树状数组关于区间修改区间求和的问题

Total Submission(s) : 77   Accepted Submission(s) : 19

Problem Description

You have N integers, A₁,A₂, ... ,A_N. You need to deal with two kinds of operations. One type of operation is to add some given number to each number in a given interval. The other is to ask for the sum of numbers in a given interval.

 

Input

<p>The first line contains two numbers <i>N</i> and <i>Q</i>. 1 ≤ <i>N</i>,<i>Q</i> ≤ 100000.<br>The second line contains <i>N</i> numbers, the initial values of <i>A</i>₁, <i>A</i>₂, ... , <i>A_N</i>. -1000000000 ≤ <i>A_i</i> ≤ 1000000000.<br>Each of the next <i>Q</i> lines represents an operation.<br>"C <i>a</i> <i>b</i> <i>c</i>" means adding <i>c</i> to each of <i>A_a</i>, <i>A_a</i>₊₁, ... , <i>A_b</i>. -10000 ≤ <i>c</i> ≤ 10000.<br>"Q <i>a</i> <i>b</i>" means querying the sum of <i>A_a</i>, <i>A_a</i>₊₁, ... , <i>A_b</i>.</p>

 

Output

<p>You need to answer all <i>Q</i> commands in order. One answer in a line.</p>

 

Sample Input

10 5
1 2 3 4 5 6 7 8 9 10
Q 4 4
Q 1 10
Q 2 4
C 3 6 3
Q 2 4

 

Sample Output

4
55
9
15

题意：

就是给你N个数M个操作，然后输出每一个查询区间的和。 

这是最基础的区间修改区间求和的实现问题。

#if 0
#include<iostream>
#include<cstring>
#include<stdio.h>

using namespace std;
const int MAXN=100000+50;
typedef long long ll;
ll  b[MAXN],c[MAXN];
ll  a[MAXN]; 

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

void add_B(ll  *a,ll  x,ll  v)
{
	for( ; x>0; x-=lowbit(x))
		a[x]+=v;
}
ll sum_B(ll  *a,ll  x)
{
	ll  s=0;
	for(; x<MAXN; x+=lowbit(x))
	{
		s+=a[x];
	}
	
	return s;
}

void add_C(ll  *a,ll  x,ll v)
{
	for( ; x<MAXN; x+=lowbit(x))
	{
		a[x]+=v;
	}
	
}
ll sum_C(ll *a, ll x)
{
	ll s=0;
	for( ; x>0; x-=lowbit(x))
	{
		s+=a[x];
	}
	return s;
}

void add(ll x,ll v)
{
	add_B(b,x-1,v);
	add_C(c,x,v*x);
}
void go_add(ll a,ll b,ll v)
{
	add(b,v);
	add(a-1,-v); //
}

ll sum(ll x)
{
	return sum_C(c,x)+sum_B(b,x)*x;
}
ll go_sum(ll a,ll b)
{
	return sum(b)-sum(a-1);
}

int main()
{


	ll n,t;
	char ssc;

	scanf("%lld%lld",&n,&t);
	
	memset(a,0,sizeof(a));
	memset(b,0,sizeof(b));
	memset(c,0,sizeof(c));
	
	for(int i=3; i<=n+2; i++)
	{
		ll x;
		scanf("%lld",&x);
		go_add(i,i,x);
	}
	

	while(t--)
	{
		
		cin>>ssc;
		if(ssc=='Q')
		{
			ll ai,bi;
			
			scanf("%lld%lld",&ai,&bi);
			ai+=2;
			bi+=2;
	
			
			printf("%lld\n",go_sum(ai,bi));	
		}
		else if(ssc=='C')
		{
			ll ai,bi;
			ll v;
			scanf("%lld%lld%lld",&ai,&bi,&v);
			
			ai+=2;
			bi+=2;
			go_add(ai,bi,v);
		}

	}


}
#endif