int main(){
scanf("%d",&n);
for(int i=1;i<=n;i++)
scanf("%d",&p[i]);
print_cut(p,n);
for(int i=0;i<=n;i++)
memo[i] = MIN;
print_bottom_cut(p,n);
printf("%d\n",memo[n]);
return 0;
}
/***********************************************************************\
** If it has been decided that the incumbent solution should change,
** several values must be updated, including the incumbent X, the
** incumbent cut, the estimate at the incumbent and the standard
** deviation of the estimate, as well as the last_update counter.
** This function performs these updates. It assumes that the candidate
** solution becomes the incumbent solution, with a height corresponding
** to the _est_ parameter.
\***********************************************************************/
void new_incumbent(prob_type *p, cell_type *c, soln_type *s, double est)
{
vector X;
double val, stdev;
int obs, idx;
int count;
i_type i;
#ifdef TRACE
printf("Inside new_incumbent\n");
#endif
/* Copy over information about the new incumbent */
copy_arr(s->incumb_x, s->candid_x, p->num->mast_cols)
s->incumb_cut = c->cuts->cnt - 1;
s->incumb_est = est;
s->last_update = c->k;
s->incumb_k = c->k;
/*
** The cut consists of an average of many pi X omega products. We
** use the mean and standard deviation of this collection of products
** in the check for optimality, so they are updated here. We loop
** through the istar indices of new incumbent cut to find the stdev.
*/
count = 0;
stdev = 0.0;
X = s->incumb_x;
if (c->cuts->cnt > 0)
{
for (obs = 0; obs < c->cuts->val[s->incumb_cut]->omega_cnt; obs++)
if (valid_omega_idx(s->omega, obs))
{
/* Find the pi from the cut's argmax for this observation */
i.sigma = c->cuts->val[s->incumb_cut]->istar[obs];
i.delta = c->sigma->lamb[i.sigma];
/*
** Couldn't this be done only in the optimality check, so we
** don't do it every time we change our minds about the incumbent ?
** Which happens more often -- an optimality check or a change of
** the incumbent x?
** What about when the the incumbent cut is updated, but X is not?
*/
/* Calculate the height for this observation and dual vector */
val = c->sigma->val[i.sigma].R + s->delta->val[i.delta][obs].R;
for (idx = 0; idx < p->num->nz_cols; idx++)
val -= c->sigma->val[i.sigma].T[idx]
* X[c->sigma->col[idx]];
for (idx = 0; idx < p->num->rv_cols; idx++)
val -= s->delta->val[i.delta][obs].T[idx]
* X[s->delta->col[idx]];
stdev += s->omega->weight[obs] * SQR(s->incumb_est - val);
count += s->omega->weight[obs];
}
s->incumb_stdev = sqrt(stdev / (double) count);
}
s->incumbent_change = TRUE;
#ifdef DEBUG
printf("\nMade a new incumbent, since it qualified");
print_cut(c->cuts, p->num, s->incumb_cut);
#endif
}
