D - Leapin‘ Lizards
Time Limit:1000MS Memory Limit:32768KB 64bit IO Format:%I64d & %I64u
Description
Your platoon of wandering lizards has entered a strange room in the labyrinth you are exploring. As you are looking around for hidden treasures, one of the rookies steps on an innocent-looking stone and the room‘s floor suddenly disappears! Each lizard in your platoon is left standing on a fragile-looking pillar, and a fire begins to rage below... Leave no lizard behind! Get as many lizards as possible out of the room, and report the number of casualties.
The pillars in the room are aligned as a grid, with each pillar one unit away from the pillars to its east, west, north and south. Pillars at the edge of the grid are one unit away from the edge of the room (safety). Not all pillars necessarily have a lizard. A lizard is able to leap onto any unoccupied pillar that is within d units of his current one. A lizard standing on a pillar within leaping distance of the edge of the room may always leap to safety... but there‘s a catch: each pillar becomes weakened after each jump, and will soon collapse and no longer be usable by other lizards. Leaping onto a pillar does not cause it to weaken or collapse; only leaping off of it causes it to weaken and eventually collapse. Only one lizard may be on a pillar at any given time.
The pillars in the room are aligned as a grid, with each pillar one unit away from the pillars to its east, west, north and south. Pillars at the edge of the grid are one unit away from the edge of the room (safety). Not all pillars necessarily have a lizard. A lizard is able to leap onto any unoccupied pillar that is within d units of his current one. A lizard standing on a pillar within leaping distance of the edge of the room may always leap to safety... but there‘s a catch: each pillar becomes weakened after each jump, and will soon collapse and no longer be usable by other lizards. Leaping onto a pillar does not cause it to weaken or collapse; only leaping off of it causes it to weaken and eventually collapse. Only one lizard may be on a pillar at any given time.
Input
The input file will begin with a line containing a single integer representing the number of test cases, which is at most 25. Each test case will begin with a line containing a single positive integer n representing the number of rows in the map, followed by a single non-negative integer d representing the maximum leaping distance for the lizards. Two maps will follow, each as a map of characters with one row per line. The first map will contain a digit (0-3) in each position representing the number of jumps the pillar in that position will sustain before collapsing (0 means there is no pillar there). The second map will follow, with an ‘L‘ for every position where a lizard is on the pillar and a ‘.‘ for every empty pillar. There will never be a lizard on a position where there is no pillar.Each input map is guaranteed to be a rectangle of size n x m, where 1 ≤ n ≤ 20 and 1 ≤ m ≤ 20. The leaping distance is
always 1 ≤ d ≤ 3.
always 1 ≤ d ≤ 3.
Output
For each input case, print a single line containing the number of lizards that could not escape. The format should follow the samples provided below.
Sample Input
4 3 1 1111 1111 1111 LLLL LLLL LLLL 3 2 00000 01110 00000 ..... .LLL. ..... 3 1 00000 01110 00000 ..... .LLL. ..... 5 2 00000000 02000000 00321100 02000000 00000000 ........ ........ ..LLLL.. ........ ........
Sample Output
Case #1: 2 lizards were left behind.
Case #2: no lizard was left behind.
Case #3: 3 lizards were left behind.
Case #4: 1 lizard was left behind.
