#148. 【NOIP2015】跳石頭
Time Limit: 20 Sec
Memory Limit: 256 MB
題目連接
http://uoj.ac/problem/148
Description
一年一度的“跳石頭”比賽又要開始了！
這項比賽將在一條筆直的河道中進行，河道中分布着一些巨大岩石。組委會已經選擇好了兩塊岩石作為比賽起點和終點。在起點和終點之間，有 N 塊岩石（不含起點和終點的岩石）。在比賽過程中，選手們將從起點出發，每一步跳向相鄰的岩石，直至到達終點。
為了提高比賽難度，組委會計划移走一些岩石，使得選手們在比賽過程中的最短跳躍距離盡可能長。由於預算限制，組委會至多從起點和終點之間移走 M 塊岩石（不能移走起點和終點的岩石）。
Under two situations the player could score one point.
⋅1. If you touch a buoy before your opponent, you will get one point. For example if your opponent touch the buoy #2 before you after start, he will score one point. So when you touch the buoy #2, you won't get any point. Meanwhile, you cannot touch buoy #3 or any other buoys before touching the buoy #2.
⋅2. Ignoring the buoys and relying on dogfighting to get point. If you and your opponent meet in the same position, you can try to fight with your opponent to score one point. For the proposal of game balance, two players are not allowed to fight before buoy #2 is touched by anybody.
There are three types of players.
Speeder: As a player specializing in high speed movement, he/she tries to avoid dogfighting while attempting to gain points by touching buoys.
Fighter: As a player specializing in dogfighting, he/she always tries to fight with the opponent to score points. Since a fighter is slower than a speeder, it's difficult for him/her to score points by touching buoys when the opponent is a speeder.
All-Rounder: A balanced player between Fighter and Speeder.
There will be a training match between Asuka (All-Rounder) and Shion (Speeder).
Since the match is only a training match, the rules are simplified: the game will end after the buoy #1 is touched by anybody. Shion is a speed lover, and his strategy is very simple: touch buoy #2,#3,#4,#1 along the shortest path.
Asuka is good at dogfighting, so she will always score one point by dogfighting with Shion, and the opponent will be stunned for T seconds after dogfighting. Since Asuka is slower than Shion, she decides to fight with Shion for only one time during the match. It is also assumed that if Asuka and Shion touch the buoy in the same time, the point will be given to Asuka and Asuka could also fight with Shion at the buoy. We assume that in such scenario, the dogfighting must happen after the buoy is touched by Asuka or Shion.
The speed of Asuka is V
⋅1. If you touch a buoy before your opponent, you will get one point. For example if your opponent touch the buoy #2 before you after start, he will score one point. So when you touch the buoy #2, you won't get any point. Meanwhile, you cannot touch buoy #3 or any other buoys before touching the buoy #2.
⋅2. Ignoring the buoys and relying on dogfighting to get point. If you and your opponent meet in the same position, you can try to fight with your opponent to score one point. For the proposal of game balance, two players are not allowed to fight before buoy #2 is touched by anybody.
There are three types of players.
Speeder: As a player specializing in high speed movement, he/she tries to avoid dogfighting while attempting to gain points by touching buoys.
Fighter: As a player specializing in dogfighting, he/she always tries to fight with the opponent to score points. Since a fighter is slower than a speeder, it's difficult for him/her to score points by touching buoys when the opponent is a speeder.
All-Rounder: A balanced player between Fighter and Speeder.
There will be a training match between Asuka (All-Rounder) and Shion (Speeder).
Since the match is only a training match, the rules are simplified: the game will end after the buoy #1 is touched by anybody. Shion is a speed lover, and his strategy is very simple: touch buoy #2,#3,#4,#1 along the shortest path.
Asuka is good at dogfighting, so she will always score one point by dogfighting with Shion, and the opponent will be stunned for T seconds after dogfighting. Since Asuka is slower than Shion, she decides to fight with Shion for only one time during the match. It is also assumed that if Asuka and Shion touch the buoy in the same time, the point will be given to Asuka and Asuka could also fight with Shion at the buoy. We assume that in such scenario, the dogfighting must happen after the buoy is touched by Asuka or Shion.
The speed of Asuka is V
Input
輸入文件第一行包含三個整數 L,N,M，分別表示起點到終點的距離，起點和終點之間的岩石數，以及組委會至多移走的岩石數。保證 L≥1 且 N≥M≥0。
接下來 N 行，每行一個整數，第 i 行的整數 Di（0<Di<L）， 表示第 i 塊岩石與起點的距離。這些岩石按與起點距離從小到大的順序給出，且不會有兩個岩石出現在同一個位置。
Output
輸出文件只包含一個整數，即最短跳躍距離的最大值。
Sample Input
25 5 2
2
11
14
17
21
Sample Output
4
HINT
題意
題解：
二分答案，然后check就好了
代碼
#include<stdio.h> #include<iostream> using namespace std; int l,n,m; int a[50005]; int L; int check(int x) { int last = 0; int ans = 0; for(int i=1;i<=n;i++) { if(a[i]-last<x) ans++; else last = a[i]; } if(ans>m)return 0; return 1; } int main() { scanf("%d%d%d",&L,&n,&m); for(int i=1;i<=n;i++) scanf("%d",&a[i]); a[n+1]=L;n++; int l = 0,r = L; while(l<=r) { int mid = (l+r)/2; if(check(mid))l=mid+1; else r=mid-1; } printf("%d\n",l-1); }