线性规划：
#include<cstdio>
#include<cstdlib>
#include<algorithm>
#include<cstring>
#include<vector>
#include<queue>
#define rint register int
#define ll long long
#define MAXN 1000+10
#define pb push_back
#define INF 0x7f7f7f7f
#define oo 0x7f7f7f7f7f7f7f7f
#define pil pair<int,ll>
#define mp make_pair
using namespace std;
int read(){
int x=,f=;char ch=getchar();
while(ch<''||ch>''){if('-'==ch)f=-;ch=getchar();}
while(ch>=''&&ch<=''){x=x*+ch-'';ch=getchar();}
return x*f;
}
struct E{
int from,to,cap,flow;
ll cost;
E(int x=,int y=,int c=,int f=,ll w=0LL){
from=x,to=y,cap=c,flow=f,cost=w;
}
};
struct Dinic{
int n,m,s,t;
vector<E> es;
vector<int> G[MAXN];
void init(int n,int s,int t){
this->n=n;
this->s=s,this->t=t;
es.clear();
for(int i=;i<=n;i++)G[i].clear();
}
void add(int x,int y,int cap,ll cost){
es.pb(E(x,y,cap,,cost));
es.pb(E(y,x,,,-cost));
m=es.size();
G[x].pb(m-),G[y].pb(m-);
}
int p[MAXN],a[MAXN];
ll d[MAXN];
int b[MAXN];
bool SPFA(int &flow,ll &cost){
p[s]=,a[s]=INF;
memset(d,0x7f,sizeof(d));
d[s]=;
memset(b,,sizeof(b));
b[s]=;
queue<int> q;
q.push(s);
while(!q.empty()){
int x=q.front();q.pop();b[x]=;
for(rint i=;i<G[x].size();i++){
E &e=es[G[x][i]];
if(e.cap>e.flow&&d[e.to]>d[x]+e.cost){
p[e.to]=G[x][i];
a[e.to]=min(a[x],e.cap-e.flow);
d[e.to]=d[x]+e.cost;
if(!b[e.to]){
b[e.to]=;
q.push(e.to);
}
}
}
}
if(oo==d[t]){
return ;
}
flow+=a[t];
cost+=a[t]*d[t];
for(rint i=t;i!=s;i=es[p[i]].from){
es[p[i]].flow+=a[t];
es[p[i]^].flow-=a[t];
}
return ;
}
pil MaxfMinc(){
int flow=;
ll cost=0LL;
while(SPFA(flow,cost));
return mp(flow,cost);
}
}D;
int n,m,s=,t=MAXN-;
int a[MAXN];
void init(){
D.init(t,s,t);
n=read(),m=read();
for(rint i=;i<=n;i++){
a[i]=read();
}
int x,y,z;
for(rint i=;i<=m;i++){
x=read(),y=read(),z=read();
D.add(x,y+,INF,1LL*z);
}
for(rint i=;i<=n+;i++){
x=a[i]-a[i-];
if(x>)D.add(s,i,x,0LL);
else D.add(i,t,-x,0LL);
if(i>)D.add(i,i-,INF,0LL);
}
}
int main()
{
init();
printf("%lld\n",D.MaxfMinc().second);
return ;
}
转化为最小费用最大流
#include<cstdio>
#include<cstdlib>
#include<algorithm>
#include<cstring>
#include<vector>
#include<queue>
#define rint register int
#define ll long long
#define MAXN 1000+10
#define pb push_back
#define INF 0x7f7f7f7f
#define oo 0x7f7f7f7f7f7f7f7f
#define pil pair<int,ll>
#define mp make_pair
using namespace std;
int read(){
int x=,f=;char ch=getchar();
while(ch<''||ch>''){if('-'==ch)f=-;ch=getchar();}
while(ch>=''&&ch<=''){x=x*+ch-'';ch=getchar();}
return x*f;
}
struct E{
int from,to,cap,flow;
ll cost;
E(int x=,int y=,int c=,int f=,ll w=0LL){
from=x,to=y,cap=c,flow=f,cost=w;
}
};
struct Dinic{
int n,m,s,t;
vector<E> es;
vector<int> G[MAXN];
void init(int n,int s,int t){
this->n=n;
this->s=s,this->t=t;
es.clear();
for(int i=;i<=n;i++)G[i].clear();
}
void add(int x,int y,int cap,ll cost){
es.pb(E(x,y,cap,,cost));
es.pb(E(y,x,,,-cost));
m=es.size();
G[x].pb(m-),G[y].pb(m-);
}
int p[MAXN],a[MAXN];
ll d[MAXN];
int b[MAXN];
bool SPFA(int &flow,ll &cost){
p[s]=,a[s]=INF;
memset(d,0x7f,sizeof(d));
d[s]=;
memset(b,,sizeof(b));
b[s]=;
queue<int> q;
q.push(s);
while(!q.empty()){
int x=q.front();q.pop();b[x]=;
for(rint i=;i<G[x].size();i++){
E &e=es[G[x][i]];
if(e.cap>e.flow&&d[e.to]>d[x]+e.cost){
p[e.to]=G[x][i];
a[e.to]=min(a[x],e.cap-e.flow);
d[e.to]=d[x]+e.cost;
if(!b[e.to]){
b[e.to]=;
q.push(e.to);
}
}
}
}
if(oo==d[t]){
return ;
}
flow+=a[t];
cost+=a[t]*d[t];
for(rint i=t;i!=s;i=es[p[i]].from){
es[p[i]].flow+=a[t];
es[p[i]^].flow-=a[t];
}
return ;
}
pil MaxfMinc(){
int flow=;
ll cost=0LL;
while(SPFA(flow,cost));
return mp(flow,cost);
}
}D;
int n,m,s=,t=MAXN-;
int main()
{
D.init(t,s,t);
int k;
n=read(),m=read();
for(rint i=;i<=n;i++){
k=read();
D.add(i,i+,INF-k,0LL);
}
D.add(s,,INF,0LL);
D.add(n+,t,INF,0LL);
int x,y;
for(rint i=;i<=m;i++){
x=read(),y=read(),k=read();
D.add(x,y+,INF,1LL*k);
}
printf("%lld\n",D.MaxfMinc().second);
return ;
}