[BZOJ1061]-[Noi2008] Volunteer Recruitment - Simplex

say it up front

Learning simplex
makes me experience it personally: read it a hundred times, and see its meaning
~~inner mmp~~

topic

solution

I'm too lazy to write the solution... (If I do, it's probably a long discussion, and me is too lazy to write...)
This question, according
to . The standard form of linear programming can be directly simplex

However, this complexity is really metaphysical. A pivot operation is 1e7 level = =? ? ?
The total number of operations is still non-guaranteed (non-polynomial)~~Can you get a card if you want a card?~~
I don't understand it very well...I also ask the big guy to advise

Regarding duality, you can take a look at the
2016 training team paper "On Linear Programming and Duality Problems - Dong Kefan"

Regarding the fully unimodular matrix, you can take a look at these two articles by Candy (I didn't understand it, I gave up)
Portal 1
Portal 2

For simplex learning materials, you can take a look at
fjzzq's blog
hrwhisper's blog

The following is the code that comes with a large constant

#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std ;

int N , M ;
double a[10005][1005] , eps = 1e-8 ;

int dcmp( double x ){ return x < -eps ? -1 : x > eps ; }

void pivot( int r , int c ){ // r is Basis
    double tmp = - a[r][c] ; a[r][c] = -1 ;
    register int j ;
    for( j = 0 ; j <= N ; j ++ ) a[r][j] /= tmp ;
    for( int i = 0 ; i <= M ; i ++ ){
        if( dcmp( a[i][c] ) == 0 || i == r ) continue ;
        tmp = a[i][c] ; a[i][c] = 0 ;
        for( j = 0 ; j <= N ; j ++ )
            a[i][j] += tmp * a[r][j] ;
    }
}

void solve(){
    while( true ){
        int x = 0 , y = 0 ;
        double rem = 1e15 ;
        for( int i = 1 ; i <= N && !x ; i ++ )
            if( a[0][i] > eps ) x = i ;
        if( !x ) break ;
        for( int i = 1 ; i <= M ; i ++ )
            if( a[i][x] <-eps && rem > - a[i][0] / a[i][x] ) 
                rem = - a[i][0] / a[i][x] , y = i ;
        if( !y ) break ; // this will not happen
        pivot( y , x ) ;
    } printf( "%.0f" , a[0][0] ) ;
}

int main(){
    scanf( "%d%d" , &N , &M ) ;
    for( int i = 1 ; i <= N ; i ++ ) scanf( "%lf" , &a[0][i] ) ;
    for( int i = 1 ; i <= M ; i ++ ){
        int st , ed ;
        scanf( "%d%d%lf" , &st , &ed , &a[i][0] ) ;
        for( int j = st ; j <= ed ; j ++ ) a[i][j] = -1 ;
    } solve() ;
}