【题目链接】
http://www.lydsy.com/JudgeOnline/problem.php?id=1061
【题意】
雇人满足每天至少需要的人数。
【思路一】
Byvoid的题解 click here
任意一个变量在两个方程组中且一正一负，根据流量守恒的原理构图。正变量看作流入量，负变量看作流出量，正负常数看作与源汇点的流量。
【代码】
1 #include<set> 2 #include<cmath> 3 #include<queue> 4 #include<vector> 5 #include<cstdio> 6 #include<cstring> 7 #include<iostream> 8 #include<algorithm> 9 #define trav(u,i) for(int i=front[u];i;i=e[i].nxt) 10 #define FOR(a,b,c) for(int a=(b);a<=(c);a++) 11 using namespace std; 12 13 typedef long long ll; 14 const int N = 2e3+10; 15 const int inf = 1e9; 16 17 ll read() { 18 char c=getchar(); 19 ll f=1,x=0; 20 while(!isdigit(c)) { 21 if(c=='-') f=-1; c=getchar(); 22 } 23 while(isdigit(c)) 24 x=x*10+c-'0',c=getchar(); 25 return x*f; 26 } 27 28 struct Edge { 29 int u,v,cap,flow,cost; 30 }; 31 struct MCMF { 32 int n,m,s,t; 33 int a[N],p[N],inq[N],d[N]; 34 vector<Edge> es; 35 vector<int> g[N]; 36 queue<int> q; 37 void init(int n) { 38 this->n=n; 39 es.clear(); 40 FOR(i,0,n) g[i].clear(); 41 } 42 void AddEdge(int u,int v,int w,int c) { 43 es.push_back((Edge){u,v,w,0,c}); 44 es.push_back((Edge){v,u,0,0,-c}); 45 int m=es.size(); 46 g[u].push_back(m-2); 47 g[v].push_back(m-1); 48 } 49 int spfa(int s,int t,int& flow,int& cost) { 50 memset(inq,0,sizeof(inq)); 51 FOR(i,0,n) d[i]=inf; 52 inq[s]=1; d[s]=0; a[s]=inf; p[s]=0; 53 q.push(s); 54 while(!q.empty()) { 55 int u=q.front(); q.pop(); inq[u]=0; 56 FOR(i,0,(int)g[u].size()-1) { 57 Edge& e=es[g[u][i]]; 58 int v=e.v; 59 if(d[v]>d[u]+e.cost && e.cap>e.flow) { 60 d[v]=d[u]+e.cost; 61 a[v]=min(a[u],e.cap-e.flow); 62 p[v]=g[u][i]; 63 if(!inq[v]) 64 inq[v]=1,q.push(v); 65 } 66 } 67 } 68 if(d[t]==inf) return 0; 69 flow+=a[t]; cost+=a[t]*d[t]; 70 for(int x=t;x!=s;x=es[p[x]].u) { 71 es[p[x]].flow+=a[t]; 72 es[p[x]^1].flow-=a[t]; 73 } 74 return 1; 75 } 76 void mcmf(int s,int t,int&flow,int&cost) { 77 flow=cost=0; 78 while(spfa(s,t,flow,cost)) ; 79 } 80 } mc; 81 82 int n,m,x[N]; 83 84 int main() 85 { 86 n=read(),m=read(); 87 mc.init(n+2); 88 int S=0,T=n+1; 89 mc.AddEdge(S,1,inf,0); 90 FOR(i,1,n) { 91 x[i]=read(); 92 mc.AddEdge(i,i+1,inf,0); 93 } 94 FOR(i,1,m) { 95 int l=read(),r=read(),c=read(); 96 mc.AddEdge(l,r+1,inf,c); 97 } 98 FOR(i,1,n+1) { 99 int c=x[i]-x[i-1]; 100 if(c>0) mc.AddEdge(S,i,c,0); 101 if(c<0) mc.AddEdge(i,T,-c,0); 102 } 103 int flow,cost; 104 mc.mcmf(S,T,flow,cost); 105 printf("%d",cost); 106 return 0; 107 }
【思路二】
一种比较神奇的构图方式 click here
【代码】
1 #include<set> 2 #include<cmath> 3 #include<queue> 4 #include<vector> 5 #include<cstdio> 6 #include<cstring> 7 #include<iostream> 8 #include<algorithm> 9 #define trav(u,i) for(int i=front[u];i;i=e[i].nxt) 10 #define FOR(a,b,c) for(int a=(b);a<=(c);a++) 11 using namespace std; 12 13 typedef long long ll; 14 const int N = 2e3+10; 15 const int inf = 1e9; 16 17 ll read() { 18 char c=getchar(); 19 ll f=1,x=0; 20 while(!isdigit(c)) { 21 if(c=='-') f=-1; c=getchar(); 22 } 23 while(isdigit(c)) 24 x=x*10+c-'0',c=getchar(); 25 return x*f; 26 } 27 28 struct Edge { 29 int u,v,cap,flow,cost; 30 }; 31 struct MCMF { 32 int n,m,s,t; 33 int a[N],p[N],inq[N],d[N]; 34 vector<Edge> es; 35 vector<int> g[N]; 36 queue<int> q; 37 void init(int n) { 38 this->n=n; 39 es.clear(); 40 FOR(i,0,n) g[i].clear(); 41 } 42 void AddEdge(int u,int v,int w,int c) { 43 es.push_back((Edge){u,v,w,0,c}); 44 es.push_back((Edge){v,u,0,0,-c}); 45 int m=es.size(); 46 g[u].push_back(m-2); 47 g[v].push_back(m-1); 48 } 49 int spfa(int s,int t,int& flow,int& cost) { 50 memset(inq,0,sizeof(inq)); 51 FOR(i,0,n) d[i]=inf; 52 inq[s]=1; d[s]=0; a[s]=inf; p[s]=0; 53 q.push(s); 54 while(!q.empty()) { 55 int u=q.front(); q.pop(); inq[u]=0; 56 FOR(i,0,(int)g[u].size()-1) { 57 Edge& e=es[g[u][i]]; 58 int v=e.v; 59 if(d[v]>d[u]+e.cost && e.cap>e.flow) { 60 d[v]=d[u]+e.cost; 61 a[v]=min(a[u],e.cap-e.flow); 62 p[v]=g[u][i]; 63 if(!inq[v]) 64 inq[v]=1,q.push(v); 65 } 66 } 67 } 68 if(d[t]==inf) return 0; 69 flow+=a[t]; cost+=a[t]*d[t]; 70 for(int x=t;x!=s;x=es[p[x]].u) { 71 es[p[x]].flow+=a[t]; 72 es[p[x]^1].flow-=a[t]; 73 } 74 return 1; 75 } 76 void mcmf(int s,int t,int&flow,int&cost) { 77 flow=cost=0; 78 while(spfa(s,t,flow,cost)) ; 79 } 80 } mc; 81 82 int n,m; 83 84 int main() 85 { 86 n=read(),m=read(); 87 mc.init(n+2); 88 int S=0,T=n+1; 89 mc.AddEdge(S,1,inf,0); 90 FOR(i,1,n) { 91 int c=read(); 92 mc.AddEdge(i,i+1,inf-c,0); 93 } 94 FOR(i,1,m) { 95 int l=read(),r=read(),c=read(); 96 mc.AddEdge(l,r+1,inf,c); 97 } 98 int flow,cost; 99 mc.mcmf(S,T,flow,cost); 100 printf("%d",cost); 101 return 0; 102 }