CORRAL - Covering the Corral

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The cows are so modest they want Farmer John to install covers around the circular corral where they occasionally gather. The corral has circumference C (1 <= C <= 1,000,000,000), and FJ can choose from a set of M (1 <= M <= 100,000) covers that have fixed starting points and sizes. At least one set of covers can surround the entire corral.

Cover i can be installed at integer location x_i (distance from starting point around corral) (0 <= x_i < C) and has integer length l_i (1 <= l_i <= C).

FJ wants to minimize the number of segments he must install. What is the minimum number of segments required to cover the entire circumference of the corral?

Consider a corral of circumference 5, shown below as a pair of connected line segments where both '0's are the same point on the corral (as are both 1's, 2's, and 3's).

Three potential covering segments are available for installation:

           Start   Length
      i     x_i     l_i
      1      0       1
      2      1       2
      3      3       3

        0   1   2   3   4   0   1   2   3  ...
corral: +---+---+---+---+--:+---+---+---+- ...
        1111                1111
            22222222            22222222

As shown, installing segments 2 and 3 cover an extent of (at least) five units around the circumference. FJ has no trouble with the overlap, so don't worry about that.


  • Line 1: Two space-separated integers: C and M.
  • Lines 2..M+1: Line i+1 contains two space-separated integers: x_i and l_i


  • Line 1: A single integer that is the minimum number of segments required to cover all segments of the circumference of the corral.


5 3
0 1
1 2
3 3


Added by:sieunhan
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:Usaco Feb10 Gold