oj.uz

Submission #789331

# Submission time Handle Problem Language Result Execution time Memory
789331 2023-07-21T09:20:16 Z 박상훈(#10042) Chorus (JOI23_chorus) C++17
100 / 100
 5534 ms 55128 KB 
#include <bits/stdc++.h>

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

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

	return (ll)(r+1) * (r2-l+1) - (sum[r2] - 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){
		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) st2.push_back(cross(st.back(), x));
		st.push_back(x);

		if (!st2.empty() && st2.back()==cap+1){
			st2.pop_back();
			st.pop_back();
		} 
	}

	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
	// monotone queue opt
	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;
		if (alien(n, mid*2-1) >= 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'){
			// mp[i] = ptA;
			prv[i] = ptB-1;
			a[ptA++] = i;
		} 
		else{
			// mp[i] = ptB;
			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]];

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

Compilation message

chorus.cpp: In function 'int main()':
chorus.cpp:138:7: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
  138 |  scanf("%d %d", &n, &k);
      |  ~~~~~^~~~~~~~~~~~~~~~~
chorus.cpp:143:7: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
  143 |  scanf("%s", s+1);
      |  ~~~~~^~~~~~~~~~~

Subtask #1
16.0 / 16.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 384 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 0 ms 340 KB Output is correct
4 Correct 1 ms 340 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 340 KB Output is correct
10 Correct 0 ms 340 KB Output is correct
11 Correct 0 ms 340 KB Output is correct
12 Correct 0 ms 340 KB Output is correct
13 Correct 0 ms 340 KB Output is correct
14 Correct 0 ms 340 KB Output is correct
15 Correct 0 ms 340 KB Output is correct
16 Correct 0 ms 340 KB Output is correct

Subtask #2
24.0 / 24.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 384 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 0 ms 340 KB Output is correct
4 Correct 1 ms 340 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 340 KB Output is correct
10 Correct 0 ms 340 KB Output is correct
11 Correct 0 ms 340 KB Output is correct
12 Correct 0 ms 340 KB Output is correct
13 Correct 0 ms 340 KB Output is correct
14 Correct 0 ms 340 KB Output is correct
15 Correct 0 ms 340 KB Output is correct
16 Correct 0 ms 340 KB Output is correct
17 Correct 1 ms 340 KB Output is correct
18 Correct 2 ms 340 KB Output is correct
19 Correct 2 ms 340 KB Output is correct
20 Correct 2 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 2 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 340 KB Output is correct
28 Correct 2 ms 340 KB Output is correct

Subtask #3
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 384 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 0 ms 340 KB Output is correct
4 Correct 1 ms 340 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 340 KB Output is correct
10 Correct 0 ms 340 KB Output is correct
11 Correct 0 ms 340 KB Output is correct
12 Correct 0 ms 340 KB Output is correct
13 Correct 0 ms 340 KB Output is correct
14 Correct 0 ms 340 KB Output is correct
15 Correct 0 ms 340 KB Output is correct
16 Correct 0 ms 340 KB Output is correct
17 Correct 1 ms 340 KB Output is correct
18 Correct 2 ms 340 KB Output is correct
19 Correct 2 ms 340 KB Output is correct
20 Correct 2 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 2 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 340 KB Output is correct
28 Correct 2 ms 340 KB Output is correct
29 Correct 15 ms 600 KB Output is correct
30 Correct 16 ms 604 KB Output is correct
31 Correct 19 ms 628 KB Output is correct
32 Correct 12 ms 596 KB Output is correct
33 Correct 12 ms 608 KB Output is correct
34 Correct 14 ms 596 KB Output is correct
35 Correct 14 ms 596 KB Output is correct
36 Correct 17 ms 604 KB Output is correct
37 Correct 21 ms 608 KB Output is correct
38 Correct 14 ms 628 KB Output is correct
39 Correct 18 ms 604 KB Output is correct
40 Correct 14 ms 612 KB Output is correct
41 Correct 14 ms 608 KB Output is correct
42 Correct 11 ms 596 KB Output is correct

