A Simple Problem with Integers
POJ - 3468You 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.
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.
You need to answer all Q commands in order. One answer in a line.
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 4Sample Output
4 55 9 15Hint
The sums may exceed the range of 32-bit integers.
线段树更新查询模板
code:
#include <iostream> #include <cstdio> #include <cstring> using namespace std; #define MAX 100000 #define ll long long #define L rt<<1 #define R rt<<1|1 struct node{ int l,r; ll sum; ll lazy; //懒惰标记 int length;//区间长度 }Tree[MAX<<2]; void PushUp(int rt){ Tree[rt].sum = Tree[L].sum + Tree[R].sum; } void PushDown(int rt){ if(Tree[rt].lazy){ Tree[L].sum = Tree[L].sum + Tree[rt].lazy * Tree[L].length; Tree[R].sum = Tree[R].sum + Tree[rt].lazy * Tree[R].length; Tree[L].lazy += Tree[rt].lazy; Tree[R].lazy += Tree[rt].lazy; Tree[rt].lazy = 0; } } void Build(int rt,int l,int r){ Tree[rt].l = l; Tree[rt].r = r; Tree[rt].lazy = 0; Tree[rt].length = r - l + 1; if(l == r){ scanf("%lld",&Tree[rt].sum); return; } int mid = l + r >> 1; Build(L,l,mid); Build(R,mid+1,r); PushUp(rt); } void UpDate(int rt,int l,int r,int lazy){ if(Tree[rt].l == l && Tree[rt].r == r){ Tree[rt].sum += Tree[rt].length * lazy; Tree[rt].lazy += lazy; return; } PushDown(rt); int mid = Tree[rt].l + Tree[rt].r >> 1; if(mid >= r) UpDate(L,l,r,lazy); else if(l > mid) UpDate(R,l,r,lazy); else{ UpDate(L,l,mid,lazy); UpDate(R,mid+1,r,lazy); } PushUp(rt); } ll Query(int rt,int l,int r){ if(Tree[rt].l == l && Tree[rt].r == r) return Tree[rt].sum; PushDown(rt); int mid = Tree[rt].l + Tree[rt].r >> 1; if(mid >= r) return Query(L,l,r); else if(l > mid) return Query(R,l,r); else{ return Query(L,l,mid) + Query(R,mid+1,r); } } int main(){ int n,m; scanf("%d%d",&n,&m); Build(1,1,n); int x,y,z; char op[3]; while(m--){ scanf("%s",op); if(op[0] == 'C'){ scanf("%d%d%d",&x,&y,&z); UpDate(1,x,y,z); } else{ scanf("%d%d",&x,&y); printf("%lld\n",Query(1,x,y)); } } return 0; }