POJ3264 Balanced Lineup【RMQ】

Balanced Lineup

Time Limit: 5000MS		Memory Limit: 65536K
Total Submissions: 64936		Accepted: 30249
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

題目大意：給你一個數列，查詢區間[l,r]的最大值和最小值的差值，RMQ模板題

AC的C++程式碼:

#include<iostream>
#include<cmath>

using namespace std;

const int N=50010;
int a[N],dpmax[N][30],dpmin[N][30];

void ST(int n)
{
	for(int i=1;i<=n;i++)
	  dpmax[i][0]=dpmin[i][0]=a[i];
	for(int j=1;(1<<j)<=n;j++)
	  for(int i=1;i+(1<<j)-1<=n;i++){
	  	  dpmax[i][j]=max(dpmax[i][j-1],dpmax[i+(1<<(j-1))][j-1]);
	  	  dpmin[i][j]=min(dpmin[i][j-1],dpmin[i+(1<<(j-1))][j-1]);
	  }
}

//查詢陣列a的[l,r]區間的最值 【倍增】RMQ的ST表演算法
int RMQ_ST(int l,int r)
{
	int k=(int)(log((double)(r-l+1))/log(2.0));
	int maxval=max(dpmax[l][k],dpmax[r-(1<<k)+1][k]);
	int minval=min(dpmin[l][k],dpmin[r-(1<<k)+1][k]);
	return (maxval-minval);
}

int main()
{
	int n,q,l,r;
	scanf("%d%d",&n,&q);
	for(int i=1;i<=n;i++)
	  scanf("%d",&a[i]);
	ST(n);
	while(q--){
		scanf("%d%d",&l,&r);
		printf("%d\n",RMQ_ST(l,r));
	}
	return 0;
}