oj.uz

Submission #789169

# Submission time Handle Problem Language Result Execution time Memory
789169 2023-07-21T06:57:37 Z 박상훈(#10042) Chorus (JOI23_chorus) C++17
61 / 100
 7000 ms 3288 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);
			}

			// if (cst[i][j]!=cost(i, j)){
			// 	printf("%d %d -> %lld %lld\n", i, j, cst[i][j], cost(i, j));
			// }
			// assert(cst[i][j] == cost(i, j));
		}
	}

	// is cost monge?
	// for (int i=1;i<=n-1;i++){
	// 	for (int j=i+1;j<=n-1;j++){
	// 		assert(cst[i][j] + cst[i+1][j+1] <= cst[i][j+1] + cst[i+1][j]);
	// 	}
	// }

	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() >= cross(st.back(), x)){
			st.pop_back();
			st2.pop_back();
		}

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

	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
	dp[0] = 0;
	dp2[0] = 0;

	for (int i=1;i<=n;i++){
		dp[i] = INF;
		for (int j=0;j<i;j++){
			ll val = dp[j] + cost(j+1, i) * 2 + lambda;
			if (dp[i] > val){
				dp[i] = val;
				dp2[i] = dp2[j] + 1;
			}
		}
	}

	// int i = 3, j = 5;
	// printf("\n");
	// for (int k=6;k<=n;k++) printf("%lld ", dp[i] + cost(i+1, k) * 2 + lambda);
	// printf("\n");
	// for (int k=6;k<=n;k++) printf("%lld ", dp[j] + cost(j+1, k) * 2 + lambda);
	// printf("\n");

	// monotone queue opt
	hull.init(n, lambda);
	hull.push(0);

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

	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:167:7: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
  167 |  scanf("%d %d", &n, &k);
      |  ~~~~~^~~~~~~~~~~~~~~~~
chorus.cpp:169:7: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
  169 |  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 1 ms 340 KB Output is correct
4 Correct 0 ms 340 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 1 ms 384 KB Output is correct
7 Correct 0 ms 340 KB Output is correct
8 Correct 0 ms 340 KB Output is correct
9 Correct 1 ms 340 KB Output is correct
10 Correct 1 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 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 1 ms 340 KB Output is correct
3 Correct 1 ms 340 KB Output is correct
4 Correct 0 ms 340 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 1 ms 384 KB Output is correct
7 Correct 0 ms 340 KB Output is correct
8 Correct 0 ms 340 KB Output is correct
9 Correct 1 ms 340 KB Output is correct
10 Correct 1 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 0 ms 340 KB Output is correct
16 Correct 0 ms 340 KB Output is correct
17 Correct 3 ms 340 KB Output is correct
18 Correct 16 ms 380 KB Output is correct
19 Correct 15 ms 380 KB Output is correct
20 Correct 16 ms 380 KB Output is correct
21 Correct 10 ms 340 KB Output is correct
22 Correct 11 ms 340 KB Output is correct
23 Correct 10 ms 340 KB Output is correct
24 Correct 13 ms 376 KB Output is correct
25 Correct 11 ms 384 KB Output is correct
26 Correct 12 ms 392 KB Output is correct
27 Correct 11 ms 380 KB Output is correct
28 Correct 11 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 1 ms 340 KB Output is correct
4 Correct 0 ms 340 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 1 ms 384 KB Output is correct
7 Correct 0 ms 340 KB Output is correct
8 Correct 0 ms 340 KB Output is correct
9 Correct 1 ms 340 KB Output is correct
10 Correct 1 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 0 ms 340 KB Output is correct
16 Correct 0 ms 340 KB Output is correct
17 Correct 3 ms 340 KB Output is correct
18 Correct 16 ms 380 KB Output is correct
19 Correct 15 ms 380 KB Output is correct
20 Correct 16 ms 380 KB Output is correct
21 Correct 10 ms 340 KB Output is correct
22 Correct 11 ms 340 KB Output is correct
23 Correct 10 ms 340 KB Output is correct
24 Correct 13 ms 376 KB Output is correct
25 Correct 11 ms 384 KB Output is correct
26 Correct 12 ms 392 KB Output is correct
27 Correct 11 ms 380 KB Output is correct
28 Correct 11 ms 340 KB Output is correct
29 Correct 835 ms 680 KB Output is correct
30 Correct 910 ms 652 KB Output is correct
31 Correct 939 ms 568 KB Output is correct
32 Correct 868 ms 584 KB Output is correct
33 Correct 887 ms 564 KB Output is correct
34 Correct 910 ms 648 KB Output is correct
35 Correct 879 ms 660 KB Output is correct
36 Correct 910 ms 580 KB Output is correct
37 Correct 890 ms 752 KB Output is correct
38 Correct 852 ms 596 KB Output is correct
39 Correct 880 ms 636 KB Output is correct
40 Correct 833 ms 600 KB Output is correct
41 Correct 851 ms 580 KB Output is correct
42 Correct 926 ms 600 KB Output is correct

