思路:二分答案,时间复杂度O(nlgn).
若个数为x,那么算出这种情况下提供的水管的最大值和最小值与n比较即可,注意x个分离器需要减去x-1个水管。
#include<cstdio>
#include<string>
#include<cstring>
#include<iostream>
#include<algorithm>
#define LL long long int
using namespace std;
LL n, k;
LL calSum(LL ba, LL i){
return ((2*ba + i - 1) * i)/2;
}
LL bin_search(LL l, LL r){
LL ans = 0x7fffffff;
while(l <= r){
LL mid = (l + r) >> 1;
LL up = min(n + mid - 1, k);
LL tmp1 = calSum(2, mid), tmp2 = calSum(up - mid + 1, mid);
if(tmp1 <= n + mid - 1 && tmp2 >= n + mid -1){
ans = min(ans, mid);
r = mid - 1;
}
else if(tmp1 > n + mid - 1) r = mid - 1;
else if(tmp2 < n + mid - 1) l = mid + 1;
}
if(ans != 0x7fffffff) return ans;
else return -1;
}
int main(){
while(cin >> n >> k){
if(n == 1) printf("0\n");
else cout << bin_search(1, k-1) << endl;
}
return 0;
}