11627 - Slalom UVA

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  pairs of left and right gates, where each right gate is  W  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 ^th  pair of gates occurs at distance  y_i  down the hill, with the horizontal position of the  i ^th  left gate given by  x_i . Each gate is further down the hill than the previous gate (i.e.  y_i  <  y_i+1  for all i ).

You may select from S pairs of skis, where the j^th pair has speed s_j. Your movement is governed by the following rule: if you select a pair of skis with speed s_j, you move with a constant downward velocity of s_jmetres per second. Additionally, at any time you may move at a horizontal speed of at most v_h metres 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, v_h, and N, separated by spaces, with 1 <= W<= 10⁸, 1 <= v_h <= 10⁶, and 1 <= N <= 10⁵.

The following N lines of the test case each contain two integers x_i and y_i, the horizontal and vertical positions respectively of the i^th left gate, with 1 <= x_i, y_i <= 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 s_j, the speed of the j^th pair of skis, with 1 <= s_j <= 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  s_j  of the pair of skis that allows you to get through the race course in the shortest time.

Output for Sample Input

2
IMPOSSIBLE

一定要注意二分时候的界限！！！！！

http://www.cnblogs.com/staginner/archive/2012/11/09/2763406.html

在判断当前sj下能够穿过所有门时，可以自顶向下，逐步约束人能够到达的x坐标上的范围，直到这个范围变成空集或者所有的门都经过了为止

#include <stdio.h>
#include <math.h>
#include <algorithm>
#include <string.h>
#include <stdlib.h>
using namespace std;
const int maxn = 10;
int W,V,N;
struct pos
{
    int x;
    int y;
}p[100000 + maxn];
int ok(int v)
{
    double x1 = p[0].x;
    double x2 = p[0].x+W;
    for(int i = 1;i<N;++i)
    {
        double d = (double)(p[i].y-p[i-1].y)/v*V;
        x1 -= d;
        x2 += d;
        x1 = max(x1,(double)p[i].x);
        x2 = min(x2,(double)p[i].x+W);
        if(x1>x2+1e-6) return 0;
    }
    return 1;
}
int main()
{
    int n;
    scanf("%d",&n);
    int i;
    for(i = 0;i<n;++i)
    {
        scanf("%d%d%d",&W,&V,&N);//门宽度，最大横向速度，门个数
        int j;
        for(j = 0;j<N;++j)
            scanf("%d %d",&p[j].x,&p[j].y);
        int L = 0;
        int R = 1000010;
        int mid;
     for(;;)
    {
        mid = (R - L) / 2 + L;
        if(mid == L) break;
        if(ok(mid)) L = mid;
        else R = mid;
    }
        int fast = 0;
        int S;
        scanf("%d",&S);//滑板数目
        for(j = 0;j<S;++j)
        {
            int speed;
            scanf("%d",&speed);
            if(speed<=mid)
            fast = max(fast,speed);
        }
         if(fast==0)
         printf("IMPOSSIBLE\n");
         else
         printf("%d\n",fast);
    }
    return 0;
}