A Simple Problem with Integers
Time Limit:5000MS Memory Limit:131072K
Case Time Limit:2000MS
Description
You have N integers, A1, A2, ... , 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 A1, A2, ... , AN. -1000000000 ≤ Ai ≤ 1000000000.
Each of the next Q lines represents an operation.
"C a b c" means adding c to each of Aa, Aa+1, ... , Ab. -10000 ≤ c ≤ 10000.
"Q a b" means querying the sum of Aa, Aa+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.
题解：本题也是线段树系列的模板题之一，要求的是成段更新+懒惰标记。PS：原题的说明有问题，上面说的“C a b c”中的c的范围其实在int32之外，需要使用long long，否则定是WA，真心坑爹，连WA多次，还是在discuss中看到的原因。
稍微讲解下代码中的一些细节: step<<1 与 step<<1|1，意思分别是step*2 和step*+1，具体为什么，可以回去复习一下位运算
AC代码如下：
1 #include <cstdio> 2 #include <cstring> 3 4 typedef long long ll; 5 const int LEN = 100000 * 4; 6 7 struct line 8 { 9 int left; 10 int right; 11 ll value; 12 ll lazy; //懒惰标记 13 }line[LEN]; 14 15 void buildt(int l, int r, int step) //建树初始化 16 { 17 line[step].left = l; 18 line[step].right = r; 19 line[step].lazy = 0; 20 line[step].value = 0; 21 if (l == r) 22 return; 23 int mid = (l + r) / 2; 24 buildt(l, mid, step<<1); 25 buildt(mid+1, r, step<<1|1); 26 } 27 28 void pushdown(int step) 29 { 30 if (line[step].left == line[step].right) //如果更新到最深处的子节点，返回 31 return; 32 if (line[step].lazy != 0){ //如果有懒惰标记，向下传递懒惰标记且更新两个子节点的值 33 line[step<<1].lazy += line[step].lazy; 34 line[step<<1|1].lazy += line[step].lazy; 35 line[step<<1].value += (line[step<<1].right - line[step<<1].left + 1) * line[step].lazy; 36 line[step<<1|1].value += (line[step<<1|1].right - line[step<<1|1].left + 1) * line[step].lazy; 37 line[step].lazy = 0; 38 } 39 } 40 41 void update(int l, int r, ll v, int step) 42 { 43 line[step].value += v * (r-l+1); //更新到当前节点，就在当前节点的value中加上增加的值 44 pushdown(step); 45 if (line[step].left == l && line[step].right == r){ //如果到达目标线段，做上懒惰标记，返回 46 line[step].lazy = v; 47 return; 48 } 49 int mid = (line[step].left + line[step].right) / 2; 50 if (r <= mid) 51 update(l, r, v, step<<1); 52 else if (l > mid) 53 update(l, r, v, step<<1|1); 54 else{ 55 update(l, mid, v, step<<1); 56 update(mid+1, r, v, step<<1|1); 57 } 58 } 59 60 ll findans(int l, int r, int step) 61 { 62 if (l == line[step].left && r == line[step].right) //如果找到目标线段，返回值 63 return line[step].value; 64 pushdown(step); 65 int mid = (line[step].left + line[step].right) / 2; 66 if (r <= mid) 67 return findans(l, r, step<<1); 68 else if (l > mid) 69 return findans(l, r, step<<1|1); 70 else 71 return findans(l, mid, step<<1) + findans(mid+1, r, step<<1|1); 72 } 73 74 int main() 75 { 76 //freopen("in.txt", "r", stdin); 77 int n, q; 78 scanf("%d %d", &n, &q); 79 buildt(1, n, 1); 80 for(int i = 1; i <= n; i++){ 81 ll t; 82 scanf("%I64d", &t); 83 update(i, i, t, 1); 84 } 85 for(int i = 0; i < q; i++){ 86 char query[2]; 87 scanf("%s", query); 88 if (query[0] == 'C'){ 89 int a, b; 90 ll c; 91 scanf("%d %d %I64d", &a, &b, &c); 92 update(a, b, c, 1); 93 } 94 else if (query[0] == 'Q'){ 95 int a, b; 96 scanf("%d %d", &a, &b); 97 printf("%I64d\n", findans(a, b, 1)); 98 } 99 } 100 return 0; 101 }