oj.uz

Submission #789171

# Submission time Handle Problem Language Result Execution time Memory
789171 2023-07-21T06:58:42 Z 박상훈(#10042) Chorus (JOI23_chorus) C++17
87 / 100
 7000 ms 53836 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 1 ms 340 KB Output is correct
5 Correct 1 ms 308 KB Output is correct
6 Correct 1 ms 308 KB Output is correct
7 Correct 1 ms 340 KB Output is correct
8 Correct 1 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 1 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 1 ms 340 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 308 KB Output is correct
6 Correct 1 ms 308 KB Output is correct
7 Correct 1 ms 340 KB Output is correct
8 Correct 1 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 1 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 2 ms 380 KB Output is correct
18 Correct 3 ms 340 KB Output is correct
19 Correct 3 ms 304 KB Output is correct
20 Correct 2 ms 312 KB Output is correct
21 Correct 2 ms 340 KB Output is correct
22 Correct 3 ms 340 KB Output is correct
23 Correct 3 ms 340 KB Output is correct
24 Correct 3 ms 308 KB Output is correct
25 Correct 3 ms 304 KB Output is correct
26 Correct 3 ms 340 KB Output is correct
27 Correct 3 ms 340 KB Output is correct
28 Correct 3 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 1 ms 340 KB Output is correct
5 Correct 1 ms 308 KB Output is correct
6 Correct 1 ms 308 KB Output is correct
7 Correct 1 ms 340 KB Output is correct
8 Correct 1 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 1 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 2 ms 380 KB Output is correct
18 Correct 3 ms 340 KB Output is correct
19 Correct 3 ms 304 KB Output is correct
20 Correct 2 ms 312 KB Output is correct
21 Correct 2 ms 340 KB Output is correct
22 Correct 3 ms 340 KB Output is correct
23 Correct 3 ms 340 KB Output is correct
24 Correct 3 ms 308 KB Output is correct
25 Correct 3 ms 304 KB Output is correct
26 Correct 3 ms 340 KB Output is correct
27 Correct 3 ms 340 KB Output is correct
28 Correct 3 ms 340 KB Output is correct
29 Correct 29 ms 668 KB Output is correct
30 Correct 34 ms 636 KB Output is correct
31 Correct 36 ms 636 KB Output is correct
32 Correct 26 ms 596 KB Output is correct
33 Correct 27 ms 572 KB Output is correct
34 Correct 29 ms 672 KB Output is correct
35 Correct 27 ms 656 KB Output is correct
36 Correct 35 ms 596 KB Output is correct
37 Correct 33 ms 596 KB Output is correct
38 Correct 28 ms 660 KB Output is correct
39 Correct 31 ms 624 KB Output is correct
40 Correct 31 ms 596 KB Output is correct
41 Correct 30 ms 588 KB Output is correct
42 Correct 22 ms 616 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 1 ms 340 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 308 KB Output is correct
6 Correct 1 ms 308 KB Output is correct
7 Correct 1 ms 340 KB Output is correct
8 Correct 1 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 1 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 2 ms 380 KB Output is correct
18 Correct 3 ms 340 KB Output is correct
19 Correct 3 ms 304 KB Output is correct
20 Correct 2 ms 312 KB Output is correct
21 Correct 2 ms 340 KB Output is correct
22 Correct 3 ms 340 KB Output is correct
23 Correct 3 ms 340 KB Output is correct
24 Correct 3 ms 308 KB Output is correct
25 Correct 3 ms 304 KB Output is correct
26 Correct 3 ms 340 KB Output is correct
27 Correct 3 ms 340 KB Output is correct
28 Correct 3 ms 340 KB Output is correct
29 Correct 29 ms 668 KB Output is correct
30 Correct 34 ms 636 KB Output is correct
31 Correct 36 ms 636 KB Output is correct
32 Correct 26 ms 596 KB Output is correct
33 Correct 27 ms 572 KB Output is correct
34 Correct 29 ms 672 KB Output is correct
35 Correct 27 ms 656 KB Output is correct
36 Correct 35 ms 596 KB Output is correct
37 Correct 33 ms 596 KB Output is correct
38 Correct 28 ms 660 KB Output is correct
39 Correct 31 ms 624 KB Output is correct
40 Correct 31 ms 596 KB Output is correct
41 Correct 30 ms 588 KB Output is correct
42 Correct 22 ms 616 KB Output is correct
43 Correct 512 ms 3688 KB Output is correct
44 Correct 901 ms 6032 KB Output is correct
45 Correct 950 ms 6028 KB Output is correct
46 Correct 675 ms 5048 KB Output is correct
47 Correct 715 ms 5136 KB Output is correct
48 Correct 688 ms 6040 KB Output is correct
49 Correct 681 ms 6064 KB Output is correct
50 Correct 925 ms 5552 KB Output is correct
51 Correct 940 ms 5588 KB Output is correct
52 Correct 677 ms 6060 KB Output is correct
53 Correct 696 ms 6088 KB Output is correct
54 Correct 890 ms 5640 KB Output is correct

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 1 ms 340 KB Output is correct
5 Correct 1 ms 308 KB Output is correct
6 Correct 1 ms 308 KB Output is correct
7 Correct 1 ms 340 KB Output is correct
8 Correct 1 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 1 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 2 ms 380 KB Output is correct
18 Correct 3 ms 340 KB Output is correct
19 Correct 3 ms 304 KB Output is correct
20 Correct 2 ms 312 KB Output is correct
21 Correct 2 ms 340 KB Output is correct
22 Correct 3 ms 340 KB Output is correct
23 Correct 3 ms 340 KB Output is correct
24 Correct 3 ms 308 KB Output is correct
25 Correct 3 ms 304 KB Output is correct
26 Correct 3 ms 340 KB Output is correct
27 Correct 3 ms 340 KB Output is correct
28 Correct 3 ms 340 KB Output is correct
29 Correct 29 ms 668 KB Output is correct
30 Correct 34 ms 636 KB Output is correct
31 Correct 36 ms 636 KB Output is correct
32 Correct 26 ms 596 KB Output is correct
33 Correct 27 ms 572 KB Output is correct
34 Correct 29 ms 672 KB Output is correct
35 Correct 27 ms 656 KB Output is correct
36 Correct 35 ms 596 KB Output is correct
37 Correct 33 ms 596 KB Output is correct
38 Correct 28 ms 660 KB Output is correct
39 Correct 31 ms 624 KB Output is correct
40 Correct 31 ms 596 KB Output is correct
41 Correct 30 ms 588 KB Output is correct
42 Correct 22 ms 616 KB Output is correct
43 Correct 512 ms 3688 KB Output is correct
44 Correct 901 ms 6032 KB Output is correct
45 Correct 950 ms 6028 KB Output is correct
46 Correct 675 ms 5048 KB Output is correct
47 Correct 715 ms 5136 KB Output is correct
48 Correct 688 ms 6040 KB Output is correct
49 Correct 681 ms 6064 KB Output is correct
50 Correct 925 ms 5552 KB Output is correct
51 Correct 940 ms 5588 KB Output is correct
52 Correct 677 ms 6060 KB Output is correct
53 Correct 696 ms 6088 KB Output is correct
54 Correct 890 ms 5640 KB Output is correct
55 Correct 6752 ms 37004 KB Output is correct
56 Execution timed out 7046 ms 53836 KB Time limit exceeded
57 Halted 0 ms 0 KB -