C - A Simple Problem with Integers ——线段树_区间更新

Think:

1知识点：线段树-区间更新-区间查询-lazy标记

2题意分析：区间更新+区间查询

3反思：

1>单点更新会超时

2>lazy标记区间更新AC

vjudge题目链接

以下为Time Limit Exceeded代码——单点更新整个区间超时

#include <cstdio>
#include <cstring>
#include <algorithm>

using namespace std;

typedef long long LL;
const int N = 101400;

struct Node{
LL num;
}node[N<<2];

void Build(int l, int r, int rt);
void Updata(int rt);
LL find(int L, int R, int l, int r, int rt);
void add_v(int L, int R, int v, int l, int r, int rt);

int main(){
int n, m, L, R, v;
char st[14];
while(~scanf("%d %d", &n, &m)){
Build(1, n, 1);
while(m--){
scanf("%s", st);
if(st[0] == 'Q'){
scanf("%d %d", &L, &R);
printf("%lld\n", find(L, R, 1, n, 1));
}
else if(st[0] == 'C'){
scanf("%d %d %d", &L, &R, &v);
add_v(L, R, v, 1, n, 1);
}
}
}
}
void Build(int l, int r, int rt){
if(l == r){
scanf("%lld", &node[rt].num);
return;
}
int mid = (l+r)/2;
Build(l, mid, rt<<1);
Build(mid+1, r, rt<<1|1);
Updata(rt);
}
void Updata(int rt){
node[rt].num = node[rt<<1].num + node[rt<<1|1].num;
}
LL find(int L, int R, int l, int r, int rt){
if(L <= l && r <= R)
return node[rt].num;
int mid = (l+r)/2;
LL sum = 0;
if(L <= mid)
sum += find(L, R, l, mid, rt<<1);
if(R > mid)
sum += find(L, R, mid+1, r, rt<<1|1);
return sum;
}
void add_v(int L, int R, int v, int l, int r, int rt){
if(l == r){
node[rt].num += v;
return;
}
int mid = (l+r)/2;
if(L <= mid)
add_v(L, R, v, l, mid, rt<<1);
if(R > mid)
add_v(L, R, v, mid+1, r, rt<<1|1);
Updata(rt);
}

以下为Accepted代码——lazy标记区间更新

#include <cstdio>
#include <cstring>
#include <algorithm>

using namespace std;

typedef long long LL;
const int N = 101400;

struct Node{
LL num;
}node[N<<2];
LL lazy[N<<2];/*lazy标记，用则更新*/

void Build(int l, int r, int rt);
void Updata(int rt);
void down(int rt, int len);/*更新lazy数组标记的当前根节点的下一层*/
LL find(int L, int R, int l, int r, int rt);
void add_v(int L, int R, int v, int l, int r, int rt);

int main(){
int n, m, L, R, v;
char st[14];
while(~scanf("%d %d", &n, &m)){
Build(1, n, 1);
while(m--){
scanf("%s", st);
if(st[0] == 'Q'){
scanf("%d %d", &L, &R);
printf("%lld\n", find(L, R, 1, n, 1));
}
else if(st[0] == 'C'){
scanf("%d %d %d", &L, &R, &v);
add_v(L, R, v, 1, n, 1);
}
}
}
}
void Build(int l, int r, int rt){
lazy[rt] = 0;
if(l == r){
scanf("%lld", &node[rt].num);
return;
}
int mid = (l+r)/2;
Build(l, mid, rt<<1);
Build(mid+1, r, rt<<1|1);
Updata(rt);
}
void Updata(int rt){
node[rt].num = node[rt<<1].num + node[rt<<1|1].num;
}
void down(int rt, int len){
if(lazy[rt]){
lazy[rt<<1] += lazy[rt];
lazy[rt<<1|1] += lazy[rt];
node[rt<<1].num += lazy[rt]*(len - (len>>1));/*lazy[rt]*(l-mid+1)*/
node[rt<<1|1].num += lazy[rt]*(len>>1);/*lazy[rt]*(l-(mid+1)+1)**/
lazy[rt] = 0;
}
}
LL find(int L, int R, int l, int r, int rt){
if(L <= l && r <= R)
return node[rt].num;
down(rt, r-l+1);
int mid = (l+r)/2;
LL sum = 0;
if(L <= mid)
sum += find(L, R, l, mid, rt<<1);
if(R > mid)
sum += find(L, R, mid+1, r, rt<<1|1);
return sum;
}
void add_v(int L, int R, int v, int l, int r, int rt){
if(L <= l && r <= R){
lazy[rt] += v;
node[rt].num += v*(r-l+1);
return;
}
down(rt, r-l+1);
int mid = (l+r)/2;
if(L <= mid)
add_v(L, R, v, l, mid, rt<<1);
if(R > mid)
add_v(L, R, v, mid+1, r, rt<<1|1);
Updata(rt);
}