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답안 #1052525

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
1052525 2024-08-10T15:41:46 Z _rain_ 3D Histogram (COCI20_histogram) C++14
110 / 110
 1290 ms 104996 KB 
#include<bits/stdc++.h>
using namespace std;
using i64 = long long;
 
template<class T1 , class T2>
	bool maximize(T1& a , T2 b)
	{
		if (a < b) return a = b , true;
		return false;
	}
template<class T1 , class T2>
	bool minimize(T1& a , T2 b)
	{
		if (a > b) return a = b , true;
		return false;
	}
 
const int maxn = 2e5;
 
//... CONVEXHULL
		struct Line
		{
			i64 a ;
			i64 b;
			Line(i64 a , i64 b) : a(a) , b(b) {};
		};
		struct Hull
		{
			Line X ;
			long double intersec;
		};
		class Convexhull
		{
			public:
				vector<Hull> line;
 
				 double getintersec(Line x , Line y)
				{
					return (long double)(y.b - x.b) / (x.a - y.a);
				}
				i64 f(Line a , i64 x)
				{
					return a.a * x + a.b;
				}
 
				void addline(Line x)
				{
					int n = line.size();
					while (n > 1 && getintersec(x , line[n - 2].X) <= line[n - 1].intersec)
						{
							--n;
							line.pop_back();
						}
					if (line.empty()) line.push_back({x , LLONG_MIN});
						else line.push_back({x , getintersec(x , line[n - 1].X)});
					return;
				}
				i64 find(i64 val)
				{
					int l = 0 , r = line.size()-1 , pos = 0;
					while (l<=r)
					{
						int m = l + r >> 1;
						if (line[m].intersec <= val)
							pos = m , l = m + 1;
						else r = m - 1;
					}
					return f(line[pos].X , val);
				}
				void add(i64 a , i64 b)
				{
					addline(Line{a,b});
					return;
				}
				void reset()
				{
					line.clear();
				}
		};
	Convexhull operator + (Convexhull a , Convexhull b)
	{
		Convexhull c;
		int id1 = 0 , id2 = 0;
		for (; id1 < a.line.size() && id2 < b.line.size() ; )
		{
			if (a.line[id1].X.a < b.line[id2].X.a)
			{
				c.addline(a.line[id1++].X);
			}
			else {
				c.addline(b.line[id2++].X);
			}
		}
		for (; id1 < a.line.size(); ++id1) c.addline(a.line[id1].X);
		for (; id2 < b.line.size(); ++id2) c.addline(b.line[id2].X);
		return c;
	}

const i64 INF = 1e18 + 7;
int n;
i64 a[maxn+2],b[maxn+2];
i64 mnA[maxn+2][2] , mnB[maxn+2][2];
 

//... BUILD SEGMENT_TREE
	Convexhull stA[maxn*4+2];
	Convexhull stB[maxn*4+2];

	void buildA(int id , int l , int r , int u , int v)
	{
		stA[id].reset();
		if (l > v || r < u) return;
		if (l==r)
		{
			stA[id].add(-mnA[l][1] , mnA[l][1] * (l+1));
			return;
		}
		else {
			int m = l + r >> 1;
			buildA(id*2,l,m,u,v);
			buildA(id*2+1,m+1,r,u,v);
			stA[id] = stA[id*2] + stA[id*2+1];
			return;
		}
	}
	void buildB(int id , int l , int r , int u , int v)
	{
		stB[id].reset();
		if (l > v || r < u) return ;
		if (l==r)
		{
			stB[id].add(-mnB[l][1] , mnB[l][1] * (l+1));
			return;
		}
		else {
			int m = l + r >> 1;
			buildB(id*2,l,m,u,v);
			buildB(id*2+1,m+1,r,u,v);
			stB[id] = stB[id*2] + stB[id*2+1];
			return;
		}
	}
	i64 getA(int id , int l , int r , int u , int v , i64 k)
	{
		if (l > v || r < u) return -INF;
		if (u <= l && r <= v) return stA[id].find(k);
		int m = l + r >> 1;
		return max(getA(id*2,l,m,u,v,k),getA(id*2+1,m+1,r,u,v,k));
	}
	i64 getB(int id , int l , int r , int u , int v , i64 k)
	{
		if (l > v || r < u) return -INF;
		if (u <= l && r <= v) return stB[id].find(k);
		int m = l + r >> 1;
		return max(getB(id*2,l,m,u,v,k),getB(id*2+1,m+1,r,u,v,k));
	}
//...;

