Buy Tickets（线段树）

Buy Tickets

Time Limit:4000MS     Memory Limit:65536KB     64bit IO Format:%I64d & %I64u

Submit Status

Description

Railway tickets were difficult to buy around the Lunar New Year in China, so we must get up early and join a long queue…

The Lunar New Year was approaching, but unluckily the Little Cat still had schedules going here and there. Now, he had to travel by train to Mianyang, Sichuan Province for the winter camp selection of the national team of Olympiad in Informatics.

It was one o’clock a.m. and dark outside. Chill wind from the northwest did not scare off the people in the queue. The cold night gave the Little Cat a shiver. Why not find a problem to think about? That was none the less better than freezing to death!

People kept jumping the queue. Since it was too dark around, such moves would not be discovered even by the people adjacent to the queue-jumpers. “If every person in the queue is assigned an integral value and all the information about those who have jumped the queue and where they stand after queue-jumping is given, can I find out the final order of people in the queue?” Thought the Little Cat.

Input

There will be several test cases in the input. Each test case consists of N + 1 lines where N (1 ≤ N ≤ 200,000) is given in the first line of the test case. The next N lines contain the pairs of values Pos_i and Val_i in the increasing order of i (1 ≤ i ≤ N). For each i, the ranges and meanings of Pos_i and Val_i are as follows:

• Pos_i ∈ [0, i − 1] — The i-th person came to the queue and stood right behind the Pos_i-th person in the queue. The booking office was considered the 0th person and the person at the front of the queue was considered the first person in the queue.
• Val_i ∈ [0, 32767] — The i-th person was assigned the value Val_i.

There no blank lines between test cases. Proceed to the end of input.

Output

For each test cases, output a single line of space-separated integers which are the values of people in the order they stand in the queue.

Sample Input

4
0 77
1 51
1 33
2 69
4
0 20523
1 19243
1 3890
0 31492

Sample Output

77 33 69 51
31492 20523 3890 19243

Hint

The figure below shows how the Little Cat found out the final order of people in the queue described in the first test case of the sample input.

 1 #include<iostream>
 2 #include<stdio.h>
 3 #include<string.h>
 4 #define N 200010
 5 #define lson p << 1
 6 #define rson p << 1 | 1
 7 using namespace std;
 8
 9 struct Nod
10 {
11     int l , r ;
12     int va ; // Gap
13 }node[N << 2];
14
15 int pos[N] , val[N] , ans[N] ;
16
17 void build ( int l , int r , int p )
18 {
19     node[p].l = l ;
20     node[p].r = r ;
21     node[p].va = r - l + 1 ;
22     if ( l == r)
23         return ;
24     int mid = ( l + r ) >> 1 ;
25     build ( l , mid , lson ) ;
26     build ( mid + 1 , r , rson ) ;
27 }
28
29 int update ( int ps , int p )
30 {
31     node[p].va-- ;   //Gap - 1 ;
32     if ( node[p].l == node[p].r ) {
33         return node[p].l ; //return the position of the insert
34     }
35     if ( node[lson].va >= ps ) {
36         update ( ps , lson ) ;//when lson‘s Gap equal to or greater than the insertion location , inserted to the left
37     }
38     else {
39         ps -= node[lson].va ;//when Gap on the left is less than the ps , insert the right side , the right of the insertion laction is
40                                 // ps minus Gap on the left
41         update ( ps , rson ) ;
42     }
43 }
44
45 int main ()
46 {
47     //freopen ( "a.txt" , "r" , stdin ) ;
48     int n ;
49     while (~scanf ("%d" , &n ) ) {
50         build ( 1 , n , 1 ) ;
51         for ( int i = 1 ; i <= n ; i++ ) {
52             scanf ("%d%d" , pos + i , val + i ) ;
53         }
54         for ( int i = n ; i >= 1 ; i-- ) {
55             int id = update ( pos[i] + 1 , 1 ) ;    // get the insert position
56             ans[id] = val[i] ;  // in ans Array
57         }
58         for ( int i = 1 ; i < n ; i++ ) {
59             printf ( "%d " , ans[i] ) ;
60         }
61         printf ( "%d\n" , ans[n] ) ;
62     }
63     return 0 ;
64 }

倒推法

集训时大神介绍了一种能节省空间的写法：

 1 #include<iostream>
 2 #include<stdio.h>
 3 #include<string.h>
 4 #define N 200010
 5 #define lson o << 1 , l , mid
 6 #define rson o << 1 | 1 , mid + 1 , r
 7 using namespace std;
 8
 9 int va[N << 2] ; // Gap
10
11 int pos[N] , val[N] , ans[N] ;
12
13 void build (int o , int l , int r )
14 {
15     va[o] = r - l + 1 ;
16     if ( l == r )
17         return ;
18     int mid = ( l + r ) >> 1 ;
19     build ( lson ) ;
20     build ( rson ) ;
21 }
22
23 int update ( int ps ,int o , int l , int r  )
24 {
25     va[o]-- ;   //Gap - 1 ;
26     if ( l == r ) {
27         return l ; //return the position of the insert
28     }
29     int mid = ( l + r ) >> 1 ;
30     if ( va[o << 1] >= ps ) {
31         update ( ps , lson ) ;//when lson‘s Gap equal to or greater than the insertion location , inserted to the left
32     }
33     else {
34         ps -= va[o << 1] ;//when Gap on the left is less than the ps , insert the right side , the right of the insertion laction is
35                                 // ps minus Gap on the left
36         update ( ps , rson ) ;
37     }
38 }
39
40 int main ()
41 {
42     //freopen ( "a.txt" , "r" , stdin ) ;
43     int n ;
44     while (~scanf ("%d" , &n ) ) {
45         build ( 1 , 1 , n ) ;
46         for ( int i = 1 ; i <= n ; i++ ) {
47             scanf ("%d%d" , pos + i , val + i ) ;
48         }
49         for ( int i = n ; i >= 1 ; i-- ) {
50             int id = update ( pos[i] + 1 , 1 , 1 , n ) ;    // get the insert position
51             ans[id] = val[i] ;  // in ans Array
52         }
53         for ( int i = 1 ; i < n ; i++ ) {
54             printf ( "%d " , ans[i] ) ;
55         }
56         printf ( "%d\n" , ans[n] ) ;
57     }
58     return 0 ;
59 }

省了4000k