1636: [Usaco2007 Jan]Balanced Lineup
Time Limit: 5 Sec Memory Limit: 64 MB
Submit: 909 Solved: 644
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Description
For the daily milking, Farmer John‘s N cows (1 <= N <= 50,000) always line up in the same order. One day Farmer John decides to organize a game of Ultimate Frisbee with some of the cows. To keep things simple, he will take a contiguous range of cows from the milking lineup to play the game. However, for all the cows to have fun they should not differ too much in height. Farmer John has made a list of Q (1 <= Q <= 200,000) potential groups of cows and their heights (1 <= height <= 1,000,000). For each group, he wants your help to determine the difference in height between the shortest and the tallest cow in the group.
每天,农夫 John 的N(1 <= N <= 50,000)头牛总是按同一序列排队. 有一天, John
决定让一些牛们玩一场飞盘比赛. 他准备找一群在对列中为置连续的牛来进行比赛.
但是为了避免水平悬殊,牛的身高不应该相差太大.
John 准备了Q (1 <= Q <= 180,000) 个可能的牛的选择和所有牛的身高 (1 <=
身高 <= 1,000,000). 他想知道每一组里面最高和最低的牛的身高差别.
注意: 在最大数据上, 输入和输出将占用大部分运行时间.
Input
* Line 1: Two space-separated integers, N and Q. * Lines 2..N+1: Line i+1 contains a single integer that is the height of cow i * Lines N+2..N+Q+1: Two integers A and B (1 <= A <= B <= N), representing the range of cows from A to B inclusive.
Output
6 3
1
7
3
4
2
5
1 5
4 6
2 2
Sample Input
* Lines 1..Q: Each line contains a single integer that is a response
to a reply and indicates the difference in height between the
tallest and shortest cow in the range.
Sample Output
6
3
0
HINT
Source
Analysis
线段树裸题，区间询问，无修改
Code
1 #include<cstdio>
2 #include<iostream>
3 #define mid (L+R)/2
4 #define lc (rt<<1)
5 #define rc (rt<<1|1)
6 #define maxn 50000
7 using namespace std;
8
9 const int inf = 0x3f3f3f3f;
10
11 int n,q,a,b;
12
13 struct node{
14 int maxx,minn;
15 }Tree[maxn*10];
16
17 void maintain(int rt){
18 Tree[rt].maxx = max(Tree[lc].maxx,Tree[rc].maxx);
19 Tree[rt].minn = min(Tree[lc].minn,Tree[rc].minn);
20 }
21
22 void build(int rt,int L,int R){
23 if(L == R){
24 scanf("%d",&Tree[rt].maxx);
25 Tree[rt].minn = Tree[rt].maxx;
26 }else{
27 build(lc,L,mid);
28 build(rc,mid+1,R);
29
30 maintain(rt);
31 }
32 }
33
34 int max_query(int rt,int L,int R,int qL,int qR){
35 if(qL <= L && R <= qR){
36 return Tree[rt].maxx;
37 }else{
38 int ans = 0;
39 if(qL <= mid) ans = max(ans,max_query(lc,L,mid,qL,qR));
40 if(qR > mid) ans = max(ans,max_query(rc,mid+1,R,qL,qR));
41 return ans;
42 }
43 }
44
45 int min_query(int rt,int L,int R,int qL,int qR){
46 if(qL <= L && R <= qR){
47 return Tree[rt].minn;
48 }else{
49 int ans = inf;
50 if(qL <= mid) ans = min(ans,min_query(lc,L,mid,qL,qR));
51 if(qR > mid) ans = min(ans,min_query(rc,mid+1,R,qL,qR));
52 return ans;
53 }
54 }
55
56 int main(){
57 scanf("%d%d",&n,&q);
58 build(1,1,n);
59
60 for(int i = 1;i <= q;i++){
61 scanf("%d%d",&a,&b);
62 printf("%d\n",max_query(1,1,n,a,b)-min_query(1,1,n,a,b));
63 }
64
65
66 return 0;
67 }
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