
24 Correct 1 ms 340 KB Output is correct
25 Correct 1 ms 340 KB Output is correct
26 Correct 1 ms 340 KB Output is correct
27 Correct 1 ms 316 KB Output is correct
28 Correct 1 ms 340 KB Output is correct
29 Correct 9 ms 572 KB Output is correct
30 Correct 11 ms 648 KB Output is correct
31 Correct 10 ms 644 KB Output is correct
32 Correct 1 ms 596 KB Output is correct
33 Correct 1 ms 576 KB Output is correct
34 Correct 9 ms 668 KB Output is correct
35 Correct 8 ms 580 KB Output is correct
36 Correct 3 ms 596 KB Output is correct
37 Correct 10 ms 660 KB Output is correct
38 Correct 8 ms 596 KB Output is correct
39 Correct 10 ms 596 KB Output is correct
40 Correct 8 ms 648 KB Output is correct
41 Correct 8 ms 596 KB Output is correct
42 Correct 5 ms 596 KB Output is correct

Subtask #4
26.0 / 26.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 0 ms 308 KB Output is correct
4 Correct 1 ms 312 KB Output is correct
5 Correct 0 ms 340 KB Output is correct
6 Correct 0 ms 340 KB Output is correct
7 Correct 0 ms 340 KB Output is correct
8 Correct 0 ms 340 KB Output is correct
9 Correct 0 ms 308 KB Output is correct
10 Correct 0 ms 340 KB Output is correct
11 Correct 1 ms 340 KB Output is correct
12 Correct 1 ms 340 KB Output is correct
13 Correct 1 ms 340 KB Output is correct
14 Correct 0 ms 340 KB Output is correct
15 Correct 1 ms 340 KB Output is correct
16 Correct 1 ms 340 KB Output is correct
17 Correct 1 ms 340 KB Output is correct
18 Correct 1 ms 340 KB Output is correct
19 Correct 1 ms 340 KB Output is correct
20 Correct 1 ms 340 KB Output is correct
21 Correct 1 ms 340 KB Output is correct
22 Correct 1 ms 340 KB Output is correct
23 Correct 1 ms 340 KB Output is correct
24 Correct 1 ms 340 KB Output is correct
25 Correct 1 ms 340 KB Output is correct
26 Correct 1 ms 340 KB Output is correct
27 Correct 1 ms 316 KB Output is correct
28 Correct 1 ms 340 KB Output is correct
29 Correct 9 ms 572 KB Output is correct
30 Correct 11 ms 648 KB Output is correct
31 Correct 10 ms 644 KB Output is correct
32 Correct 1 ms 596 KB Output is correct
33 Correct 1 ms 576 KB Output is correct
34 Correct 9 ms 668 KB Output is correct
35 Correct 8 ms 580 KB Output is correct
36 Correct 3 ms 596 KB Output is correct
37 Correct 10 ms 660 KB Output is correct
38 Correct 8 ms 596 KB Output is correct
39 Correct 10 ms 596 KB Output is correct
40 Correct 8 ms 648 KB Output is correct
41 Correct 8 ms 596 KB Output is correct
42 Correct 5 ms 596 KB Output is correct
43 Correct 189 ms 3816 KB Output is correct
44 Correct 292 ms 6152 KB Output is correct
45 Correct 321 ms 6224 KB Output is correct
46 Correct 4 ms 5460 KB Output is correct
47 Correct 12 ms 5504 KB Output is correct
48 Correct 245 ms 6240 KB Output is correct
49 Correct 225 ms 6244 KB Output is correct
50 Correct 72 ms 5612 KB Output is correct
51 Correct 280 ms 5628 KB Output is correct
52 Correct 226 ms 6220 KB Output is correct
53 Correct 262 ms 6260 KB Output is correct
54 Correct 306 ms 5708 KB Output is correct

Subtask #5
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 0 ms 308 KB Output is correct
4 Correct 1 ms 312 KB Output is correct
5 Correct 0 ms 340 KB Output is correct
6 Correct 0 ms 340 KB Output is correct
7 Correct 0 ms 340 KB Output is correct
8 Correct 0 ms 340 KB Output is correct
9 Correct 0 ms 308 KB Output is correct
10 Correct 0 ms 340 KB Output is correct
11 Correct 1 ms 340 KB Output is correct
12 Correct 1 ms 340 KB Output is correct
13 Correct 1 ms 340 KB Output is correct
14 Correct 0 ms 340 KB Output is correct
15 Correct 1 ms 340 KB Output is correct
16 Correct 1 ms 340 KB Output is correct
17 Correct 1 ms 340 KB Output is correct
18 Correct 1 ms 340 KB Output is correct
19 Correct 1 ms 340 KB Output is correct
20 Correct 1 ms 340 KB Output is correct
21 Correct 1 ms 340 KB Output is correct
22 Correct 1 ms 340 KB Output is correct
23 Correct 1 ms 340 KB Output is correct
24 Correct 1 ms 340 KB Output is correct
25 Correct 1 ms 340 KB Output is correct
26 Correct 1 ms 340 KB Output is correct
27 Correct 1 ms 316 KB Output is correct
28 Correct 1 ms 340 KB Output is correct
29 Correct 9 ms 572 KB Output is correct
30 Correct 11 ms 648 KB Output is correct
31 Correct 10 ms 644 KB Output is correct
32 Correct 1 ms 596 KB Output is correct
33 Correct 1 ms 576 KB Output is correct
34 Correct 9 ms 668 KB Output is correct
35 Correct 8 ms 580 KB Output is correct
36 Correct 3 ms 596 KB Output is correct
37 Correct 10 ms 660 KB Output is correct
38 Correct 8 ms 596 KB Output is correct
39 Correct 10 ms 596 KB Output is correct
40 Correct 8 ms 648 KB Output is correct
41 Correct 8 ms 596 KB Output is correct
42 Correct 5 ms 596 KB Output is correct
43 Correct 189 ms 3816 KB Output is correct
44 Correct 292 ms 6152 KB Output is correct
45 Correct 321 ms 6224 KB Output is correct
46 Correct 4 ms 5460 KB Output is correct
47 Correct 12 ms 5504 KB Output is correct
48 Correct 245 ms 6240 KB Output is correct
49 Correct 225 ms 6244 KB Output is correct
50 Correct 72 ms 5612 KB Output is correct
51 Correct 280 ms 5628 KB Output is correct
52 Correct 226 ms 6220 KB Output is correct
53 Correct 262 ms 6260 KB Output is correct
54 Correct 306 ms 5708 KB Output is correct
55 Correct 2438 ms 38304 KB Output is correct
56 Correct 3651 ms 58948 KB Output is correct
57 Correct 4046 ms 58992 KB Output is correct
58 Correct 39 ms 51192 KB Output is correct
59 Correct 92 ms 52376 KB Output is correct
60 Correct 3489 ms 59044 KB Output is correct
61 Correct 3163 ms 58968 KB Output is correct
62 Correct 785 ms 53236 KB Output is correct
63 Correct 2763 ms 53732 KB Output is correct
64 Correct 2940 ms 55596 KB Output is correct
65 Correct 3358 ms 58980 KB Output is correct
66 Correct 3892 ms 53980 KB Output is correct
67 Correct 3325 ms 59124 KB Output is correct