CF1180 B. Nick and Array
题目传送门:https://codeforces.com/problemset/problem/1180/B
题目大意:
给定一串长度为\(n\)的序列\(A\),每次操作可以任选一个数\(i(1\leqslant i\leqslant n)\),使得\(A_i=-A_i-1\),求在进行若干次操作后,使\(\prod\limits_{i=1}^nA_i\)最大的序列\(A\)
如果\(A_i\geqslant0\),则有\(|-A_i-1|>|A_i|\),故我们可以将所有的非负整数\(A_i\)都改为\(-A_i-1\)
若\(n\)为奇数,则我们需要再将一个负整数\(A_i\)改为\(-A_i-1\)
记\(S=\prod\limits_{i=1}^n|A_i|\),而对负整数的操作,会使得\(|A_i|\)变为\(|A_i|-1\),若我们对\(A_k\)进行操作,则会使\(S=S-\frac{S}{|A_k|}=S(\frac{|A_k|-1}{|A_k|})\),故我们找到最大的\(|A_k|\)进行操作即可
/*program from Wolfycz*/
#include<map>
#include<cmath>
#include<cstdio>
#include<vector>
#include<cstring>
#include<iostream>
#include<algorithm>
#define Fi first
#define Se second
#define ll_inf 1e18
#define MK make_pair
#define sqr(x) ((x)*(x))
#define pii pair<int,int>
#define int_inf 0x7f7f7f7f
using namespace std;
typedef long long ll;
typedef unsigned int ui;
typedef unsigned long long ull;
inline char gc(){
static char buf[1000000],*p1=buf,*p2=buf;
return p1==p2&&(p2=(p1=buf)+fread(buf,1,1000000,stdin),p1==p2)?EOF:*p1++;
}
template<typename T>inline T frd(T x){
int f=1; char ch=gc();
for (;ch<'0'||ch>'9';ch=gc()) if (ch=='-') f=-1;
for (;ch>='0'&&ch<='9';ch=gc()) x=(x<<1)+(x<<3)+ch-'0';
return x*f;
}
template<typename T>inline T read(T x){
int f=1; char ch=getchar();
for (;ch<'0'||ch>'9';ch=getchar()) if (ch=='-') f=-1;
for (;ch>='0'&&ch<='9';ch=getchar()) x=(x<<1)+(x<<3)+ch-'0';
return x*f;
}
inline void print(int x){
if (x<0) putchar('-'),x=-x;
if (x>9) print(x/10);
putchar(x%10+'0');
}
const int N=1e5;
int A[N+10];
int main(){
// freopen(".in","r",stdin);
// freopen(".out","w",stdout);
int n=read(0),Max=0,ID=0;
for (int i=1;i<=n;i++){
A[i]=read(0);
if (A[i]>=0) A[i]=-A[i]-1;
if (Max<abs(A[i])) Max=abs(A[i]),ID=i;
}
if (n&1) A[ID]=-A[ID]-1;
for (int i=1;i<=n;i++) printf("%d%c",A[i],i==n?'\n':' ');
return 0;
}