卧薪尝胆,厚积薄发。
千钧一发
Date: Mon Jan 28 20:33:11 CST 2019 In Category: NoCategory

Description:

$n$ 个物品,选出一些获得他们的价值,如果两个的特征值平方加起来是平方数并且它们互质那就不能同时选,求最大价值。
$1\leqslant n\leqslant 1000$

Solution:

如果把不能同时选的连边,那么两个奇数一定不满足第一个条件,偶数一定不满足第二个条件,因此是一个二分图,于是可以这些点分别往源汇连对应价值的边,然后不能同时选的连 $\inf$ 的边,然后求最小割就行了。

Code:


#include<algorithm>
#include<iostream>
#include<cstdlib>
#include<cstdio>
#include<cmath>
#include<queue>
#include<cctype>
#include<cstring>
using namespace std;
int n;
#define MAXN 1010
int a[MAXN],b[MAXN];
struct edge
{
int to,nxt,f;
}e[(MAXN * 2 + MAXN * MAXN) * 2];
int edgenum = 0;
#define MAXP (MAXN * 2)
int lin[MAXP] = {0};
void add(int a,int b,int f)
{
e[edgenum] = (edge){b,lin[a],f};lin[a] = edgenum++;
e[edgenum] = (edge){a,lin[b],0};lin[b] = edgenum++;
return;
}
int ch[MAXP];
int s,t;
bool BFS()
{
queue<int> q;q.push(s);
memset(ch,-1,sizeof(ch));ch[s] = 0;
while(!q.empty())
{
int k = q.front();q.pop();
for(int i = lin[k];i != -1;i = e[i].nxt)
{
if(ch[e[i].to] == -1 && e[i].f)
{
ch[e[i].to] = ch[k] + 1;
q.push(e[i].to);
}
}
}
return (ch[t] != -1);
}
int flow(int k,int f)
{
if(k == t)return f;
int r = 0;
for(int i = lin[k];i != -1 && f > r;i = e[i].nxt)
{
if(ch[e[i].to] == ch[k] + 1 && e[i].f)
{
int l = flow(e[i].to,min(e[i].f,f - r));
e[i].f -= l;r += l;e[i ^ 1].f += l;
}
}
if(r == 0)ch[k] = -1;
return r;
}
#define INF 0x3f3f3f3f
int dinic()
{
int ans = 0,r;
while(BFS())while(r = flow(s,INF))ans += r;
return ans;
}
int gcd(int a,int b){return (b == 0 ? a : gcd(b,a % b));}
bool check1(int a,int b)
{
long long s = 1ll * a * a + 1ll * b * b;
long long k = sqrt(s);
if(k * k == s)return true;
else return false;
}
bool check2(int a,int b)
{
return (gcd(a,b) == 1);
}
int main()
{freopen("t.in","r",stdin);
scanf("%d",&n);
for(int i = 1;i <= n;++i)scanf("%d",&a[i]);
for(int i = 1;i <= n;++i)scanf("%d",&b[i]);
s = n + 1;t = s + 1;
memset(lin,-1,sizeof(lin));
int sum = 0;
for(int i = 1;i <= n;++i)
{
if(a[i] & 1)add(s,i,b[i]);
else add(i,t,b[i]);
sum += b[i];
}
for(int i = 1;i <= n;++i)if((a[i] & 1) == 1)
for(int j = 1;j <= n;++j)if((a[j] & 1) == 0)
if(check1(a[i],a[j]) && check2(a[i],a[j]))add(i,j,INF);
cout << sum - dinic() << endl;
return 0;
}
In tag: 图论-dinic
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