### POJ3468 A Simple Problem with Integers 【線段樹】+【成段更新】

A Simple Problem with Integers
 Time Limit: 5000MS Memory Limit: 131072K Total Submissions: 57666 Accepted: 17546 Case Time Limit: 2000MS

Description

You have N integers, A1A2, ... , AN. 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 A1A2, ... , AN. -1000000000 ≤ Ai ≤ 1000000000.
Each of the next Q lines represents an operation.
"C a b c" means adding c to each of AaAa+1, ... , Ab. -10000 ≤ c ≤ 10000.
"Q a b" means querying the sum of AaAa+1, ... , Ab.

Output

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

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```

Hint

The sums may exceed the range of 32-bit integers.

## 2014-9-4 16:25:07更新

```#include <stdio.h>
#include <string.h>
#define maxn 100002
#define lson l, mid, rt << 1
#define rson mid + 1, r, rt << 1 | 1
typedef long long ll;

struct Node{
ll lazy, sum;
} tree[maxn << 2];

void pushUp(int rt){
tree[rt].sum = tree[rt << 1].sum + tree[rt << 1 | 1].sum;
}

void pushDown(int l, int r, int rt)
{
int mid = (l + r) >> 1;
tree[rt << 1].sum += (mid - l + 1) * tree[rt].lazy;
tree[rt << 1 | 1].sum += (r - mid) * tree[rt].lazy;
tree[rt << 1].lazy += tree[rt].lazy;
tree[rt << 1 | 1].lazy += tree[rt].lazy;
tree[rt].lazy = 0;
}

void build(int l, int r, int rt)
{
tree[rt].lazy = 0;
if(l == r){
scanf("%lld", &tree[rt].sum);
return;
}
int mid = (l + r) >> 1;
build(lson); build(rson);
pushUp(rt);
}

void update(int left, int right, ll val, int l, int r, int rt)
{
if(left == l && right == r){
tree[rt].sum += (r - l + 1) * val;
tree[rt].lazy += val; return;
}
int mid = (l + r) >> 1;
if(tree[rt].lazy) pushDown(l, r, rt);
if(right <= mid) update(left, right, val, lson);
else if(left > mid) update(left, right, val, rson);
else {
update(left, mid, val, lson);
update(mid + 1, right, val, rson);
}
pushUp(rt);
}

ll query(int left, int right, int l, int r, int rt)
{
if(left == l && right == r) return tree[rt].sum;
int mid = (l + r) >> 1;
if(tree[rt].lazy) pushDown(l, r, rt);
if(right <= mid) return query(left, right, lson);
else if(left > mid) return query(left, right, rson);
return query(left, mid, lson) + query(mid + 1, right, rson);
}

int main()
{
int n, m, i, a, b;
char com[2];
ll c;
while(scanf("%d%d", &n, &m) == 2){
build(1, n, 1);
while(m--){
scanf("%s%d%d", com, &a, &b);
if(com[0] == 'Q')
printf("%lld\n", query(a, b, 1, n, 1));
else{
scanf("%lld", &c);
update(a, b, c, 1, n, 1);
}
}
}
return 0;
}```

## RE了三次，發現是query函數內的pushdown函數位置放錯了。。改了下，終於A掉了。

```//#define DEBUG
#include <stdio.h>
#define maxn 100002
#define lson l, mid, rt << 1
#define rson mid + 1, r, rt << 1 | 1

long long tree[maxn << 2], arr[maxn], lazy[maxn << 2];

void pushUp(int rt)
{
tree[rt] = tree[rt << 1] + tree[rt << 1 | 1];
}

void pushDown(int l, int r, int rt)
{
int mid = (l + r) >> 1;

tree[rt << 1] += (mid - l + 1) * lazy[rt];
tree[rt << 1 | 1] += (r - mid) * lazy[rt];

lazy[rt << 1] += lazy[rt];
lazy[rt << 1 | 1] += lazy[rt];
lazy[rt] = 0;
}

void build(int l, int r, int rt)
{
lazy[rt] = 0;
if(l == r){
tree[rt] = arr[r]; return;
}

int mid = (l + r) >> 1;
build(lson);
build(rson);

pushUp(rt);
}

void update(int left, int right, long long val, int l, int r, int rt)
{
if(left == l && right == r){
lazy[rt] += val; tree[rt] += val * (r - l + 1); return;
} //include l == r

if(lazy[rt]) pushDown(l, r, rt);

int mid = (l + r) >> 1;
if(right <= mid) update(left, right, val, lson);
else if(left > mid) update(left, right, val, rson);
else{
update(left, mid, val, lson);
update(mid + 1, right, val, rson);
}

pushUp(rt);
}

long long query(int left, int right, int l, int r, int rt)
{
if(left == l && right == r)
return tree[rt];

if(lazy[rt]) pushDown(l, r, rt);

int mid = (l + r) >> 1;
if(right <= mid){
return query(left, right, lson);
}else if(left > mid){
return query(left, right, rson);
}else{
return query(left, mid, lson) + query(mid + 1, right, rson);
}
}

int main()
{
#ifdef DEBUG
freopen("../stdin.txt", "r", stdin);
freopen("../stdout.txt", "w", stdout);
#endif

int n, q, i, a, b;
long long c;
char com[2];
while(scanf("%d%d", &n, &q) == 2){
for(i = 1; i <= n; ++i)
scanf("%lld", arr + i);
build(1, n, 1);

while(q--){
scanf("%s%d%d", com, &a, &b);
if(com[0] == 'C'){
scanf("%lld", &c);
update(a, b, c, 1, n, 1);
}else printf("%lld\n", query(a, b, 1, n, 1));
}
}
return 0;
}```