Codefoces 429 D. Tricky Function

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D. Tricky Function

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Iahub and Sorin are the best competitive programmers in their town. However, they can't both qualify to an important contest. The selection will be made with the help of a single problem. Blatnatalag, a friend of Iahub, managed to get hold of the problem before the contest. Because he wants to make sure Iahub will be the one qualified, he tells Iahub the following task.

You're given an (1-based) array a with n elements. Let's define function f(i, j) (1 ≤ i, j ≤ n) as (i - j)2 + g(i, j)2. Function g is calculated by the following pseudo-code:

int g(int i, int j) {
    int sum = 0;
    for (int k = min(i, j) + 1; k <= max(i, j); k = k + 1)
        sum = sum + a[k];
    return sum;
}

Find a value mini ≠ j  f(i, j).

Probably by now Iahub already figured out the solution to this problem. Can you?

Input

The first line of input contains a single integer n (2 ≤ n ≤ 100000). Next line contains n integers a[1], a[2], ..., a[n] ( - 104 ≤ a[i] ≤ 104).

Output

Output a single integer — the value of mini ≠ j  f(i, j).

Sample test(s)

input

4
1 0 0 -1

output

1

input

2
1 -1

output

2

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>

using namespace std;

typedef long long int LL;

const int maxn=100100;
const LL INF=1LL<<62;

LL a[maxn];
int n;

struct POINT
{
    LL x,y;
}p[maxn],temp[maxn];

bool cmpxy(POINT a,POINT b)
{
    if(a.x!=b.x) return a.x<b.x;
    return a.y<b.y;
}

bool cmpy(POINT a,POINT b)
{
    return a.y<b.y;
}

inline LL square(LL x)
{
    return x*x;
}

LL dist(POINT a,POINT b)
{
    return square(a.x-b.x)+square(a.y-b.y);
}

LL Close_pair(int left,int right)
{
    LL d=INF;
    if(left==right) return INF;
    if(left+1==right) return dist(p[left],p[right]);
    int mid=(left+right)/2;
    d=min(Close_pair(left,mid),Close_pair(mid+1,right));

    int k=0;
    for(int i=left;i<=right;i++)
    {
        if(square(p[i].x-p[mid].x)<=d)
        {
            temp[k++]=p[i];
        }
    }
    sort(temp,temp+k,cmpy);
    for(int i=0;i<k;i++)
    {
        for(int j=i+1;j<k&&square(temp[i].y-temp[j].y)<d;j++)
        {
            d=min(d,dist(temp[i],temp[j]));
        }
    }

    return d;
}

int main()
{
    scanf("%d",&n);
    for(int i=1;i<=n;i++)
    {
        scanf("%I64d",a+i);
        p[i].x=i;
        p[i].y=p[i-1].y+a[i];
    }
    sort(p+1,p+1+n,cmpxy);
    printf("%I64d\n",Close_pair(1,n));
    return 0;
}