M 有效算法
本题考验二分知识,思路是二分k的取值,就按第一组样例来说当我们k取值为1的时候我们遍历数组想让|8-x|<=k1的话x的取值范围是7-9,想让|3-x|<=k 2的话x的取值范围是1-5,两者x的区间不重合,说明肯定没有x能同时让|8-x|<=k1和|3-x|<=k 2,所以不成立,当k=2的时候我们发现每一组x的区间都有重合的地方,那么此时a数组一定是可以全都变成x的,并且当k>2时毫无疑问绝对都可以符合,k的取值是否达标具有单调性,所以可以用二分来枚举。
题解如下:
cpp
#define _CRT_SECURE_NO_WARNINGS
#include<bits/stdc++.h>
#include<unordered_map>
using namespace std;
#define for1 for(int i = 1;i <= n;i++)
#define for0 for(int i = 0;i < n;i++)
#define forn1 for(int j = 1;j <= n;j++)
#define forn0 for(int j = 0;j < n;j++)
#define form1 for (int j = 1; j <= m; j++)
#define form0 for (int j = 0; j < m; j++)
#define IOS ios::sync_with_stdio(0),cin.tie(0),cout.tie(0)
#define arrn int* arr = new int[n+2];arr[0] = 0,arr[n+1]=0
#define carr cin >> arr[i]
#define inf 0x3f3f3f3f
#define INF 0x3f3f3f3f3f3f3f3f
#define endl '\n'
#define mod 1000000007
#define t() int _; cin >> _; while (_--)
int a[300010];
int b[300010];
int n;
bool cheak(int k)
{
long long ml = a[1] - 1ll * b[1] * k;
long long mr = a[1] + 1ll * b[1] * k;
for (int i = 2; i <= n; i++)
{
long long ll = a[i] - 1ll * b[i] * k;
long long rr = a[i] + 1ll * b[i] * k;
if (ll > ml)ml = ll;
if (rr < mr)mr = rr;
}
if (mr < ml)return false;
return true;
}
int main() {
IOS;
int t;
cin >> t;
while (t--)
{
cin >> n;
for(int i = 1; i <= n; i++)
cin >> a[i];
for(int i = 1; i <= n; i++)
cin >> b[i];
int l = 0, r = 1e9;
while (l <= r)
{
int mid = (l + r) >> 1;
if (cheak(mid))r = mid-1;
else l = mid+1;
}
cout << l << endl;
}
return 0;
}