【cf528B】Clique Problem


The clique problem is one of the most well-known NP-complete problems. Under some simplification it can be formulated as follows. Consider an undirected graph G. It is required to find a subset of vertices C of the maximum size such that any two of them are connected by an edge in graph G. Sounds simple, doesn’t it? Nobody yet knows an algorithm that finds a solution to this problem in polynomial time of the size of the graph. However, as with many other NP-complete problems, the clique problem is easier if you consider a specific type of a graph.

Consider n distinct points on a line. Let the i-th point have the coordinate xi and weight wi. Let’s form graph G, whose vertices are these points and edges connect exactly the pairs of points (i, j), such that the distance between them is not less than the sum of their weights, or more formally: |xi - xj| ≥ wi + wj.

Find the size of the maximum clique in such graph.


The first line contains the integer n (1 ≤ n ≤ 200 000) — the number of points.

Each of the next n lines contains two numbers xi, wi (0 ≤ xi ≤ 109, 1 ≤ wi ≤ 109) — the coordinate and the weight of a point. All xi are different.


Print a single number — the number of vertexes in the maximum clique of the given graph.

Sample test(s)



If you happen to know how to solve this problem without using the specific properties of the graph formulated in the problem statement, then you are able to get a prize of one million dollars!

The picture for the sample test.





  1. 大神,这道CF的题有一个技巧分享一下吧(弱弱的不敢大声说话),当前的点的重量:从最左边到最右边的线段(在X轴上,左区间到右区间),满足|xi-xj|>=wi+wj;两点之间的距离大于两点之间的权值加起来,画图之后显然就是一道经典的模板贪心题了(最多不重叠线段),按照每条权值线段的右端点从小到大排好序。。贪心。。如果解释的不详细你就忽略吧!!!