답안 #312188

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
312188 2020-10-12T15:12:49 Z minhcool 수열 (APIO14_sequence) C++17
71 / 100
110 ms 131076 KB
#include<bits/stdc++.h>
using namespace std;

#define int long long
#define fi first
#define se second
#define pb push_back
#define ins insert
#define er erase

typedef pair<int, int> ii;
typedef pair<ii, int> iii;
typedef pair<ii, ii> iiii;

const int oo = 1e18 + 7, mod = 1e9 + 7;

/*
For educational purposes, I will implement the solution both in divide_and_conquer_DP style - O(N * K * log2(N)) (probably get 71 points) and convex hull trick style - O(N * K)
This code is divide_and_conquer DP
*/

const int N = 2e5 + 5, K = 205;

int n, k, a[N], suff[N];
int dp[N], lst_dp[N], opt[N];
int lst[N][K];

int f(int i, int j){
    return lst_dp[j] + (suff[j + 1] - suff[i + 1]) * suff[i + 1];
}

/*
Condition of D&Q DP: optimal position of x <= optimal position of (x + 1)
Suppose we are trying to calculate the value of opt[x] with l <= x <= r
We take the middle element mid = (l + r) >> 1 and calulate its opt value = y
=> opt[x] < y with l <= x < mid, and opt[x] > y with mid < x <= r
We can easily see that the complexity is O(n * log2(n))
I will say that this D&Q is nice
*/

void divide(int l, int r, int optl, int optr){
    if(l > r) return;
    //cout << l << " " << r << " " << optl << " " << optr << "\n";
    if(optl == optr){
        for(int i = l; i <= r; i++){
            opt[i] = optl;
        }
        return;
    }
    int mid = (l + r) >> 1;
    ii best = {-1, oo};
    for(int i = optl; i <= min(optr, mid - 1); i++){
        best = max(best, {f(mid, i), i});
        //if(mid == 4) cout << mid << " " << f(mid, i) << "\n";
    }
    opt[mid] = best.se;
    divide(l, mid - 1, optl, best.se);
    divide(mid + 1, r, best.se, optr);
}

signed main(){
	ios_base::sync_with_stdio(0);
	cin >> n >> k;
	for(int i = 1; i <= n; i++) cin >> a[i];
	for(int i = n; i >= 1; i--) suff[i] = (suff[i + 1] + a[i]);
	for(int i = 1; i <= k; i++){
	    for(int j = 1; j <= n; j++){
	        opt[j] = 0;
	        lst_dp[j] = dp[j];
	    }
	    divide(1, n, 0, n - 1);
	    for(int j = 1; j <= n; j++) lst[j][i] = opt[j];
	    for(int j = 1; j <= n; j++) dp[j] = f(j, opt[j]);
	    //for(int j = 1; j <= n; j++) cout << i << " " << j << " " << dp[j] << " " << opt[j] << "\n";
	}
    int ind = k;
    for(int i = k + 1; i <= n; i++){
        if(dp[i] > dp[ind]) ind = i;
    }
    cout << dp[ind] << "\n";
    vector<int> pos;
    pos.clear();
    int tmp = k;
    while(tmp){
        pos.pb(ind);
        ind = lst[ind][tmp];
        tmp--;
    }
    for(int i = pos.size() - 1; i >= 0; i--) cout << pos[i] << " ";
}

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 384 KB contestant found the optimal answer: 108 == 108
2 Correct 0 ms 384 KB contestant found the optimal answer: 999 == 999
3 Correct 0 ms 384 KB contestant found the optimal answer: 0 == 0
4 Correct 0 ms 384 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 1 ms 384 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 0 ms 384 KB contestant found the optimal answer: 1 == 1
7 Correct 0 ms 384 KB contestant found the optimal answer: 1 == 1
8 Correct 0 ms 384 KB contestant found the optimal answer: 1 == 1
9 Correct 1 ms 384 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 1 ms 416 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 0 ms 384 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 0 ms 384 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 1 ms 384 KB contestant found the optimal answer: 140072 == 140072
14 Correct 0 ms 384 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 0 ms 384 KB contestant found the optimal answer: 805 == 805
16 Correct 1 ms 384 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 0 ms 384 KB contestant found the optimal answer: 999919994 == 999919994
# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 512 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 1 ms 512 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 1 ms 512 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 1 ms 512 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 0 ms 512 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 1 ms 384 KB contestant found the optimal answer: 933702 == 933702
7 Correct 0 ms 512 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 1 ms 512 KB contestant found the optimal answer: 687136 == 687136
9 Correct 1 ms 512 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 0 ms 384 KB contestant found the optimal answer: 29000419931 == 29000419931
# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 640 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 1 ms 640 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 2 ms 768 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 1 ms 640 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 1 ms 768 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 2 ms 768 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 2 ms 640 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 1 ms 640 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 1 ms 640 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 1 ms 768 KB contestant found the optimal answer: 490686959791 == 490686959791
# 결과 실행 시간 메모리 Grader output
1 Correct 2 ms 2048 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 1 ms 2048 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 7 ms 2048 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 2 ms 2048 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 11 ms 2048 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 9 ms 2048 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 9 ms 2048 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 7 ms 2048 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 3 ms 2048 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 5 ms 2048 KB contestant found the optimal answer: 12345131038664 == 12345131038664
# 결과 실행 시간 메모리 Grader output
1 Correct 11 ms 16768 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 10 ms 16768 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 88 ms 16864 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 12 ms 16768 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 95 ms 16872 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 89 ms 16888 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 83 ms 16896 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 62 ms 16904 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 84 ms 16896 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 110 ms 16908 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798
# 결과 실행 시간 메모리 Grader output
1 Runtime error 79 ms 131076 KB Execution killed with signal 9 (could be triggered by violating memory limits)
2 Halted 0 ms 0 KB -