Codeforces Round #300——C贪心——Tourist's Notes

A tourist hiked along the mountain range. The hike lasted for n days, during each day the tourist noted height above the sea level. On the i-th day height was equal to some integer h_i. The tourist pick smooth enough route for his hike, meaning that the between any two consecutive days height changes by at most 1, i.e. for all i‘s from 1 to n - 1 the inequality |h_i - h_i + 1| ≤ 1 holds.

At the end of the route the tourist rafted down a mountain river and some notes in the journal were washed away. Moreover, the numbers in the notes could have been distorted. Now the tourist wonders what could be the maximum height during his hike. Help him restore the maximum possible value of the maximum height throughout the hike or determine that the notes were so much distorted that they do not represent any possible height values that meet limits |h_i - h_i + 1| ≤ 1.

The first line contains two space-separated numbers, n and m (1 ≤ n ≤ 10⁸, 1 ≤ m ≤ 10⁵) — the number of days of the hike and the number of notes left in the journal.

Next m lines contain two space-separated integers d_i and h_di (1 ≤ d_i ≤ n, 0 ≤ h_di ≤ 10⁸) — the number of the day when the i-th note was made and height on the d_i-th day. It is guaranteed that the notes are given in the chronological order, i.e. for all i from 1 to m - 1 the following condition holds: d_i < d_i + 1.

If the notes aren‘t contradictory, print a single integer — the maximum possible height value throughout the whole route.

If the notes do not correspond to any set of heights, print a single word ‘IMPOSSIBLE‘ (without the quotes).

For the first sample, an example of a correct height sequence with a maximum of 2: (0, 0, 1, 2, 1, 1, 0, 1).

In the second sample the inequality between h₇ and h₈ does not hold, thus the information is inconsistent.

/*
   坑点在于第一天和最后一天还要有个max1的判断
   先对日期进行排序
   从i到i+1天所能走的最长的路a[i+1].d - a[i].d
   必须要走的路为 abs(a[i+1].h - a[i].h)
   剩下的是可以宽松的路程，来回除2最后再加上最后到得位置（最高）可以一开始往上再往下，也可以先往上再往下再往上
   再判掉不可能的情况就esay了
*/
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;

struct edge{
    int d, h;
}a[100010];

bool cmp(edge i,edge j){
    return i.d < j.d;
}
int main()
{
    int n, m;
    while(~scanf("%d%d", &n, &m)){
        for(int i = 1; i <= m ;i++)
            scanf("%d%d", &a[i].d, &a[i].h);
        sort(a + 1, a + 1 + m, cmp);
        int max1 = 0;
        int flag = 0;
        for(int i = 1; i < m - 1; i++){
            int t1 = max(a[i+1].h, a[i].h);
            int t2 = min(a[i+1].h, a[i].h);
            if(a[i+1].d - a[i].d - t1 + t2 < 0) {flag = 1; break;}
            max1 = max(max1, (a[i+1].d - a[i].d - t1 + t2 )/2 + t1);
        }
        if(m >= 2){
      int  t1 = max(a[m].h, a[m-1].h);
      int  t2 = min(a[m].h, a[m-1].h);
        if(a[m].d - a[m-1].d - t1 + t2 < 0) {flag = 1;}
        max1 = max(max1, (a[m].d - a[m-1].d - t1 + t2)/2 + t1 );
        }
        max1 = max(a[m].h + n - a[m].d, max1);
        max1 = max(max1, a[1].h + a[1].d - 1);
        if(flag == 1) printf("IMPOSSIBLE\n");
        else 
       printf("%d\n", max1);
    }
   return 0;
}