POJ3264 Balanced Lineup (RMQ)

Balanced Lineup

Time Limit: 5000MSMemory Limit: 65536KTotal Submissions: 46339Accepted: 21738Case 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

可以线段树，也可以RMQ
都是模版，练练。
F[i, j]表示从第i个数起连续2^j个数中的最大值
利用倍增的思想。

#include <iostream>#include <cmath>#include <cstdio>using namespace std;const int maxn = 200005;int MAX[maxn][20];int MIN[maxn][20];int n, q;//f[i, j]表示从第i个数起连续2^j个数中的最大值void init() {    int i, j, lg = floor(log10(double(n))/log10(double(2)));    for (j = 1; j <= lg; ++j) {        //i + 2^(j-1) + 2^(j-1) - 1 <= n ==> i <= n + 1 - 2^j        for (i = 1; i <= n+1-(1<<j); ++i) {            //i ~ i + 2^(j-1) - 1, i + 2^(j-1) ~ i + 2^(j-1) + 2^(j-1) - 1            // ==> i ~ i + 2^j - 1            MAX[i][j] = max(MAX[i][j-1], MAX[i+(1<<(j-1))][j-1]);            MIN[i][j] = min(MIN[i][j-1], MIN[i+(1<<(j-1))][j-1]);        }    }}int main() {    int h, i, a, b, lg;    scanf("%d%d", &n, &q);    for (i = 1; i <= n; ++i) {        scanf("%d", &h);        MAX[i][0] = MIN[i][0] = h;    }    init();    for (i = 1; i <= q; ++i) {        scanf("%d%d", &a, &b);        if (a > b) swap(a, b);        lg = floor(log10(double(b-a+1))/log10(double(2)));        printf("%d\n", max(MAX[a][lg], MAX[b-(1<<lg)+1][lg])-min(MIN[a][lg], MIN[b-(1<<lg)+1][lg]));    }    return 0;}