void build_LEFT(int l , int r)
{
	mnA[r+1][0] = mnB[r+1][0] = INF;
	for (int i = r; i >= l; --i)
	{
		mnA[i][0]=min(mnA[i+1][0],a[i]);
		mnB[i][0]=min(mnB[i+1][0],b[i]);
	}
	return;
}
void build_RIGHT(int l , int r)
{
	mnA[l-1][1] = mnB[l-1][1] = INF;
	for (int i = l; i <= r; ++i)
	{
		mnA[i][1]=min(mnA[i-1][1],a[i]);
		mnB[i][1]=min(mnB[i-1][1],b[i]);
	}
	buildA(1,1,n,l,r);
	buildB(1,1,n,l,r);
	return; 
}

i64 case1(int l , int m , int r) // LEFT IS MINA , RIGHT IS MINB
{
	i64 res = 0;
	int j = r;
	for (int i = l; i <= m; ++i)
	{
		while (j > m && mnA[j][1] < mnA[i][0]) --j;
		int low = m + 1 , high = j , pos = -1;
		while (low <= high)
				{
					int mid = low + high >> 1;
					if (mnB[i][0] >= mnB[mid][1])
					{
						pos = mid;
						high = mid - 1;
					}
					else low = mid + 1;
				}
		if (pos == -1) continue;
		i64 x = getB(1,1,n,pos,j,i);
		if (x < 0) continue;
		res = max(res , x * mnA[i][0]);
	}
	return res;
}
i64 case2(int l , int m , int r) // LEFT IS MINB , RIGHT IS MINA
{
	i64 res = 0;
	int j = r;
	for (int i = l; i <= m; ++i)
	{
		while (j > m && mnB[j][1] < mnB[i][0]) --j;
		int low = m + 1 , high = j , pos = -1;
		while (low <= high)
				{
					int mid = low + high >> 1;
					if (mnA[i][0] >= mnA[mid][1])
					{
						pos = mid;
						high = mid - 1;
					}
					else low = mid + 1;
				}
		if (pos == -1) continue;
		i64 x = getA(1,1,n,pos,j,i);
		if (x < 0) continue;
		res = max(res , x * mnB[i][0]);
	}
	return res;
}
i64 case3(int l , int m , int r) // LEFT IS MINA-MINB
{
	int j = r;
	i64 res = 0;
	for (int i = l; i <= m; ++i)
	{
		while (j > m && (mnA[j][1] < mnA[i][0] || mnB[j][1] < mnB[i][0])) --j;
		res = max(res , mnB[i][0] * mnA[i][0] * (j - i + 1));
	}
	return res;
}
i64 case4(int l , int m , int r) // RIGHT IS MINB-MINA
{
	int j = l;
	i64 res = 0;
	for (int i = r; i >= m; --i)
	{
		while (j < m && (mnA[j][0] < mnA[i][1] || mnB[j][0] < mnB[i][1])) ++j;
		res = max(res , mnB[i][1] * mnA[i][1] * (i - j + 1));
	}
	return res;
}
 
i64 solve(int l , int r)
{
	if (l > r) return 0;
	if (l==r) return a[l]*b[l];

	int m = l + r >> 1;
	build_LEFT(l,m);
	build_RIGHT(m,r);
	i64 res = 0;
	res = max(res , case1(l,m,r));
	res = max(res , case2(l,m,r));
	res = max(res , case3(l,m,r));
	res = max(res , case4(l,m,r));

	res = max({res , solve(l,m), solve(m+1,r)});
	return res;
}
 
int main()
{
	ios_base::sync_with_stdio(0);
	cin.tie(0); cout.tie(0);
	#define name "main"
	if (fopen(name".inp","r"))
	{
		(void)freopen(name".inp","r",stdin);
		(void)freopen(name".out","w",stdout);
	}
	cin >> n;
	for (int i = 1; i <= n; ++i) cin >> a[i] >> b[i];
	cout << solve(1,n);
}

