1. 819B Mister B and PR Shifts
大意: 给定排列$p$, 定义排列$p$的特征值为$\sum |p_i-i|$, 可以循环右移任意位, 求最小特征值和对应移动次数.
右移过程中维护增加的个数和减少的个数即可.
#include <iostream> #include <sstream> #include <algorithm> #include <cstdio> #include <cmath> #include <set> #include <map> #include <queue> #include <string> #include <cstring> #include <bitset> #include <functional> #include <random> #define REP(i,a,n) for(int i=a;i<=n;++i) #define PER(i,a,n) for(int i=n;i>=a;--i) #define hr putchar(10) #define pb push_back #define lc (o<<1) #define rc (lc|1) #define mid ((l+r)>>1) #define ls lc,l,mid #define rs rc,mid+1,r #define x first #define y second #define io std::ios::sync_with_stdio(false) #define endl '\n' #define DB(a) ({REP(__i,1,n) cout<<a[__i]<<',';hr;}) using namespace std; typedef long long ll; typedef pair<int,int> pii; const int P = 1e9+7, INF = 0x3f3f3f3f; ll gcd(ll a,ll b) {return b?gcd(b,a%b):a;} ll qpow(ll a,ll n) {ll r=1%P;for (a%=P;n;a=a*a%P,n>>=1)if(n&1)r=r*a%P;return r;} ll inv(ll x){return x<=1?1:inv(P%x)*(P-P/x)%P;} inline int rd() {int x=0;char p=getchar();while(p<'0'||p>'9')p=getchar();while(p>='0'&&p<='9')x=x*10+p-'0',p=getchar();return x;} //head const int N = 1e6+50; int n, a[N]; int dl[N], dr[N]; int main() { scanf("%d",&n); REP(i,1,n) scanf("%d",a+i); ll ret = 0, ans = 0; int L = 0, R = 0; REP(i,1,n) { ret += abs(a[i]-i); if (a[i]>i) { ++L; --dl[a[i]-i]; ++dr[a[i]-i]; } else if (a[i]<=i) { ++R; if (a[i]!=1) { --dl[n-i+a[i]]; ++dr[n-i+a[i]]; } } } ans = ret; int pos = 0; REP(i,1,n-1) { ret += R-L; R += dr[i]; L += dl[i]; if (a[n-i+1]!=1) --R,++L; ret -= abs(a[n-i+1]-n-1); ret += abs(a[n-i+1]-1); if (ret<ans) pos = i, ans = ret; } printf("%lld %d\n", ans, pos); }