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POJ 3264-Balanced Lineup（线段树：单点更新+区间查询）

2024-07-18 08:36:50   224人阅读

Balanced Lineup
Time Limit: 5000MS Memory Limit: 65536K
Total Submissions: 34522 Accepted: 16224
Case Time Limit: 2000MS

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.

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

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 Input

6 3
1
7
3
4
2
5
1 5
4 6
2 2

Sample Output

6
3
0

Source

USACO 2007 January Silver
经ysj一说我也准备噜线段树了 那天下午他来给我讲了一下线段树，先敲个模板再说。。
题意是找某个区间的最大值和最小值的差值。
#include <cstdio>
#include <iostream>
#include <algorithm>
#include <cstring>
#include <cctype>
#include <cmath>
#include <cstdlib>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <list>
#define LL long long
using namespace std;
const int INF=1<<27;
const int maxn=200010;
LL minn[maxn],maxx[maxn];
void update(LL root,LL l,LL r,LL p,LL v)//单点更新
{
	if(l==r) maxx[root]=v;minn[root]=v;
	if(l<r)
	{
		LL mid=(l+r)/2;
		if(p<=mid) update(root*2,l,mid,p,v);
		else update(root*2+1,mid+1,r,p,v);
		maxx[root]=max(maxx[root*2],maxx[root*2+1]);
		minn[root]=min(minn[root*2],minn[root*2+1]);
	}
}
LL query_min(LL root,LL l,LL r,LL ql,LL qr)
{
	LL mid=(l+r)/2,ans=INF;
	if(ql<=l&&qr>=r) return minn[root];
	if(ql<=mid) ans=min(ans,query_min(root*2,l,mid,ql,qr));
	if(qr>mid) ans=min(ans,query_min(root*2+1,mid+1,r,ql,qr));
	return ans;
}
LL query_max(LL root,LL l,LL r,LL ql,LL qr)
{
	LL mid=(l+r)/2,ans=-INF;
	if(ql<=l&&qr>=r) return maxx[root];
	if(ql<=mid) ans=max(ans,query_max(root*2,l,mid,ql,qr));
	if(qr>mid) ans=max(ans,query_max(root*2+1,mid+1,r,ql,qr));
	return ans;
}
int main()
{
  int N,Q,i,v;
  while(~scanf("%lld%lld",&N,&Q))
  {
  	for(i=1;i<=N;i++)
	{
		scanf("%lld",&v);
		update(1,1,N,i,v);
	}
	while(Q--)
	{
		int ql,qr;
		scanf("%lld%lld",&ql,&qr);
		printf("%lld\n",query_max(1,1,N,ql,qr)-query_min(1,1,N,ql,qr));
	}
  }
  return 0;
}



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