Compilation message

histogram.cpp: In member function 'i64 Convexhull::find(i64)':
histogram.cpp:63:17: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
   63 |       int m = l + r >> 1;
      |               ~~^~~
histogram.cpp: In function 'Convexhull operator+(Convexhull, Convexhull)':
histogram.cpp:84:14: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<Hull>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   84 |   for (; id1 < a.line.size() && id2 < b.line.size() ; )
      |          ~~~~^~~~~~~~~~~~~~~
histogram.cpp:84:37: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<Hull>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   84 |   for (; id1 < a.line.size() && id2 < b.line.size() ; )
      |                                 ~~~~^~~~~~~~~~~~~~~
histogram.cpp:94:14: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<Hull>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   94 |   for (; id1 < a.line.size(); ++id1) c.addline(a.line[id1].X);
      |          ~~~~^~~~~~~~~~~~~~~
histogram.cpp:95:14: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<Hull>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   95 |   for (; id2 < b.line.size(); ++id2) c.addline(b.line[id2].X);
      |          ~~~~^~~~~~~~~~~~~~~
histogram.cpp: In function 'void buildA(int, int, int, int, int)':
histogram.cpp:119:14: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
  119 |    int m = l + r >> 1;
      |            ~~^~~
histogram.cpp: In function 'void buildB(int, int, int, int, int)':
histogram.cpp:136:14: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
  136 |    int m = l + r >> 1;
      |            ~~^~~
histogram.cpp: In function 'i64 getA(int, int, int, int, int, i64)':
histogram.cpp:147:13: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
  147 |   int m = l + r >> 1;
      |           ~~^~~
histogram.cpp: In function 'i64 getB(int, int, int, int, int, i64)':
histogram.cpp:154:13: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
  154 |   int m = l + r >> 1;
      |           ~~^~~
histogram.cpp: In function 'i64 case1(int, int, int)':
histogram.cpp:192:20: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
  192 |      int mid = low + high >> 1;
      |                ~~~~^~~~~~
histogram.cpp: In function 'i64 case2(int, int, int)':
histogram.cpp:217:20: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
  217 |      int mid = low + high >> 1;
      |                ~~~~^~~~~~
histogram.cpp: In function 'i64 solve(int, int)':
histogram.cpp:260:12: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
  260 |  int m = l + r >> 1;
      |          ~~^~~
histogram.cpp: In function 'int main()':
histogram.cpp:280:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  280 |   (void)freopen(name".inp","r",stdin);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~
histogram.cpp:281:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  281 |   (void)freopen(name".out","w",stdout);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~

Subtask #1
20.0 / 20.0

# 결과 실행 시간 메모리 Grader output
1 Correct 12 ms 44124 KB Output is correct
2 Correct 15 ms 44124 KB Output is correct
3 Correct 13 ms 44124 KB Output is correct
4 Correct 12 ms 44124 KB Output is correct
5 Correct 15 ms 44288 KB Output is correct
6 Correct 14 ms 44120 KB Output is correct
7 Correct 11 ms 44124 KB Output is correct
8 Correct 12 ms 44124 KB Output is correct
9 Correct 12 ms 44168 KB Output is correct
10 Correct 12 ms 44124 KB Output is correct
11 Correct 6 ms 43612 KB Output is correct
12 Correct 18 ms 44124 KB Output is correct

Subtask #2
90.0 / 90.0

# 결과 실행 시간 메모리 Grader output
1 Correct 12 ms 44124 KB Output is correct
2 Correct 15 ms 44124 KB Output is correct
3 Correct 13 ms 44124 KB Output is correct
4 Correct 12 ms 44124 KB Output is correct
5 Correct 15 ms 44288 KB Output is correct
6 Correct 14 ms 44120 KB Output is correct
7 Correct 11 ms 44124 KB Output is correct
8 Correct 12 ms 44124 KB Output is correct
9 Correct 12 ms 44168 KB Output is correct
10 Correct 12 ms 44124 KB Output is correct
11 Correct 6 ms 43612 KB Output is correct
12 Correct 18 ms 44124 KB Output is correct
13 Correct 1182 ms 97616 KB Output is correct
14 Correct 939 ms 97364 KB Output is correct
15 Correct 1290 ms 98132 KB Output is correct
16 Correct 1135 ms 97880 KB Output is correct
17 Correct 1170 ms 104276 KB Output is correct
18 Correct 1140 ms 103088 KB Output is correct
19 Correct 1142 ms 101628 KB Output is correct
20 Correct 1259 ms 104016 KB Output is correct
21 Correct 1244 ms 97876 KB Output is correct
22 Correct 1159 ms 104996 KB Output is correct
23 Correct 99 ms 48732 KB Output is correct
24 Correct 1088 ms 97516 KB Output is correct