B. Approximating a Constant Range
Time Limit: 20 Sec
Memory Limit: 256 MB
题目连接
http://codeforces.com/contest/602/problem/B
Description
When Xellos was doing a practice course in university, he once had to measure the intensity of an effect that slowly approached equilibrium. A good way to determine the equilibrium intensity would be choosing a sufficiently large number of consecutive data points that seems as constant as possible and taking their average. Of course, with the usual sizes of data, it's nothing challenging — but why not make a similar programming contest problem while we're at it?
You're given a sequence of n data points a1, ..., an. There aren't any big jumps between consecutive data points — for each 1 ≤ i < n, it's guaranteed that |ai + 1 - ai| ≤ 1.
A range [l, r] of data points is said to be almost constant if the difference between the largest and the smallest value in that range is at most 1. Formally, let M be the maximum and m the minimum value of ai for l ≤ i ≤ r; the range [l, r] is almost constant if M - m ≤ 1.
Find the length of the longest almost constant range.
Input
The first line of the input contains a single integer n (2 ≤ n ≤ 100 000) — the number of data points.
The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 100 000).
Output
Print a single number — the maximum length of an almost constant range of the given sequence.
Sample Input
5
1 2 3 3 2
Sample Output
4
HINT
题意
给你n个数，要求你找到最长的区间，使得这个区间的最大值减去最小值之差的绝对值小于等于1
题解：
枚举每一个数，以这个数为这个区间的最小值，能够往左边延伸多少，往右边延伸多少
再枚举每一个数，以这个数为区间的最大值，能够往左边延伸多少，往右边延伸多少就好了
可以O(n) 也可以 像我一样 用倍增然后二分去找
代码：
#include<iostream>
#include<stdio.h>
#include<algorithm>
using namespace std;
#define maxn 100005
int n;
int dp[maxn][];
int dp1[maxn][];
int a[maxn];
int L[maxn],R[maxn];
int mm[maxn];
void initrmp(int n)
{
mm[]=-;
for(int i=;i<=n;i++)
{
mm[i]=((i&(i-))==)?mm[i-]+:mm[i-];
dp[i][]=a[i];
dp1[i][]=a[i];
}
for(int j = ;j<=mm[n];j++)
for(int i=;i+(<<j)-<=n;i++)
dp[i][j]=max(dp[i][j-],dp[i+(<<(j-))][j-]);
for(int j = ;j<=mm[n];j++)
for(int i=;i+(<<j)-<=n;i++)
dp1[i][j]=min(dp1[i][j-],dp1[i+(<<(j-))][j-]);
}
int queryMax(int l,int r)
{
int k = mm[r-l+];
return max(dp[l][k],dp[r-(<<k)+][k]);
}
int queryMin(int l,int r)
{
int k = mm[r-l+];
return min(dp1[l][k],dp1[r-(<<k)+][k]);
}
int main()
{
scanf("%d",&n);
for(int i=;i<=n;i++)
scanf("%d",&a[i]);
int Ans = ;
initrmp(n);
for(int i=;i<=n;i++)
{
int l=,r=i;
while(l<=r)
{
int mid = (l+r)/;
if(abs(a[i]-queryMin(mid,i))<= && abs(a[i]-queryMax(mid,i))<=)r=mid-;
else l=mid+;
}
L[i]=l;
l=i,r=n;
while(l<=r)
{
int mid = (l+r)/;
if(abs(a[i]-queryMin(i,mid))<= && abs(a[i]-queryMax(i,mid))<=)l=mid+;
else r=mid-;
}
R[i]=l-;
}
for(int i=;i<=n;i++)
Ans = max(Ans,R[i]-L[i]+);
for(int i=;i<=n;i++)
{
int l=,r=i;
while(l<=r)
{
int mid = (l+r)/;
if(abs(a[i]-queryMin(mid,i))<= && abs(a[i]-queryMax(mid,i))<=)r=mid-;
else l=mid+;
}
L[i]=l;
l=i,r=n;
while(l<=r)
{
int mid = (l+r)/;
if(abs(a[i]-queryMin(i,mid))<= && abs(a[i]-queryMax(i,mid))<=)l=mid+;
else r=mid-;
}
R[i]=l-;
}
for(int i=;i<=n;i++)
Ans = max(Ans,R[i]-L[i]+);
cout<<Ans<<endl;
}