Submission #420438

#	Time	Username	Problem	Language	Result	Execution time	Memory
420438		MetalPower	Cigle (COI21_cigle)	C++14	100 / 100	623 ms	67388 KiB

cigle

#include <bits/stdc++.h>
using namespace std;

const int MX = 5005;

void chmax(int& a, int b){
	if(b > a) a = b;
}

int N, arr[MX], dp[MX][MX];

// Observation #1 : We can easily solve this in O(N^3)
	// dp(i, j) is the largest beauty of the wall if the highest row includes [i, j]
	// the transition is we add another row [j + 1, k] for every j + 1 <= k <= N
	// calculating is easy two pointer

// Observation #2 : if the size of row[j + 1, k] is higher than row[i, j]
	// then for every other k >= current_k 
	// the value of the dp is constant
	// this is also correct for the opposite
	
// So we can solve this in O(N^2) by precomputing the transitions for every j
	// and using two pointer to increment k and decrement i

struct segtree{
	int v[MX * 2];

	void build(int p){
		for(int i = MX; i < 2 * MX; i++) v[i] = dp[i - MX][p];
		for(int i = MX - 1; i > 0; i--) v[i] = max(v[i << 1], v[i << 1 | 1]);
	}

	int range(int l, int r){ // [l, r]
		int res = 0;
		for(l += MX, r += MX + 1; l < r; l >>= 1, r >>= 1){
			if(l & 1) chmax(res, v[l++]);
			if(r & 1) chmax(res, v[--r]);
		}
		return res;
	}
} st;

int main(){
	ios_base::sync_with_stdio(0); cin.tie(NULL); cout.tie(NULL);

	cin >> N;

	for(int i = 0; i < N; i++) cin >> arr[i];

	for(int p = 0; p < N; p++){
		int i = p, k = p + 1, cnt = -1, bot = 0, top = 0;

		st.build(p);

		while(i >= 0 && k < N){
			if(bot == top){
				cnt++; chmax(dp[p + 1][k], st.range(0, i) + cnt);
				bot += arr[i--]; top += arr[k++];
			}else if(bot < top){
				bot += arr[i--];
			}else if(top < bot){
				top += arr[k++];
			}
		}

		for(int j = p + 1; j < N; j++) chmax(dp[p + 1][j], dp[p + 1][j - 1]);
	}

	int ans = 0;

	for(int p = 0; p < N; p++) chmax(ans, dp[p][N - 1]);

	cout << ans << '\n';
}

• Subtask 1: 9 / 9
• Subtask 2: 11 / 11
• Subtask 3: 13 / 13
• Subtask 4: 15 / 15
• Subtask 5: 52 / 52