Weakness and Poorness"/>
codeforces578C. Weakness and Poorness
time limit per test 2 seconds memory limit per test 256 megabytes input standard input output standard outputYou 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.
InputThe 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).
OutputOutput 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.
Sample test(s) input3 1 2 3output
1.000000000000000input
4 1 2 3 4output
2.000000000000000input
10 1 10 2 9 3 8 4 7 5 6output
4.500000000000000Note
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.
这题可以用三分,但是在三分判断条件的时候要注意,用循环限定次数比较好,因为double精度不够高。
#include<iostream>
#include<stdio.h>
#include<stdlib.h>
#include<string.h>
#include<math.h>
#include<vector>
#include<map>
#include<set>
#include<queue>
#include<stack>
#include<string>
#include<algorithm>
using namespace std;
#define ll long long
#define inf 99999999
#define maxn 200060
#define eps 1e-10
int n;
double a[maxn],b[maxn],sum1[maxn],sum2[maxn],c[maxn]; double cal(double x)
{ int i,j,f; double maxnum=0; sum1[0]=sum2[0]=0; for(i=1;i<=n;i++){ b[i]=a[i]-x; sum1[i]=max(b[i],sum1[i-1]+b[i]);maxnum=max(maxnum,sum1[i]); c[i]=x-a[i]; sum2[i]=max(c[i],sum2[i-1]+c[i]);maxnum=max(maxnum,sum2[i]); } return maxnum; } int main()
{ int m,i,j; double l,r,m1,m2,minx,maxx; while(scanf("%d",&n)!=EOF) { for(i=1;i<=n;i++){ scanf("%lf",&a[i]); } l=-10005;r=10005; for(i=0;i<100;i++){ double d=(l+r)/2.0;m1=d;m2=(d+r)/2.0;if(cal(m2)-cal(m1)>=0){ r=m2; } else l=m1; } printf("%.9f\n",cal(l)); } return 0;
}
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codeforces578C. Weakness and Poorness
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