CodeChef FORESTGA 二分
Forest Gathering |
All submissions for this problem are available.
Read problems statements in Mandarin Chinese, Russian and Vietnamese as well.
Chef is the head of commercial logging industry that recently bought a farm containing N trees. You are given initial height of the i-th tree by Hi and the rate of growth of height as Ri meters per month. For simplicity, you can assume that all the trees are perfect cylinders of equal radius. This allows us to consider only the height of trees when we talk about the amount of wood.
In Chef's country, laws don't allow one to cut a tree partially, so one has to cut the tree completely for gathering wood. Also, laws prohibit cutting trees of heights (strictly) lower than L meters.
Today Chef received an order of W meters (of height) of wood. Chef wants to deliver this order as soon as possible. Find out how minimum number of months he should wait after which he will able to fulfill the order. You can assume that Chef's company's sawing machines are very efficient and take negligible amount of time to cut the trees.
Input
There is a single test case per test file.
The first line of the input contains three space separated integers N, W and L denoting the number of trees in the farm, the amount of wood (in meters) that have to be gathered and the minimum allowed height of the tree to cut.
Each of next N lines contain two space separated integers denoting Hi and Ri respectively.
Output
Output a single integer denoting the number of months that have to pass before Chef will be able to fulfill the order.
Constraints
- 1 ≤ N ≤ 105
- 1 ≤ W, L ≤ 1018
- 1 ≤ Hi, Ri ≤ 109
Subtasks
- Subtask #1 [40 points]: 1 ≤ N, W, L ≤ 104
- Subtask #2 [60 points]: No additional constraints
Example
Input: 3 74 51 2 2 5 7 2 9 Output: 7
Explanation
After 6 months, heights of each tree will be 14, 47 and 56 respectively. Chef is allowed to cut only the third tree, sadly it is not enough to fulfill an order of 74 meters of wood.
After 7 months, heights of each tree will be 16, 54 and 65 respectively. Now Chef is allowed to cut second and third trees. Cutting both of them would provide him 119 meters of wood, which is enough to fulfill the order.
题意：给你n棵数，首先给你三个树，树的数量n，需要砍的长度w，树的最小砍伐高度l；
n行，起始高度和每天增加长度；
思路：二分查找答案，防止爆long long 用减法；
#include<bits/stdc++.h> using namespace std; #define ll long long #define mod 100000007 #define esp 0.00000000001 const int N=2e5+10,M=1e6+10,inf=1e9; struct is { ll b,inc; }a[N]; ll x,w,l; int check(ll mid) { ll c=l; ll g=w; for(ll i=1;i<=x;i++) { ll k=(c-a[i].b)/a[i].inc; ll j=(g-a[i].b)/a[i].inc; if((c-a[i].b)%a[i].inc!=0) k++; if((g-a[i].b)%a[i].inc!=0) j++; if(mid>=k) { if(mid>=j) return 1; else g-=mid*a[i].inc+a[i].b; } } if(g<=0) return 1; return 0; } int main() { ll i,t; while(~scanf("%lld%lld%lld",&x,&w,&l)) { for(ll i=1;i<=x;i++) scanf("%lld%lld",&a[i].b,&a[i].inc); ll st=0; ll en=1e18; while(st<en) { ll mid=(st+en)>>1; if(check(mid)) en=mid; else st=mid+1; } if(check(st)) printf("%lld\n",st); else if(check(st-1)) printf("%lld\n",st-1); } return 0; }
