【LOJ】#2090. 「ZJOI2016」旅行者

题解

每次按较长边把矩形分成两半，找一个中间轴，轴上的每个点跑一边最短路更新所有的答案

然后把矩形分成两半，递归下去

代码

#include <bits/stdc++.h>
#define enter putchar('\n')
#define space putchar(' ')
#define pii pair<int,int>
#define fi first
#define se second
#define mp make_pair
#define pb push_back
#define eps 1e-8
//#define ivorysi
using namespace std;
typedef long long int64;
typedef double db;
template<class T>
void read(T &res) {
    res = 0;T f = 1;char c = getchar();
    while(c < '0' || c > '9') {
        if(c == '-') f = -1;
        c = getchar();
    }
    while(c >= '0' && c <= '9') {
        res = res * 10 - '0' + c;
        c = getchar();
    }
    res *= f;
}
template<class T>
void out(T x) {
    if(x < 0) {x = -x;putchar('-');}
    if(x >= 10) out(x / 10);
    putchar('0' + x % 10);
}
int N,M,Q;
int id(int x,int y) {return (x - 1) * M + y;}
pii point(int s) {return mp((s - 1) / M + 1,(s - 1) % M + 1);}
struct qry_node {
	int s,t,id;
}qry[100005],tmp[100005];
struct node {
	int to,next,val;
}E[200005];
int head[20005],sumE;
int R[20005],C[20005],ans[100005],dis[20005];
bool vis[20005];
priority_queue<pii > que;
void add(int u,int v,int c) {
	E[++sumE].to = v;
	E[sumE].next = head[u];
	E[sumE].val = c;
	head[u] = sumE;
}
bool in_Matrix(int x,int X1,int Y1,int X2,int Y2) {
	pii p = point(x);
	return p.fi >= X1 && p.fi <= X2 && p.se >= Y1 && p.se <= Y2;
}
void Dijkstra(int st,int X1,int Y1,int X2,int Y2) {
	for(int i = X1 ; i <= X2 ; ++i) {
		for(int j = Y1 ; j <= Y2 ; ++j) {
			dis[id(i,j)] = 0x7fffffff;
			vis[id(i,j)] = 0;
		}
	}
	dis[st] = 0;
	que.push(mp(-dis[st],st));
	while(!que.empty()) {
		pii now = que.top();que.pop();
		if(vis[now.se]) continue;
		vis[now.se] = 1;
		int u = now.se;
		for(int i = head[u] ; i ; i = E[i].next) {
			int v = E[i].to;
			if(!vis[v] && in_Matrix(v,X1,Y1,X2,Y2) && dis[v] > dis[u] + E[i].val) {
				dis[v] = dis[u] + E[i].val;
				que.push(mp(-dis[v],v));
			}
		}
	}
}
void update(int &x,int y) {
	x = min(x,y);
}
void Solve(int l,int r,int X1,int Y1,int X2,int Y2) {
	if(Y1 > Y2 || X1 > X2) return;
	if(Y1 == Y2 && X1 == X2) return;
	if(l > r) return;
	if(X2 - X1 <= Y2 - Y1) {
		int mid = (Y2 + Y1) >> 1;
		for(int i = X1 ; i <= X2 ; ++i) {
			Dijkstra(id(i,mid),X1,Y1,X2,Y2);
			for(int k = l ; k <= r ; ++k) {
				update(ans[qry[k].id],dis[qry[k].s] + dis[qry[k].t]);
			}
		}
		int p = l - 1,m = l - 1;
		for(int k = l ; k <= r ; ++k) {
			if(in_Matrix(qry[k].s,X1,Y1,X2,mid - 1) && in_Matrix(qry[k].t,X1,Y1,X2,mid - 1)) {
				tmp[++p] = qry[k];
			}
		}
		m = p;
		for(int k = l ; k <= r ; ++k) {
			if(in_Matrix(qry[k].s,X1,mid + 1,X2,Y2) && in_Matrix(qry[k].t,X1,mid + 1,X2,Y2)) {
				tmp[++p] = qry[k];
			}
		}
		for(int i = l ; i <= p ; ++i) qry[i] = tmp[i];
		Solve(l,m,X1,Y1,X2,mid - 1);
		Solve(m + 1,p,X1,mid + 1,X2,Y2);
	}
	else {
		int mid = (X1 + X2) >> 1;
		for(int j = Y1 ; j <= Y2 ; ++j) {
			Dijkstra(id(mid,j),X1,Y1,X2,Y2);
			for(int k = l ; k <= r ; ++k) {
				update(ans[qry[k].id],dis[qry[k].s] + dis[qry[k].t]);
			}
		}
		int p = l - 1,m = l - 1;
		for(int k = l ; k <= r ; ++k) {
			if(in_Matrix(qry[k].s,X1,Y1,mid - 1,Y2) && in_Matrix(qry[k].t,X1,Y1,mid - 1,Y2)) {
				tmp[++p] = qry[k];
			}
		}
		m = p;
		for(int k = l ; k <= r ; ++k) {
			if(in_Matrix(qry[k].s,mid + 1,Y1,X2,Y2) && in_Matrix(qry[k].t,mid + 1,Y1,X2,Y2)) {
				tmp[++p] = qry[k];
			}
		}
		for(int i = l ; i <= p ; ++i) qry[i] = tmp[i];
		Solve(l,m,X1,Y1,mid - 1,Y2);
		Solve(m + 1,p,mid + 1,Y1,X2,Y2);
	}
}
void Init() {
	read(N);read(M);
	for(int i = 1 ; i <= N ; ++i) {
		for(int j = 1 ; j <= M - 1; ++j) {
			read(R[id(i,j)]);
			add(id(i,j),id(i,j + 1),R[id(i,j)]);
			add(id(i,j + 1),id(i,j),R[id(i,j)]);
		}
	}
	for(int i = 1 ; i <= N - 1 ; ++i) {
		for(int j = 1 ; j <= M ; ++j) {
			read(C[id(i,j)]);
			add(id(i,j),id(i + 1,j),C[id(i,j)]);
			add(id(i + 1,j),id(i,j),C[id(i,j)]);
		}
	}
	read(Q);
	int x,y;
	for(int i = 1 ; i <= Q ; ++i) {
		read(x);read(y);qry[i].s = id(x,y);
		read(x);read(y);qry[i].t = id(x,y);
		qry[i].id = i;
		ans[i] = 0x7fffffff;
		if(qry[i].s == qry[i].t) ans[i] = 0;
	}

}
int main() {
#ifdef ivorysi
	freopen("f1.in","r",stdin);
#endif
	Init();
	Solve(1,Q,1,1,N,M);
	for(int i = 1 ; i <= Q ; ++i) {out(ans[i]);enter;}
}