A Simple Problem with Integers（线段树）

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

The first line contains two numbers N and Q. 1 ≤ N,Q ≤ 100000.
The second line contains N numbers, the initial values of A₁, A₂, ... , A_N. -1000000000 ≤ A_i ≤ 1000000000.
Each of the next Q lines represents an operation.
"C abc" means adding c to each of A_a, A_a+1, ... , A_b. -10000 ≤ c ≤ 10000.
"Q ab" means querying the sum of A_a, A_a+1, ... , A_b.

Output

You need to answer all Q commands in order. One answer in a line.

Sample Input

10 51 2 3 4 5 6 7 8 9 10Q 4 4Q 1 10Q 2 4C 3 6 3Q 2 4

Sample Output

455915

解题思路：

区间更新，区间求和的模板题。

注意：数据会超Int范围。

AC代码：

#include <iostream>#include <cstdio>using namespace std;#define lson l, m, rt << 1#define rson m + 1, r, rt << 1 | 1const int maxn = 100005;__int64 add[maxn << 2], sum[maxn << 2];void PushUp(int rt){    sum[rt] = sum[rt << 1] + sum[rt << 1 | 1];}void PushDown(int rt,int m){    if (add[rt])    {        add[rt << 1] += add[rt];        add[rt << 1 | 1] += add[rt];        sum[rt << 1] += add[rt] * (m - (m >> 1));        sum[rt << 1 | 1] += add[rt] * (m >> 1);        add[rt] = 0;    }}void build(int l,int r,int rt){    add[rt] = 0;    if (l == r)    {        scanf("%I64d", &sum[rt]);        return ;    }    int m = (l + r) >> 1;    build(lson);    build(rson);    PushUp(rt);}void update(int L, int R, __int64 c, int l, int r, int rt){    if (L <= l && r <= R)    {        add[rt] += c;        sum[rt] += c * (r - l + 1);        return ;    }    PushDown(rt , r - l + 1);    int m = (l + r) >> 1;    if (L <= m) update(L , R , c , lson);    if (m < R) update(L , R , c , rson);    PushUp(rt);}__int64 query(int L,int R,int l,int r,int rt){    if (L <= l && r <= R)    {        return sum[rt];    }    PushDown(rt , r - l + 1);    int m = (l + r) >> 1;    __int64 ret = 0;    if (L <= m) ret += query(L , R , lson);    if (m < R) ret += query(L , R , rson);    return ret;}int main(){    int n, q, a, b, c;    char ord[2];    scanf("%d%d", &n, &q);    build(1, n, 1);    while(q--)    {        scanf("%s", ord);        if(ord[0] == 'C')        {            scanf("%d%d%d", &a, &b, &c);            update(a, b, c, 1, n, 1);        }        else        {            scanf("%d%d", &a, &b);            printf("%I64d\n", query(a, b, 1, n, 1));        }    }    return 0;}