SGU 520 Fire in the Country(博弈+搜索)
Description
To save the country, a small fire robot was left on its territory. He managed to extinguish fire in all cities except the capital before running out of liquid. The robot can't extinguish fire anymore, so the country is still in danger at the moment.
There are n cities in the country connected by m two-way roads. Each road connects a pair of cities. There is at most one road between any pair of cities. The cities are numbered from 1 to n, with capital having the number 1.
The fire spreads very quickly. On the very first day only the capital is on fire. But with every subsequent day, the fire devours all the cities connected by a road with the cities that are already on fire. Once the fire gets to a certain city, this city will continue to stay on fire till the very end.
The robot can't extinguish the fire anymore and there are no other means of firefighting left in the country, so obviously the country is going to be burned down to the ground. And you don't have to be a hero and save it. The key thing is that the robot is going to be destroyed by fire as well, and you need to figure out who will actually pay for the loss of government property.
Two pilots, Nikolay and Vladimir, are on Earth's natural satellite. They alternately take turns controlling the robot. The pilots alternate each day. Robot's speed is equal to the speed of fire, so the robot can get to the neighboring city in a day. Each pilot does not want the robot to be destroyed on his turn. For such a valuable loss they will have to pay a huge fee to the government.
On the first day the robot is located in the capital. Nikolay controls the robot on the first day. Thus, Nikolay controls the robot on the days with odd numbers, and Vladimir controls it on the days with even numbers. Taking turn, a pilot has to move the robot from the current city to any city connected by a road with the current one. If a pilot moves the robot to a city which is on fire, the robot is destroyed.
You task is to figure out who will pay the fine for the destroyed robot, assuming both pilots act optimally.
Input
Output
Nikolay
" — if it is Nikolay, "
Vladimir
" — if it is Vladimir).
#include <cstdio>
#include <cstring>
#include <queue>
using namespace std; const int MAXN = ;
const int MAXE = ; int n, m, f, ecnt;
int head[MAXN], dis[MAXN];
int to[MAXE], next[MAXE]; void add_edge(int u, int v) {
to[ecnt] = v; next[ecnt] = head[u]; head[u] = ecnt++;
to[ecnt] = u; next[ecnt] = head[v]; head[v] = ecnt++;
} void bfs() {
queue<int> que; que.push();
dis[] = ;
while(!que.empty()) {
int u = que.front(); que.pop();
for(int p = head[u]; p; p = next[p]) {
int &v = to[p];
if(!dis[v]) {
dis[v] = dis[u] + ;
que.push(v);
}
}
}
} int win[MAXN]; int dfs(int u) {
if(win[u] != -) return win[u];
for(int p = head[u]; p; p = next[p]) {
int &v = to[p];
if(dis[v] == dis[u] + ) {
if(dis[u] & ) {if(dfs(v)) return win[u] = ;}
else if(!dfs(v)) return win[u] = ;
}
}
return win[u] = !(dis[u] & );
} int main() {
scanf("%d%d", &n, &m);
ecnt = ;
while(m--) {
int u, v;
scanf("%d%d", &u, &v);
add_edge(u, v);
}
bfs();
memset(win, -, sizeof(win));
if(dfs()) puts("Vladimir");
else puts("Nikolay");
}
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