【UOJ #179】线性规划 单纯形模板

http://uoj.ac/problem/179

终于写出来了单纯性算法的板子，抄的网上大爷的qwq

辅助线性规划找非基变量时要加个随机化才能A，我也不知道为什么，卡精度吗？

2017-3-6UPD：问了网上的大爷，知道是防止被卡时间（因为单纯形的复杂度是指数级的）。

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

const int N = 23;
const double eps = 1e-8;

double a

, ans
;
int n, m, t, id[N << 1];

void pivot(int l, int e) {
swap(id[e], id[n + l]);
double r = a[l][e]; a[l][e] = 1;
for (int j = 0; j <= n; ++j)
a[l][j] /= r;
for (int i = 0; i <= m; ++i)
if (i != l) {
r = a[i][e]; a[i][e] = 0;
for (int j = 0; j <= n; ++j)
a[i][j] -= r * a[l][j];
}
}

int main() {
scanf("%d%d%d", &n, &m, &t);
int i, j, l, e; double k, kk;
for (j = 1; j <= n; ++j) scanf("%lf", &a[0][j]), id[j] = j;
for (i = 1; i <= m; ++i) {
for (j = 1; j <= n; ++j)
scanf("%lf", &a[i][j]);
scanf("%lf", &a[i][0]);
}

while (true) {
l = e = 0; k = -eps;
for (i = 1; i <= m; ++i)
if (a[i][0] < k) {
k = a[i][0];
l = i;
}
if (!l) break;
k = -eps;
for (j = 1; j <= n; ++j)
if (a[l][j] < k && (!e || (rand() & 1))) {
k = a[l][j];
e = j;
}
if (!e) {puts("Infeasible"); return 0;}
pivot(l, e);
}

while (true) {
for (j = 1; j <= n; ++j)
if (a[0][j] > eps)
break;
if ((e = j) > n) break;
k = 1e18; l = 0;
for (i = 1; i <= m; ++i)
if (a[i][e] > eps && (kk = (a[i][0] / a[i][e])) < k) {
k = kk;
l = i;
}
if (!l) {puts("Unbounded"); return 0;}
pivot(l, e);
}

printf("%.10lf\n", -a[0][0]);
if (!t) return 0;
for (i = 1; i <= m; ++i) ans[id[n + i]] = a[i][0];
for (i = 1; i <= n; ++i) printf("%.10lf ", ans[i]);
return 0;
}