Farmer John’s cows have discovered that the clover growing along the ridge of the hill in his field is particularly good. To keep the clover watered, Farmer John is installing water sprinklers along the ridge of the hill.
To make installation easier, each sprinkler head must be installed along the ridge of the hill (which we can think of as a one-dimensional number line of length L (1 <= L <= 1,000,000); L is even).
Each sprinkler waters the ground along the ridge for some distance in both directions. Each spray radius is an integer in the range A…B (1 <= A <= B <= 1000). Farmer John needs to water the entire ridge in a manner that covers each location on the ridge by exactly one sprinkler head. Furthermore, FJ will not water past the end of the ridge in either direction.
Each of Farmer John’s N (1 <= N <= 1000) cows has a range of clover that she particularly likes (these ranges might overlap). The ranges are defined by a closed interval (S,E). Each of the cow’s preferred ranges must be watered by a single sprinkler, which might or might not spray beyond the given range.
Find the minimum number of sprinklers required to water the entire ridge without overlap.
Input
-
Line 1: Two space-separated integers: N and L
-
Line 2: Two space-separated integers: A and B
-
Lines 3…N+2: Each line contains two integers, S and E (0 <= S < E <= L) specifying the start end location respectively of a range preferred by some cow. Locations are given as distance from the start of the ridge and so are in the range 0…L.
Output -
Line 1: The minimum number of sprinklers required. If it is not possible to design a sprinkler head configuration for Farmer John, output -1.
Sample Input
2 8
1 2
6 7
3 6
Sample Output
3
Hint
INPUT DETAILS:
Two cows along a ridge of length 8. Sprinkler heads are available in integer spray radii in the range 1…2 (i.e., 1 or 2). One cow likes the range 3-6, and the other likes the range 6-7.
OUTPUT DETAILS:
Three sprinklers are required: one at 1 with spray distance 1, and one at 4 with spray distance 2, and one at 7 with spray distance 1. The second sprinkler waters all the clover of the range like by the second cow (3-6). The last sprinkler waters all the clover of the range liked by the first cow (6-7). Here’s a diagram:
|-----c2----|-c1| cows' preferred ranges
|---1---|-------2-------|---3---| sprinklers
+---+---+---+---+---+---+---+---+
0 1 2 3 4 5 6 7 8
The sprinklers are not considered to be overlapping at 2 and 6.
题意：
n块田要浇水。喷水器半径范围为[a,b]。有一些范围的田要求只能被一种喷水器覆盖。求最少几个喷水器覆盖n块田。
思路：
定义f[i]，代表覆盖[0,i]的最小喷水器数目。
那么只需要从[i - 2 * b,i - 2 * a]转移过来即可，f[i] = min{f[j] + 1}。
也就是维护一个[i - 2 * b,i - 2 * a]的单调递增队列。当这个点属于被覆盖的时候，就不执行f[i] = q[head] + 1。
同时注意题意，两个喷水器覆盖同一点不代表重叠，因此如果[a,b]代表只能一个喷水器覆盖的区间，f[a]和f[b]都是可以发生转移的，因此应该取开区间。
