描述
Ryuji is not a good student, and he doesn’t want to study. But there are n books he should learn, each book has its knowledge a[i].
Unfortunately, the longer he learns, the fewer he gets.
That means, if he reads books from ll to rr, he will get a[l] \times L + a[l+1] \times (L-1) + \cdots + a[r-1] \times 2 + a[r]a[l]×L+a[l+1]×(L−1)+⋯+a[r−1]×2+a[r] (LL is the length of [ ll, rr ] that equals to r - l + 1r−l+1).
Now Ryuji has qq questions, you should answer him:
\11. If the question type is 11, you should answer how much knowledge he will get after he reads books [ ll, rr ].
\22. If the question type is 22, Ryuji will change the ith book’s knowledge to a new value.
Input
First line contains two integers nn and qq (nn, q \le 100000q≤100000).
The next line contains n integers represent a[i]( a[i] \le 1e9)ai .
Then in next qq line each line contains three integers aa, bb, cc, if a = 1a=1, it means question type is 11, and bb, ccrepresents [ ll , rr ]. if a = 2a=2 , it means question type is 22 , and bb, cc means Ryuji changes the bth book’ knowledge to cc
Output
For each question, output one line with one integer represent the answer.
样例输入
5 3
1 2 3 4 5
1 1 3
2 5 0
1 4 5
样例输出
10
8
题目来源
思路
题目给了n个数,有两种操作,第一种是求区间[l,r]
的区间内所有前缀和的和,第二种是单点修改.
比如我们举个栗子
1 2 3 4 5 6 7 8 9 10
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7
1 2 3 4 5 6
1 2 3 4 5
1 2 3 4
1 2 3
1 2
1
用两个树状数组维护一下,第一个维护一下 的和,如上面的数字。
然后查询的时候我们只需要用上面的区间和减去 的区间和。
单点修改直接改就行。
代码
#include <bits/stdc++.h>
using namespace std;
#define mem(a, b) memset(a, b, sizeof(a))
typedef long long ll;
typedef pair<ll, ll> pir;
const ll N = 1e5 + 10;
ll a[N];
struct binaryTree
{
ll c[N], NN;
ll init(ll n)
{
mem(c, 0);
NN = n;
}
ll lowbit(ll x)
{
return x & -x;
}
ll sum(ll n)
{
ll sum = 0;
while (n > 0)
{
sum += c[n];
n = n - lowbit(n);
}
return sum;
}
ll query(ll l, ll r)
{
return sum(r) - sum(l - 1);
}
void add(ll i, ll k)
{
while (i <= NN)
{
c[i] += k;
i += lowbit(i);
}
}
} ac1, ac2;
int main()
{
//freopen("in.txt", "r", stdin);
ll n, q, op, x, y;
scanf("%lld%lld", &n, &q);
ac1.init(n), ac2.init(n);
for (ll i = 1; i <= n; i++)
{
scanf("%lld", &a[i]);
ac1.add(i, a[i]);
ac2.add(i, (n - i + 1) * a[i]);
}
while (q--)
{
scanf("%lld%lld%lld", &op, &x, &y);
if (op == 1)
{
ll L = n - y;
ll ans = ac2.query(x, y) - L * ac1.query(x, y);
printf("%lld\n", ans);
}
else if (op == 2)
{
ac1.add(x, y - a[x]);
ac2.add(x, (y - a[x]) * (n - x + 1));
a[x] = y;
}
}
return 0;
}