The three-c-linear method of solving the---ARC approximation

• Topic Links:

  Https://arc100.contest.atcoder.jp/tasks/arc100_a

• Analysis:

  In the game to do this problem to think of a blind way is to move the average up and down to take the minimum value, and then the big guy YJW Seniors said this is a strict monotone single-peak function of the direct three-way it's better, though I've heard it before, it's the first time.

• The three-way

  has a maximum function f (x) that defines the field as \ ([l,r]\) , we find two points within the defined field \ ( Lmid,rmid (Lmid<rmid) \)

  • If \ (f (lmid) <f (rmid) \) , or span class= "Math inline" >\ (lmid\) and \ (rmid\) are all on the left of a single peak, or \ (lmid\) on the left, \ (rmid\) on the right, but no matter what \ (lmid\) is on the left of a single peak, so \ (l=lmid\)

  • If \ (f (lmid) <f (rmid) \) , the analysis is similar, \ (r=rmid\)

  • If \ (f (lmid) ==f (rmid) \) emmm This actually I do not know how to deal with, casually according to the above one situation but always feel not very stable

• Code:

#include <iostream> #include <cstdio> #include <cstdlib> #include <cstring> #include <cctype > #include <map> #include <queue> #include <algorithm> #define RI Register int #define LL long longusing namespace Std;const int maxn=200005;const int inf=0x7fffffff;template <class t>inline void Read (T &x)    {X=0;int Ne=0;char C;    while (!isdigit (C=getchar ())) ne=c== '-';    x=c-48;    while (IsDigit (C=getchar ())) x= (x<<3) + (x<<1) +c-48;    x=ne?-x:x; return;}    int N;ll a[maxn];ll sum=0;inline ll solve (int k) {ll cnt=0;    For (RI i=1;i<=n;i++) cnt+=abs (a[i]-k); return CNT;}    int main () {read (n);       For (Ri i=1;i<=n;i++) {read (a[i]);    A[i]=a[i]-i;    } ll Ans,lmid,rmid;    ll L=-1e9,r=1e9;            while (l<r-1) {lmid= (l+r) >>1,rmid= (lmid+r) >>1;        if (Solve (LMID) >solve (rmid)) L=lmid;    else R=rmid;    } if (Solve (L) <solve (R)) Ans=l;    else ans=r; printf ("%lld\n", Solve (ans));   return 0;} 

ARC C-linear Approximation---Three-part method