ternary|Codeforces Round #320 (Div. 2) [Bayan Thanks-Round]


E. Weakness and Poorness time limit per test 2 seconds memory limit per test 256 megabytes input standard input output standard output You are given a sequence of n integers a1,?a2,?...,?an.
Determine a real number x such that the weakness of the sequence a1?-?x,?a2?-?x,?...,?an?-?x is as small as possible.
The weakness of a sequence is defined as the maximum value of the poorness over all segments (contiguous subsequences) of a sequence.
The poorness of a segment is defined as the absolute value of sum of the elements of segment.
Input The first line contains one integer n (1?≤?n?≤?200?000), the length of a sequence.
The second line contains n integers a1,?a2,?...,?an (|ai|?≤?10?000).
Output Output a real number denoting the minimum possible weakness of a1?-?x,?a2?-?x,?...,?an?-?x. Your answer will be considered correct if its relative or absolute error doesn't exceed 10?-?6.
Examples input

3 1 2 3

output
1.000000000000000

input
4 1 2 3 4

output
2.000000000000000

input
10 1 10 2 9 3 8 4 7 5 6

output
4.500000000000000

Note For the first case, the optimal value of x is 2 so the sequence becomes ?-?1, 0, 1 and the max poorness occurs at the segment "-1" or segment "1". The poorness value (answer) equals to 1 in this case.
For the second sample the optimal value of x is 2.5 so the sequence becomes ?-?1.5,??-?0.5,?0.5,?1.5 and the max poorness occurs on segment "-1.5 -0.5" or "0.5 1.5". The poorness value (answer) equals to 2 in this case.


三分查找:如果遇到凸性或凹形函数时,可以用三分查找求那个凸点或凹点。

【ternary|Codeforces Round #320 (Div. 2) [Bayan Thanks-Round]】
#include using namespace std; #define rep(i,a,n) for(int i=a; i=a; --i) #define mem(a,t) memset(a,t,sizeof(a)) #define pb push_back #define mp make_pair #define sz(a) (int)a.size() #define fi first #define se second typedef long long LL; #define N 200005 int a[N]; int n; const double eps=1e-12; double fun(double x) { double tmp=0,ans=0,tmin=0,tmax=0; rep(i,0,n){ tmp+=(a[i]-x); ans=max(ans,fabs(tmp-tmin)); ans=max(ans,fabs(tmp-tmax)); tmin=min(tmin,tmp); tmax=max(tmax,tmp); } return ans; } int main() { //freopen("in.txt","r",stdin); double l,r; scanf("%d",&n); l=1e7; r=-1e7; rep(i,0,n){ scanf("%d",&a[i]); l=min(l,1.*a[i]); r=max(r,1.*a[i]); } double f1,f2,mid1,mid2; rep(i,0,500){ mid1=l+(r-l)/3; mid2=r-(r-l)/3; f1=fun(mid1); f2=fun(mid2); if(f1










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