oj.uz

Submission #202251

# Submission time Handle Problem Language Result Execution time Memory
202251 2020-02-14T14:31:18 Z thiago4532 Building Bridges (CEOI17_building) C++17
100 / 100
 182 ms 12152 KB 
    #include <bits/stdc++.h>
    #define int int64_t
    using namespace std;
    const int maxn = 1e5 + 10;
    int h[maxn], pref[maxn], w[maxn];
    int n, dp[maxn];
     
    struct frac {
        int a, b;
     
        bool operator<(frac const& c) const {
            return a*c.b < c.a*b;
        }
    };
     
    bool flag = 0;
    struct line {
    	int a, b;
    	frac x;
     
    	bool operator<(line const& l) const {
    		if(flag == 0) return a > l.a;
    		else return x < l.x;
    	}
    };
     
    typedef set<line>::iterator sit;
     
    set<line> lines;
     
    bool hasPrev(sit it)
    {
    	return (it != lines.begin());
    }
     
    bool hasNext(sit it)
    {
    	return (next(it) != lines.end() && ++it != lines.end());
    }
     
    template<typename Arg>
    bool bad(Arg&& l1, Arg&& l2, Arg&& l3) {
    	return (l2.a - l1.a)*(l3.b - l1.b) >= (l3.a -  l1.a)*(l2.b - l1.b);
    }
     
    frac intersect(line const& l1, line const& l2) {
    	return {l2.b-l1.b, l1.a-l2.a};
    }
     
    void get_x(sit it) {
    	if (hasPrev(it))
    	{
    		line l = *it;
     
    		l.x = intersect(*prev(it), *it);
     
    		lines.erase(it); lines.insert(l);
    	}
    }
     
    void add(line const& l) {
    	auto it = lines.lower_bound(l);
    	if(it != lines.end() && it->a == l.a){
    		if(it->b <= l.b) return;
    		lines.erase(it);
    	}
     
    	lines.insert(l);
    	it = lines.find(l);
     
    	if (hasPrev(it) && hasNext(it) && bad(*prev(it), *it, *next(it))) {
    		lines.erase(it);
    		return;
    	}
     
    	while(hasNext(it) && hasNext(next(it)) && bad(*it, *next(it), *next(next(it)))) 
    		lines.erase(next(it));
     
    	while(hasPrev(it) && hasPrev(prev(it)) && bad(*prev(prev(it)), *prev(it), *it))
    		lines.erase(prev(it));
     
        if (hasNext(it)) get_x(next(it));
    	get_x(it);
    }
     
    inline int f(line const& l, int x) {
    	return l.a*x + l.b;
    }
     
    int query(int x) {
    	flag = true;
    	auto it = lines.upper_bound({0, 0, {x, 1}});
    	flag = false;
    	it--;
    	return f(*it, x);
    }
     
     
    int32_t main() {
    	cin >> n;
    	for(int i=1;i<=n;i++)
    		cin >> h[i];
     
    	for(int i=1;i<=n;i++)
    		cin >> w[i], pref[i] = pref[i-1] + w[i];
     
    	dp[1] = 0;
    	add({-2*h[1], h[1]*h[1] + dp[1] - pref[1]});
     
    	for(int i=2;i<=n;i++) {
    		// dp[i] = 0x3f3f3f3f3f3f3f3f;
     
    		// for(int j=1;j<i;j++) {
    		// 	dp[i] = min(dp[i], dp[j] - pref[j] + h[j]*h[j] - 2*h[j] * h[i]);
    		// }
     
    		dp[i] = query(h[i]);
     
    		dp[i] += h[i]*h[i] + pref[i-1];
    		add({-2*h[i], h[i]*h[i] + dp[i] - pref[i]});
    	}
    	cout << dp[n] << "\n";
    	return 0;
    }

Subtask #1
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 376 KB Output is correct
2 Correct 5 ms 380 KB Output is correct
3 Correct 5 ms 376 KB Output is correct
4 Correct 6 ms 376 KB Output is correct
5 Correct 6 ms 376 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 173 ms 4712 KB Output is correct
2 Correct 170 ms 4600 KB Output is correct
3 Correct 170 ms 4600 KB Output is correct
4 Correct 164 ms 4344 KB Output is correct
5 Correct 148 ms 5880 KB Output is correct

Subtask #3
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 376 KB Output is correct
2 Correct 5 ms 380 KB Output is correct
3 Correct 5 ms 376 KB Output is correct
4 Correct 6 ms 376 KB Output is correct
5 Correct 6 ms 376 KB Output is correct
6 Correct 173 ms 4712 KB Output is correct
7 Correct 170 ms 4600 KB Output is correct
8 Correct 170 ms 4600 KB Output is correct
9 Correct 164 ms 4344 KB Output is correct
10 Correct 148 ms 5880 KB Output is correct
11 Correct 170 ms 4608 KB Output is correct
12 Correct 173 ms 4600 KB Output is correct
13 Correct 132 ms 4536 KB Output is correct
14 Correct 182 ms 4732 KB Output is correct
15 Correct 180 ms 12152 KB Output is correct
16 Correct 148 ms 5880 KB Output is correct
17 Correct 85 ms 4476 KB Output is correct
18 Correct 86 ms 4600 KB Output is correct