HDU 1754 I Hate It 树状数组求区间最值

题意：给n（1<=n<=200000）个人的初始成绩，现在要实时更新修改某一个人的成绩，查询[l , r]区间内成绩的最大值。

        具体参看：http://www.cnblogs.com/ambition/archive/2011/04/06/bit_rmq.html

Sure原创，转载请注明出处

#include <iostream>
#include <cstdio>
#include <memory.h>
#define MAX(a , b) ((a) > (b) ? (a) : (b))
using namespace std;
const int maxn = 200002;
int num[maxn],maxval[maxn];     //maxval[i] 表示 [i-lowbit(i)+1 , i]区间内的最大值
int m,n;

void read()
{
    for(int i=1;i<=n;i++)
    {
        scanf("%d",&num[i]);
    }
    return;
}

inline int lowbit(int x)
{
    return x & (-x);
}

void init()    //初始化maxval[]  < nlogn
{
    for(int i=1;i<=n;i++)
    {
        maxval[i] = num[i];
        for(int j=1;j<lowbit(i);j <<= 1)
        {
            maxval[i] = MAX(maxval[i] , maxval[i-j]);
        }
    }
    return;
}

void update(int pos,int val)    //把pos位值更新为val  logn
{
    num[pos] = val;
    for(int i=pos;i<=n;i+=lowbit(i))
    {
        maxval[i] = val;
        for(int j=1;j<lowbit(i);j <<= 1)
        {
            maxval[i] = MAX(maxval[i] , maxval[i-j]);
        }
    }
    return;
}

int query(int l,int r)   //询问[l,r]区间最大值  logn
{
    int ans = num[r];
    while(true)
    {
        ans = MAX(ans , num[r]);
        if(l == r) break;
        for(r -= 1;r-l >= lowbit(r);r -= lowbit(r))
        {
            ans = MAX(ans , maxval[r]);
        }
    }
    return ans;
}

void solve()
{
    char str[3];
    int x,y;
    while(m--)
    {
        scanf("%s %d %d",str,&x,&y);
        if(str[0] == 'U') update(x,y);
        else printf("%d\n",query(x,y));
    }
    return;
}

int main()
{
    while(~scanf("%d %d",&n,&m))
    {
        read();
        init();
        solve();
    }
    return 0;
}