Tag: 最小路径覆盖

题目传送门：http://cojs.tk/cogs/problem/problem.php?pid=396

这题，大家都说贪心可以过QAQ
但我总觉得贪心有问题…
贪心那块，不会证明小于a且a+b为完全平方数的数至多存在一个解
于是还是最小路径覆盖比较靠谱吧！

#include<bits/stdc++.h>
#define LL long long
using namespace std;

const int N = 100000;
const int INF = 10000000;

int head[N],to[N],nxt[N],flow[N],dis[N],cur[N]; 
int n,m,S,T; queue<int> que;

inline int read(){
	char c=getchar(); int ret=0,f=1;
	while (c<'0'||c>'9') {if(c=='-')f=-1;c=getchar();}
	while (c<='9'&&c>='0') {ret=ret*10+c-'0';c=getchar();}
	return ret*f;
}

#define id(x,ty) ((x)*2+ty)
inline int Add_Edge(int u, int v, int f) {
	static int TT = 1;
	to[++TT] = v; nxt[TT] = head[u]; head[u] = TT; flow[TT] = 1;
	to[++TT] = u; nxt[TT] = head[v]; head[v] = TT; flow[TT] = 0;
	return TT - 1;
}

inline bool BFS(){
	memset(dis,-1,sizeof(dis));
	que.push(S); dis[S] = 0;
	while (!que.empty()) {
		int w = que.front(); que.pop();
		for (int i=head[w];i;i=nxt[i]) if (flow[i] && !~dis[to[i]]) 
			dis[to[i]]  = dis[w] + 1, que.push(to[i]);
	} return ~dis[T];
}

inline int DFS(int w, int f) {
	if (w == T) return f;
	else {
		int ret = 0;
		for (int &i=head[w];i;i=nxt[i]) if (flow[i] && dis[to[i]] == dis[w] + 1) {
			int tmp = DFS(to[i], min(f, flow[i]));
			flow[i] -= tmp; flow[i^1] += tmp; ret += tmp; f -= tmp;
			if (!f) break;
		} return ret;
	}
}	

inline int Dinic(){
	int ret = 0;
	while (BFS()) {
		memcpy(cur,head,sizeof(head));
		ret += DFS(S,INF);
	} return ret;
}

int main(){
	freopen("balla.in","r",stdin);
	freopen("balla.out","w",stdout);
	n = read(); S = 0; T = 1; 
	for (int i=1,w=0;i<=1600;i++) {
		Add_Edge(S,id(i,0),1); Add_Edge(id(i,1),T,1);
		for (int j=i-1;j;j--) if (i + j == (int)sqrt(i+j)*(int)sqrt(i+j)) Add_Edge(id(i,0),id(j,1),1);
		w += Dinic(); if (i - w > n) cout<<i-1, exit(0);
	}
	return 0;
}