11627 - Slalom (二分+贪心)

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 areNpairs of left and right gates, where each right gate isWmetres 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. Thei^thpair of gates occurs at distancey_idown the hill, with the horizontal position of thei^thleft gate given byx_i. Each gate is further down the hill than the previous gate (i.e.y_i<y_i+1for alli).

You may select fromSpairs of skis, where thej^thpair has speeds_j. Your movement is governed by the following rule: if you select a pair of skis with speeds_j, you move with a constant downward velocity ofs_jmetres per second. Additionally, at any time you may move at a horizontal speed of at mostv_hmetres 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 integersW,v_h, andN, separated by spaces, with 1 <=W<= 10⁸, 1 <=v_h<= 10⁶, and 1 <=N<= 10⁵.

The followingNlines of the test case each contain two integersx_iandy_i, the horizontal and vertical positions respectively of thei^thleft gate, with 1 <=x_i,y_i<= 10⁸.

The next line of the test case contains an integerS, the number of skis, with 1 <=S<= 10⁶.

The followingSlines of the test case each contain one integers_j, the speed of thej^thpair 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 lineIMPOSSIBLE. Otherwise, print the vertical speeds_jof 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：给定n个门和门的长度，n双滑雪板，求最大能通过所有门的滑雪板的速度。

思路：二分答案，然后去判断，判断的时候每次只要维护一个区间就可以了。

代码：

#include <stdio.h>
#include <string.h>
#include <algorithm>
using namespace std;

const int N = 100005;

int T, n, S, s[N * 10];
double w, v;
struct Sk {
    double s, e, y;
} sk[N];

void init() {
    scanf("%lf%lf%d", &w, &v, &n);
    for (int i = 0; i < n; i ++) {
	scanf("%lf%lf", &sk[i].s, &sk[i].y);
	sk[i].e = sk[i].s + w;
    }
    scanf("%d", &S);
    for (int i = 0; i < S; i ++)
	scanf("%d", &s[i]);
    sort(s, s + S);
}

bool judge(int sv) {
    double s = sk[n - 1].s, e = sk[n - 1].e;
    for (int i = n - 1; i > 0; i --) {
	double time = (sk[i].y - sk[i - 1].y) / sv;
	s = max(s - time * v, sk[i - 1].s);
	e = min(e + time * v, sk[i - 1].e);
	if (s > sk[i - 1].e || e < sk[i - 1].s || s > e)
	    return false;
    }
    return true;
}

void solve() {
    if (!judge(s[0])) {
	printf("IMPOSSIBLE\n");
	return;
    }
    int l = 0, r = S - 1;
    while (l < r) {
	int mid = (l + r)>>1;
	if (judge(s[mid])) l = mid + 1;
	else r = mid;
    }
    if (!judge(s[l]))
	l--;
    printf("%d\n", s[l]);
}

int main() {
    scanf("%d", &T);
    while (T--) {
	init();
	solve();
    }
    return 0;
}