题意：有一些蜥蜴进了一个有机关的迷宫，触发了机关，迷宫在坍塌，所以要尽可能多的蜥蜴跳出迷宫，迷宫中有一些柱子，每个柱子有一个数量代表这个柱子只能支撑多少次蜥蜴跳过来，而蜥蜴有一个最大弹跳范围d（哈密顿距离），给出迷宫的每个柱子承受的次数以及蜥蜴的位置还有弹跳范围d，求最少有多少个蜥蜴跳不出来
思路：最大流，建图方法是：对每个柱子的点拆开 i → i‘ 容量为承受次数，i‘ 连其他与这个柱子距离小于d的柱子容量为无限大（这里的无限大设10就已经够了，或者承受次数也可以，反正数据不大），如果这根柱子可以跳出边界了那就 i‘ 连 汇点t 容量无限大或承受次数。 然后对蜥蜴的连边是，源点s连蜥蜴容量为1，蜥蜴连蜥蜴所在的点的柱子 i 容量为1。这样跑一下最大流就得到最大可跳出迷宫的数量，用总数减一下就得到答案。
题目不难，有几个比较坑的点：
1. 输出 如果答案是0或1，lizard不用加s并且后面用was，否则要有s后面用were
2. 输入数据： 题目说d范围0~3，但discuss上有人说数据有d=4的情况； 题目说保证蜥蜴在的点的柱子承受次数不会是0，但实际上有这种情况，而且如果蜥蜴能立刻跳出边界则算他能逃出，否则算不能逃出。。
坑爹囧rz
代码
#include <iostream> #include <cstdio> #include <cstring> #include <algorithm> #include <vector> #include <queue> using namespace std; typedef long long ll; typedef pair<int,int> pii; const int INF = 1e9; const double eps = 1e-6; const int maxn = 2000; int cas = 1; struct Edge{ int from,to,cap,flow; Edge() {} Edge(int a,int b,int c,int d) { from=a,to=b,cap=c,flow=d; } }; struct Dinic{ int n,m,s,t; vector<Edge> edges; vector<int> G[maxn]; bool vis[maxn]; int d[maxn]; int cur[maxn]; void AddEdge(int from,int to,int cap) { edges.push_back(Edge(from,to,cap,0)); edges.push_back(Edge(to,from,0,0)); m=edges.size(); G[from].push_back(m-2); G[to].push_back(m-1); } void init(int x) { memset(d,0,sizeof(d)); edges.clear(); for(int i=0;i<=x;i++) G[i].clear(); } bool BFS() { memset(vis,0,sizeof(vis)); queue<int> Q; Q.push(s); d[s]=0; vis[s]=1; while(!Q.empty()) { int x=Q.front(); Q.pop(); for(int i=0;i<G[x].size();i++) { Edge &e = edges[G[x][i]]; if(!vis[e.to] && e.cap>e.flow) { vis[e.to]=1; d[e.to]=d[x]+1; Q.push(e.to); } } } return vis[t]; } int DFS(int x,int a) { if(x==t || a==0) return a; int flow = 0, f; for(int &i=cur[x];i<G[x].size();i++) { Edge &e=edges[G[x][i]]; if(d[x]+1==d[e.to] && (f=DFS(e.to,min(a,e.cap-e.flow)))>0) { e.flow += f; edges[G[x][i]^1].flow -= f; flow += f; a -= f; if(a==0) break; } } return flow; } int Maxflow(int s,int t) { this->s=s; this->t=t; int flow = 0; while(BFS()) { memset(cur,0,sizeof(cur)); flow+=DFS(s,INF); } return flow; } }; Dinic dinic; int n,m,d; char g1[25][25],g2[25][25]; inline int id_p(int x,int y) {return (x*m+y)*2;} inline int id_l(int x,int y) {return x*m+y+1000;} inline bool inside(int x,int y) {return x>=1 && x<=n && y>=1 && y<=m;} int s = 0, t = 1999; inline bool canout(int i,int j) { // cout<<i<<‘ ‘<<j<<endl; for(int x=i-d;x<=i+d;x++) for(int y=j-d;y<=j+d;y++) { if(abs(x-i)+abs(y-j)>d || (x==i && y==j)) continue; if(!inside(x,y)) return 1; } return 0; } void run() { scanf("%d%d",&n,&d); for(int i=1;i<=n;i++) scanf("%s",g1[i]+1); for(int i=1;i<=n;i++) scanf("%s",g2[i]+1); m=strlen(g1[1]+1); for(int i=1;i<=n;i++) for(int j=1;j<=m;j++) g1[i][j]-=‘0‘; dinic.init(t); int sum = 0; for(int i=1;i<=n;i++) for(int j=1;j<=m;j++) { if(g1[i][j]==0) continue; int u1 = id_p(i,j); int u2 = u1^1; dinic.AddEdge(u1,u2,g1[i][j]); for(int x=i-d;x<=i+d;x++) for(int y=j-d;y<=j+d;y++) { if(abs(x-i)+abs(y-j)>d || (x==i && y==j)) continue; if(!inside(x,y)) { dinic.AddEdge(u2,t,g1[i][j]); goto bk; } else { dinic.AddEdge(u2,id_p(x,y),g1[i][j]); } } bk:; } for(int i=1;i<=n;i++) for(int j=1;j<=m;j++) { if(g2[i][j]!=‘L‘) continue; if(g1[i][j]==0 && canout(i,j)) continue; sum++; dinic.AddEdge(s,id_l(i,j),1); dinic.AddEdge(id_l(i,j),id_p(i,j),1); } int ans = sum - dinic.Maxflow(s,t); printf("Case #%d: ",cas++); //cout<<sum<<‘ ‘; if(ans==0) puts("no lizard was left behind."); else if(ans==1) puts("1 lizard was left behind."); else printf("%d lizards were left behind.\n",ans); } int main() { #ifdef LOCAL freopen("case.txt","r",stdin); #endif int _; scanf("%d",&_); while(_--) run(); return 0; }