Billboard(线段树)

题目来源:HDU2795

描述

At the entrance to the university, there is a huge rectangular billboard of size $h*w$ ($h$ is its height and $w$ is its width). The board is the place where all possible announcements are posted: nearest programming competitions, changes in the dining room menu, and other important information.

On September 1, the billboard was empty. One by one, the announcements started being put on the billboard.

Each announcement is a stripe of paper of unit height. More specifically, the i-th announcement is a rectangle of size $1 * w_i$.

When someone puts a new announcement on the billboard, she would always choose the topmost possible position for the announcement. Among all possible topmost positions she would always choose the leftmost one.

If there is no valid location for a new announcement, it is not put on the billboard (that’s why some programming contests have no participants from this university).

Given the sizes of the billboard and the announcements, your task is to find the numbers of rows in which the announcements are placed.

Input

There are multiple cases (no more than 40 cases).

The first line of the input file contains three integer numbers, $h$, $w$, and $n$ $(1 ≤ h,w ≤ 10^9; 1 ≤ n ≤ 200,000)$ - the dimensions of the billboard and the number of announcements.

Each of the next $n$ lines contains an integer number $w_i$ $(1 ≤ w_i ≤ 10^9)$ - the width of i-th announcement.

Output

For each announcement (in the order they are given in the input file) output one number - the number of the row in which this announcement is placed. Rows are numbered from $1$ to $h$, starting with the top row. If an announcement can’t be put on the billboard, output “-1” for this announcement.

Sample Input

1
2
3
4
5
6
3 5 5
2
4
3
3
3

Sample Output

1
2
3
4
5
1
2
1
3
-1

思路

  • 以$h$建立线段树,初始值都是$w$。维护区间最大值。
  • 每次查询从左往右第一个大于等于$w_i$的点,并将该点的值减去$w_i$。
  • 注意当$h>n$的时候,可以取$h=n$
  • 具体细节见代码。

代码

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
#include <bits/stdc++.h>
using namespace std;
#define clr(a,x) memset(a, x, sizeof(a))
#define mp(x,y) make_pair(x,y)
#define pb(x) push_back(x)
#define X first
#define Y second
#define fastin ios_base::sync_with_stdio(0);cin.tie(0);
typedef long long ll;
typedef long double ld;
typedef pair<int, int> PII;
typedef vector<int> VI;
const int INF = 0x3f3f3f3f;
const int mod = 1e9 + 7;
const double eps = 1e-6;
const int maxn = 2e5 + 5;
#define lson rt << 1
#define rson rt << 1 | 1
#define Lson l, m, lson
#define Rson m + 1, r, rson
int seg[maxn << 2];
int h, w, n;

void PushUp(int rt)
{
seg[rt] = max(seg[lson], seg[rson]);
}

void build(int l, int r, int rt)
{
if (l == r)
{
seg[rt] = w;
return;
}
int m = (l + r) >> 1;
build(Lson);
build(Rson);
PushUp(rt);
}

int query(int x, int l, int r, int rt)
{
int m = (l + r) >> 1, ans = 0;
if (l == r)
{
seg[rt] -= x;
return l;
}
if (seg[lson] >= x) ans = query(x, l, m, lson);
else ans = query(x, m + 1, r, rson);
PushUp(rt);
return ans;
}

int main()
{
#ifndef ONLINE_JUDGE
freopen("1.in", "r", stdin);
freopen("1.out", "w", stdout);
#endif
fastin
while (cin >> h >> w >> n)
{
h = min(h, n);
clr(seg, 0);
build(1, h, 1);
while (n--)
{
int a;
cin >> a;
if (seg[1] < a)
cout << -1 << endl;
else
cout << query(a, 1, h, 1) << endl;
}
}
return 0;
}
捐助作者