ACM: 二分题 uva 11627

 

Problem E: Slalom

You
are competing in a ski slalom, and you need to select the best skis
for the race. The format of the race is that there
are N[/i] pairs
of left and right gates, where each right gate
is W[/i] metres
to the right of its corresponding left gate, and you may neither
pass to the left of the left gate nor to the right of the right
gate. The i[/i]th pair
of gates occurs at distance yi[/i] down
the hill, with the horizontal position of thei[/i]th left
gate given by xi[/i].
Each gate is further down the hill than the previous gate
(i.e. yi[/i] < yi+1[/i] for
all i[/i]).
You
may select from S pairs of
skis, where
the jth pair
has speed sj. Your movement is
governed by the following rule: if you select a pair of skis with
speed sj, you move with a
constant downward velocity
of sj metres
per second. Additionally, at any time you may move at a horizontal
speed of at most vhmetres per
second.
You
may start and finish at any two horizontal positions. Determine
which pair of skis will allow you to get through the race course,
passing through all the gates, in the shortest amount of time.

Input
Specification

The
first line of input contains a single integer, the number of test
cases to follow.
The
first line of each test case contains the three
integers W, vh,
and N, separated by spaces, with 1
<= W <=
108, 1
<= vh <=
106, and 1
<= N <=
105.
The
following N lines of the
test case each contain two
integers xi and yi,
the horizontal and vertical positions respectively of
the ith left
gate, with 1
<= xi, yi <=
108.
The
next line of the test case contains an
integer S, the number of skis, with 1
<= S <=
106.
The
following S lines of the
test case each contain one
integer sj, the speed of
the jth pair of
skis, with 1
<= sj <=
106.

Sample
Input

2 

3 2 3 

1 1 

5 2 

1 3 

3 

3 

2 

1 

3 2 3 

1 1 

5 2 

1 3 

1 

3

Output
Specification

Output
one line for each test case. If it is impossible to complete the
race with any pair of skis, print the
line IMPOSSIBLE.
Otherwise, print the vertical
speed sj[/i] of
the pair of skis that allows you to get through the race course in
the shortest time.

Output for
Sample Input

2 

IMPOSSIBLE

题意: 现在又n双滑雪板, 每双有一个速度Sj, 在滑雪比赛中, 通过n个障碍, 左右像个w距离, (xi, xi+w);

      海拔yi, Sj是竖直方向速度, 并且有一个固定的水平速度vh, 要你选择出能通过全部障碍, 速度最大

      的一双滑雪板.

解题思路:

      1. 因为水平移动的速度vh是固定, 那么可以通过全部障碍而丢失一个, 显然当Sj越小时候越容易

         完成比赛. 可以采用二分方法, 枚举出最优的竖直方向速度, 然后在给出的Sj中找出最接近的

         一个即可.

代码:

#include <cstdio>#include <iostream>#include <cstring>using namespace std;#define MAX 100005#define max(a,b) (a)>(b)?(a):(b)#define min(a,b) (a)<(b)?(a):(b)const int INF = (1<<28);

struct node{ int x, y;}a[MAX];

int w, vh, n;int S;

bool judge(int v){ double x1 = a[0].x; double x2 = a[0].x+w; for(int i = 1; i < n; ++i) {  double dist = vh * (double)(a[i].y-a[i-1].y)/(v*1.0);  x1 -= dist;  x2 += dist;  x1 = max(x1, (double)a[i].x);  x2 = min(x2, (double)(a[i].x)+w);  if(x1 > x2+1e-10) return false; } return true;}

int main(){// freopen("input.txt", "r", stdin); int caseNum; scanf("%d", &caseNum); while(caseNum--) {  scanf("%d %d %d", &w, &vh, &n);  for(int i = 0; i < n; ++i)   scanf("%d %d", &a[i].x, &a[i].y);    int left = 0, right = INF, mid;  while(true)  {   mid = (left+right)/2;   if(left == mid) break;   if( judge(mid) ) left = mid;   else right = mid;  }    int result = 0, temp;  scanf("%d", &S);  for(int i = 0; i < S; ++i)  {   scanf("%d", &temp);   if(temp <= mid)    result = max(result, temp);  }    if(result == 0) printf("IMPOSSIBLE\n");  else printf("%d\n", result); } return 0;}