oj.uz

Submission #789337

# Submission time Handle Problem Language Result Execution time Memory
789337 2023-07-21T09:24:28 Z 박상훈(#10042) Chorus (JOI23_chorus) C++17
100 / 100
 5390 ms 53172 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){
		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
	// 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:139:7: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
  139 |  scanf("%d %d", &n, &k);
      |  ~~~~~^~~~~~~~~~~~~~~~~
chorus.cpp:144:7: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
  144 |  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 0 ms 340 KB Output is correct
3 Correct 0 ms 340 KB Output is correct
4 Correct 0 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 1 ms 340 KB Output is correct
12 Correct 0 ms 340 KB Output is correct
13 Correct 1 ms 340 KB Output is correct
14 Correct 1 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 340 KB Output is correct
2 Correct 0 ms 340 KB Output is correct
3 Correct 0 ms 340 KB Output is correct
4 Correct 0 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 1 ms 340 KB Output is correct
12 Correct 0 ms 340 KB Output is correct
13 Correct 1 ms 340 KB Output is correct
14 Correct 1 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 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 2 ms 340 KB Output is correct
28 Correct 1 ms 380 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 0 ms 340 KB Output is correct
3 Correct 0 ms 340 KB Output is correct
4 Correct 0 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 1 ms 340 KB Output is correct
12 Correct 0 ms 340 KB Output is correct
13 Correct 1 ms 340 KB Output is correct
14 Correct 1 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 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 2 ms 340 KB Output is correct
28 Correct 1 ms 380 KB Output is correct
29 Correct 11 ms 600 KB Output is correct
30 Correct 13 ms 612 KB Output is correct
31 Correct 13 ms 604 KB Output is correct
32 Correct 3 ms 596 KB Output is correct
33 Correct 5 ms 596 KB Output is correct
34 Correct 11 ms 596 KB Output is correct
35 Correct 10 ms 612 KB Output is correct
36 Correct 14 ms 596 KB Output is correct
37 Correct 15 ms 612 KB Output is correct
38 Correct 11 ms 596 KB Output is correct
39 Correct 12 ms 612 KB Output is correct
40 Correct 10 ms 612 KB Output is correct
41 Correct 11 ms 596 KB Output is correct
42 Correct 6 ms 604 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 0 ms 340 KB Output is correct
3 Correct 0 ms 340 KB Output is correct
4 Correct 0 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 1 ms 340 KB Output is correct
12 Correct 0 ms 340 KB Output is correct
13 Correct 1 ms 340 KB Output is correct
14 Correct 1 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 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 2 ms 340 KB Output is correct
28 Correct 1 ms 380 KB Output is correct
29 Correct 11 ms 600 KB Output is correct
30 Correct 13 ms 612 KB Output is correct
31 Correct 13 ms 604 KB Output is correct
32 Correct 3 ms 596 KB Output is correct
33 Correct 5 ms 596 KB Output is correct
34 Correct 11 ms 596 KB Output is correct
35 Correct 10 ms 612 KB Output is correct
36 Correct 14 ms 596 KB Output is correct
37 Correct 15 ms 612 KB Output is correct
38 Correct 11 ms 596 KB Output is correct
39 Correct 12 ms 612 KB Output is correct
40 Correct 10 ms 612 KB Output is correct
41 Correct 11 ms 596 KB Output is correct
42 Correct 6 ms 604 KB Output is correct
43 Correct 206 ms 3460 KB Output is correct
44 Correct 378 ms 5652 KB Output is correct
45 Correct 364 ms 5660 KB Output is correct
46 Correct 50 ms 4880 KB Output is correct
47 Correct 58 ms 4920 KB Output is correct
48 Correct 315 ms 5664 KB Output is correct
49 Correct 333 ms 5652 KB Output is correct
50 Correct 356 ms 5200 KB Output is correct
51 Correct 384 ms 5104 KB Output is correct
52 Correct 302 ms 5632 KB Output is correct
53 Correct 304 ms 5652 KB Output is correct
54 Correct 375 ms 5156 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 0 ms 340 KB Output is correct
3 Correct 0 ms 340 KB Output is correct
4 Correct 0 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 1 ms 340 KB Output is correct
12 Correct 0 ms 340 KB Output is correct
13 Correct 1 ms 340 KB Output is correct
14 Correct 1 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 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 2 ms 340 KB Output is correct
28 Correct 1 ms 380 KB Output is correct
29 Correct 11 ms 600 KB Output is correct
30 Correct 13 ms 612 KB Output is correct
31 Correct 13 ms 604 KB Output is correct
32 Correct 3 ms 596 KB Output is correct
33 Correct 5 ms 596 KB Output is correct
34 Correct 11 ms 596 KB Output is correct
35 Correct 10 ms 612 KB Output is correct
36 Correct 14 ms 596 KB Output is correct
37 Correct 15 ms 612 KB Output is correct
38 Correct 11 ms 596 KB Output is correct
39 Correct 12 ms 612 KB Output is correct
40 Correct 10 ms 612 KB Output is correct
41 Correct 11 ms 596 KB Output is correct
42 Correct 6 ms 604 KB Output is correct
43 Correct 206 ms 3460 KB Output is correct
44 Correct 378 ms 5652 KB Output is correct
45 Correct 364 ms 5660 KB Output is correct
46 Correct 50 ms 4880 KB Output is correct
47 Correct 58 ms 4920 KB Output is correct
48 Correct 315 ms 5664 KB Output is correct
49 Correct 333 ms 5652 KB Output is correct
50 Correct 356 ms 5200 KB Output is correct
51 Correct 384 ms 5104 KB Output is correct
52 Correct 302 ms 5632 KB Output is correct
53 Correct 304 ms 5652 KB Output is correct
54 Correct 375 ms 5156 KB Output is correct
55 Correct 3155 ms 34432 KB Output is correct
56 Correct 4896 ms 53060 KB Output is correct
57 Correct 5056 ms 53148 KB Output is correct
58 Correct 539 ms 45348 KB Output is correct
59 Correct 750 ms 46496 KB Output is correct
60 Correct 4231 ms 53172 KB Output is correct
61 Correct 4256 ms 53100 KB Output is correct
62 Correct 5197 ms 47384 KB Output is correct
63 Correct 5390 ms 47704 KB Output is correct
64 Correct 4161 ms 49848 KB Output is correct
65 Correct 4220 ms 53160 KB Output is correct
66 Correct 5049 ms 48128 KB Output is correct
67 Correct 4244 ms 53172 KB Output is correct