算法模板之RMQ线段树（HDU 1754 I Hate It）

RMQ (Range Minimum/Maximum Query)问题是指：对于长度为n的数列A，回答若干询问RMQ(A,i,j)(i,j<=n)，返回数列A中下标在i,j里的最小(大）值，也就是说，RMQ问题是指求区间最值的问题。

模板总结归纳：

const int MAXNODE = 1 << 19;
const int MAXN = 2e6 + 10;

struct NODE{
	int value;
	int left, right;
}node[MAXNODE];

int father[MAXN];

void BuildTree(int i, int left, int right){
	node[i].left = left;
	node[i].right = right;
	node[i].value = 0;
	if(left == right) {
		father[left] = i;
		return;
	}
	BuildTree(i << 1, left, (int)(floor(left + right)/ 2.0));
	BuildTree((i << 1) + 1, (int)(floor((left + right)/ 2.0)) + 1, right);
}

void UpdateTree(int ri){
	if(ri == 1) return;
	int fi = ri / 2;
	int a = node[fi << 1].value;
	int b = node[(fi << 1) + 1].value;
	node[fi].value = max(a, b);
	UpdateTree(ri / 2);
}

int MAX;
void Query(int i, int l, int r){
	if(node[i].left == l && node[i].right == r){
		MAX = max(MAX, node[i].value);
		return;
	}
	i = i << 1;
	if(l <= node[i].right){
		if(r <= node[i].right) Query(i, l, r);
		else Query(i, l, node[i].right);
	}
	i++;
	if(r >= node[i].left){
		if(l >= node[i].left) Query(i, l, r);
			else Query(i, node[i].left, r);
	}
}

实战模板题 ： HDU1754 I Hate It

//HDU 1754 I Hate It
//RMQ线段树
 
#include<cstdio>
#include<iostream>
#include<cmath>
#include<string>
#include<algorithm>
using namespace std;

const int MAXNODE = 1 << 19;
const int MAXN = 2e6 + 10;

struct NODE{
	int value;
	int left, right;
}node[MAXNODE];

int father[MAXN];

void BuildTree(int i, int left, int right){
	node[i].left = left;
	node[i].right = right;
	node[i].value = 0;
	if(left == right) {
		father[left] = i;
		return;
	}
	BuildTree(i << 1, left, (int)(floor(left + right)/ 2.0));
	BuildTree((i << 1) + 1, (int)(floor((left + right)/ 2.0)) + 1, right);
}

void UpdateTree(int ri){
	if(ri == 1) return;
	int fi = ri / 2;
	int a = node[fi << 1].value;
	int b = node[(fi << 1) + 1].value;
	node[fi].value = max(a, b);
	UpdateTree(ri / 2);
}

int MAX;
void Query(int i, int l, int r){
	if(node[i].left == l && node[i].right == r){
		MAX = max(MAX, node[i].value);
		return;
	}
	i = i << 1;
	if(l <= node[i].right){
		if(r <= node[i].right) Query(i, l, r);
		else Query(i, l, node[i].right);
	}
	i++;
	if(r >= node[i].left){
		if(l >= node[i].left) Query(i, l, r);
			else Query(i, node[i].left, r);
	}
}

int main()
{
	int n, m, g;
	ios::sync_with_stdio(false);
	while(cin  >> n >> m){
		BuildTree(1, 1, n);
		for(int i = 1; i <= n; i++)
		{
			cin >> g;
			node[father[i]].value = g;
			UpdateTree(father[i]);
		}
		string op;
		int a, b;
		while(m--)
		{
			cin >> op >> a >> b;
			if(op[0] == 'Q'){
				MAX = 0;
				Query(1, a, b);
				cout << MAX << endl;
			}
			else{
				node[father[a]].value = b;
				UpdateTree(father[a]);
			}
		}
	}
	return 0;
}