codeforces#303div2_C 贪心

codeforces#303div2_C  贪心

C. Woodcutters

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

Little Susie listens to fairy tales before bed every day. Today's fairy tale was about wood cutters and the little girl immediately started imagining the choppers cutting wood. She imagined the situation that is described below.

There are n trees located along the road at points with coordinates x1, x2, ..., xn. Each tree has its height hi. Woodcutters can cut down a tree and fell it to the left or to the right. After that it occupies one of the segments [xi - hi, xi] or [xi;xi + hi]. The tree that is not cut down occupies a single point with coordinate xi. Woodcutters can fell a tree if the segment to be occupied by the fallen tree doesn't contain any occupied point. The woodcutters want to process as many trees as possible, so Susie wonders, what is the maximum number of trees to fell.

Input

The first line contains integer n (1 ≤ n ≤ 105) — the number of trees.

Next n lines contain pairs of integers xi, hi (1 ≤ xi, hi ≤ 109) — the coordinate and the height of the і-th tree.

The pairs are given in the order of ascending xi. No two trees are located at the point with the same coordinate.

Output

Print a single number — the maximum number of trees that you can cut down by the given rules.

Sample test(s)

input

5
1 2
2 1
5 10
10 9
19 1

output

3

input

5
1 2
2 1
5 10
10 9
20 1

output

4

Note

In the first sample you can fell the trees like that:

• fell the 1-st tree to the left — now it occupies segment [ - 1;1]
• fell the 2-nd tree to the right — now it occupies segment [2;3]
• leave the 3-rd tree — it occupies point 5
• leave the 4-th tree — it occupies point 10
• fell the 5-th tree to the right — now it occupies segment [19;20]

In the second sample you can also fell 4-th tree to the right, after that it will occupy segment [10;19].

题意：第n次打cf误解题意了。。。。。看来以后得多看英语。。。

思路：贪心，显然，第一棵树倒向左边，最后一棵树倒向右边最优，考虑中间的树，倒向左边不影响后续的树，优先倒向左边，否则能倒向右边则倒向右边，倒向右边会限制右边的树。

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cstdlib>
#include<set>
#include<map>
#include<string>
#include<stack>
#include<queue>
#include<vector>

using namespace std;

const int maxn=1000100;
const int INF=(1<<29);
typedef long long ll;

ll x[maxn],h[maxn];
int n;

int main()
{
    while(cin>>n){
        for(int i=1;i<=n;i++){
            scanf("%I64d%I64d",&x[i],&h[i]);
        }
        if(n==1){
            puts("1");
            continue;
        }
        int cnt=2;
        for(int i=2;i<=n-1;i++){
            if(x[i-1]<x[i]-h[i]){
                cnt++;
            }
            else if(x[i]+h[i]<x[i+1]){
                x[i]+=h[i];
                cnt++;
            }
        }
        cout<<cnt<<endl;
    }
    return 0;
}