Subtask #4
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 1 ms 340 KB Output is correct
4 Correct 0 ms 340 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 1 ms 384 KB Output is correct
7 Correct 0 ms 340 KB Output is correct
8 Correct 0 ms 340 KB Output is correct
9 Correct 1 ms 340 KB Output is correct
10 Correct 1 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 0 ms 340 KB Output is correct
16 Correct 0 ms 340 KB Output is correct
17 Correct 3 ms 340 KB Output is correct
18 Correct 16 ms 380 KB Output is correct
19 Correct 15 ms 380 KB Output is correct
20 Correct 16 ms 380 KB Output is correct
21 Correct 10 ms 340 KB Output is correct
22 Correct 11 ms 340 KB Output is correct
23 Correct 10 ms 340 KB Output is correct
24 Correct 13 ms 376 KB Output is correct
25 Correct 11 ms 384 KB Output is correct
26 Correct 12 ms 392 KB Output is correct
27 Correct 11 ms 380 KB Output is correct
28 Correct 11 ms 340 KB Output is correct
29 Correct 835 ms 680 KB Output is correct
30 Correct 910 ms 652 KB Output is correct
31 Correct 939 ms 568 KB Output is correct
32 Correct 868 ms 584 KB Output is correct
33 Correct 887 ms 564 KB Output is correct
34 Correct 910 ms 648 KB Output is correct
35 Correct 879 ms 660 KB Output is correct
36 Correct 910 ms 580 KB Output is correct
37 Correct 890 ms 752 KB Output is correct
38 Correct 852 ms 596 KB Output is correct
39 Correct 880 ms 636 KB Output is correct
40 Correct 833 ms 600 KB Output is correct
41 Correct 851 ms 580 KB Output is correct
42 Correct 926 ms 600 KB Output is correct
43 Execution timed out 7015 ms 3288 KB Time limit exceeded
44 Halted 0 ms 0 KB -

Subtask #5
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 1 ms 340 KB Output is correct
4 Correct 0 ms 340 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 1 ms 384 KB Output is correct
7 Correct 0 ms 340 KB Output is correct
8 Correct 0 ms 340 KB Output is correct
9 Correct 1 ms 340 KB Output is correct
10 Correct 1 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 0 ms 340 KB Output is correct
16 Correct 0 ms 340 KB Output is correct
17 Correct 3 ms 340 KB Output is correct
18 Correct 16 ms 380 KB Output is correct
19 Correct 15 ms 380 KB Output is correct
20 Correct 16 ms 380 KB Output is correct
21 Correct 10 ms 340 KB Output is correct
22 Correct 11 ms 340 KB Output is correct
23 Correct 10 ms 340 KB Output is correct
24 Correct 13 ms 376 KB Output is correct
25 Correct 11 ms 384 KB Output is correct
26 Correct 12 ms 392 KB Output is correct
27 Correct 11 ms 380 KB Output is correct
28 Correct 11 ms 340 KB Output is correct
29 Correct 835 ms 680 KB Output is correct
30 Correct 910 ms 652 KB Output is correct
31 Correct 939 ms 568 KB Output is correct
32 Correct 868 ms 584 KB Output is correct
33 Correct 887 ms 564 KB Output is correct
34 Correct 910 ms 648 KB Output is correct
35 Correct 879 ms 660 KB Output is correct
36 Correct 910 ms 580 KB Output is correct
37 Correct 890 ms 752 KB Output is correct
38 Correct 852 ms 596 KB Output is correct
39 Correct 880 ms 636 KB Output is correct
40 Correct 833 ms 600 KB Output is correct
41 Correct 851 ms 580 KB Output is correct
42 Correct 926 ms 600 KB Output is correct
43 Execution timed out 7015 ms 3288 KB Time limit exceeded
44 Halted 0 ms 0 KB -