Subtask #4
26.0 / 26.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 384 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 0 ms 340 KB Output is correct
4 Correct 1 ms 340 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 340 KB Output is correct
10 Correct 0 ms 340 KB Output is correct
11 Correct 0 ms 340 KB Output is correct
12 Correct 0 ms 340 KB Output is correct
13 Correct 0 ms 340 KB Output is correct
14 Correct 0 ms 340 KB Output is correct
15 Correct 0 ms 340 KB Output is correct
16 Correct 0 ms 340 KB Output is correct
17 Correct 1 ms 340 KB Output is correct
18 Correct 2 ms 340 KB Output is correct
19 Correct 2 ms 340 KB Output is correct
20 Correct 2 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 2 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 340 KB Output is correct
28 Correct 2 ms 340 KB Output is correct
29 Correct 15 ms 600 KB Output is correct
30 Correct 16 ms 604 KB Output is correct
31 Correct 19 ms 628 KB Output is correct
32 Correct 12 ms 596 KB Output is correct
33 Correct 12 ms 608 KB Output is correct
34 Correct 14 ms 596 KB Output is correct
35 Correct 14 ms 596 KB Output is correct
36 Correct 17 ms 604 KB Output is correct
37 Correct 21 ms 608 KB Output is correct
38 Correct 14 ms 628 KB Output is correct
39 Correct 18 ms 604 KB Output is correct
40 Correct 14 ms 612 KB Output is correct
41 Correct 14 ms 608 KB Output is correct
42 Correct 11 ms 596 KB Output is correct
43 Correct 244 ms 3464 KB Output is correct
44 Correct 418 ms 5648 KB Output is correct
45 Correct 434 ms 5616 KB Output is correct
46 Correct 311 ms 4880 KB Output is correct
47 Correct 318 ms 4916 KB Output is correct
48 Correct 391 ms 5652 KB Output is correct
49 Correct 357 ms 5648 KB Output is correct
50 Correct 431 ms 5084 KB Output is correct
51 Correct 420 ms 5020 KB Output is correct
52 Correct 376 ms 5652 KB Output is correct
53 Correct 358 ms 5564 KB Output is correct
54 Correct 423 ms 5132 KB Output is correct

Subtask #5
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 384 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 0 ms 340 KB Output is correct
4 Correct 1 ms 340 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 340 KB Output is correct
10 Correct 0 ms 340 KB Output is correct
11 Correct 0 ms 340 KB Output is correct
12 Correct 0 ms 340 KB Output is correct
13 Correct 0 ms 340 KB Output is correct
14 Correct 0 ms 340 KB Output is correct
15 Correct 0 ms 340 KB Output is correct
16 Correct 0 ms 340 KB Output is correct
17 Correct 1 ms 340 KB Output is correct
18 Correct 2 ms 340 KB Output is correct
19 Correct 2 ms 340 KB Output is correct
20 Correct 2 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 2 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 340 KB Output is correct
28 Correct 2 ms 340 KB Output is correct
29 Correct 15 ms 600 KB Output is correct
30 Correct 16 ms 604 KB Output is correct
31 Correct 19 ms 628 KB Output is correct
32 Correct 12 ms 596 KB Output is correct
33 Correct 12 ms 608 KB Output is correct
34 Correct 14 ms 596 KB Output is correct
35 Correct 14 ms 596 KB Output is correct
36 Correct 17 ms 604 KB Output is correct
37 Correct 21 ms 608 KB Output is correct
38 Correct 14 ms 628 KB Output is correct
39 Correct 18 ms 604 KB Output is correct
40 Correct 14 ms 612 KB Output is correct
41 Correct 14 ms 608 KB Output is correct
42 Correct 11 ms 596 KB Output is correct
43 Correct 244 ms 3464 KB Output is correct
44 Correct 418 ms 5648 KB Output is correct
45 Correct 434 ms 5616 KB Output is correct
46 Correct 311 ms 4880 KB Output is correct
47 Correct 318 ms 4916 KB Output is correct
48 Correct 391 ms 5652 KB Output is correct
49 Correct 357 ms 5648 KB Output is correct
50 Correct 431 ms 5084 KB Output is correct
51 Correct 420 ms 5020 KB Output is correct
52 Correct 376 ms 5652 KB Output is correct
53 Correct 358 ms 5564 KB Output is correct
54 Correct 423 ms 5132 KB Output is correct
55 Correct 3168 ms 34352 KB Output is correct
56 Correct 4922 ms 53172 KB Output is correct
57 Correct 5301 ms 55072 KB Output is correct
58 Correct 3720 ms 47304 KB Output is correct
59 Correct 3820 ms 48452 KB Output is correct
60 Correct 4552 ms 55120 KB Output is correct
61 Correct 4413 ms 55124 KB Output is correct
62 Correct 5534 ms 49340 KB Output is correct
63 Correct 5352 ms 49656 KB Output is correct
64 Correct 4744 ms 51676 KB Output is correct
65 Correct 4537 ms 55128 KB Output is correct
66 Correct 5072 ms 50220 KB Output is correct
67 Correct 4411 ms 55036 KB Output is correct