/*
* APIO 2016 Gap
* T = 1
> Two pointers, left right approaching the center
* T = 2
> pigeon hole principle
> get minimum and maximum,
> then divide the array into n - 1 approx. equal parts
> By PHP, one of these parts will be empty
> Thus, maximum gap >= the length of a part
> Now we can simply compare with seg[i].left - seg[i - 1].right
*/
#include "gap.h"
#include <iostream>
using namespace std;
#define ll long long
const ll mn = 0ll, mx = 1e18;
ll res = mn, arr[100005];
ll findGap(int t, int n){
if(t == 1){
ll lf = mn, rg = mx, k = 0;
for(int i = n; i > 0; i -= 2){
MinMax(lf, rg, &arr[k], &arr[n - 1 - k]);
lf = arr[k] + 1;
rg = arr[n - 1 - k] - 1;
k ++;
}
for(int i = 1; i < n; i ++)
res = max(res, arr[i] - arr[i - 1]);
}
if(t == 2){
ll lf, rg;
MinMax(mn, mx, &lf, &rg);
if(n == 2) return rg - lf;
ll len = rg - lf - 1ll;
ll st = lf + 1, ed = lf;
for(int i = 0; i < n - 1; i ++){
ll e = st + len / (n - 1) - 1;
if(i < len % (n - 1)) e ++;
MinMax(st, e, &lf, &rg);
if(lf != -1){
res = max(res, lf - ed);
ed = rg;
}
st = e + 1ll;
}
res = max(res, st - ed);
}
return res;
}
