[kuangbin带你飞]专题七 线段树 ABCDE 题解，持续更新

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【A HDU 1166】

#include <cstdio>
#include <cstring>
#include <iostream>
using namespace std;
const int maxn = 500005;
struct node{
int l,r,sum;
}Tree[maxn<<2];
int a[maxn];
void Push_Up(int rt){
Tree[rt].sum = Tree[rt<<1].sum+Tree[rt<<1|1].sum;
}
void Build(int l,int r,int rt){
Tree[rt].l=l,Tree[rt].r=r;
if(l==r){
Tree[rt].sum=a[l];
return ;
}
int mid=(Tree[rt].l+Tree[rt].r)>>1;
Build(l,mid,rt<<1);
Build(mid+1,r,rt<<1|1);
Push_Up(rt);
}
void Update(int id,int val,int l,int r,int rt){
if(Tree[rt].l==id&&Tree[rt].r==id){
Tree[rt].sum+=val;
return ;
}
int mid=(Tree[rt].l+Tree[rt].r)>>1;
if(id<=mid) Update(id,val,l,mid,rt<<1);
else Update(id,val,mid+1,r,rt<<1|1);
Push_Up(rt);
}
int query_ans(int L,int R,int l,int r,int rt){
if(L<=Tree[rt].l&&Tree[rt].r<=R){
return Tree[rt].sum;
}
int ret=0;
int mid=(Tree[rt].l+Tree[rt].r)>>1;
if(L<=mid) ret+=query_ans(L,R,l,mid,rt<<1);
if(mid<R)  ret+=query_ans(L,R,mid+1,r,rt<<1|1);
return ret;
}
int main(){
int tt,n,l,r,ncase=1;
scanf("%d",&tt);
while(tt--){
scanf("%d",&n);
for(int i=1; i<=n; i++) scanf("%d",&a[i]);
memset(Tree,0,sizeof(Tree));
Build(1,n,1);
char op[10];
printf("Case %d:\n",ncase++);
while(scanf("%s",op)){
if(strcmp(op,"End")==0) break;
scanf("%d%d",&l,&r);
if(op[0]=='Q') printf("%d\n",query_ans(l,r,1,n,1));
if(op[0]=='A') Update(l,r,1,n,1);
if(op[0]=='S') Update(l,-r,1,n,1);
}
}
return 0;
}

【B HDU 1754 I Hate It】

#include <cstdio>
#include <iostream>
#include <algorithm>
using namespace std;
const int maxn = 200010;
struct node{
int l,r,maxx;
}Tree[maxn<<2];
int a[maxn];
void Push_Up(int rt){
Tree[rt].maxx = max(Tree[rt<<1].maxx,Tree[rt<<1|1].maxx);
}
void Build(int l,int r,int rt){
Tree[rt].l=l,Tree[rt].r=r;
if(l==r){
Tree[rt].maxx=a[l];
return ;
}
int mid=(l+r)>>1;
Build(l,mid,rt<<1);
Build(mid+1,r,rt<<1|1);
Push_Up(rt);
}
void Update(int id,int val,int l,int r,int rt){
if(Tree[rt].l==id&&Tree[rt].r==id){
Tree[rt].maxx=val;
return ;
}
int mid=(Tree[rt].l+Tree[rt].r)>>1;
if(id<=mid) Update(id,val,l,mid,rt<<1);
else        Update(id,val,mid+1,r,rt<<1|1);
Push_Up(rt);
}
int query_ans(int L,int R,int l,int r,int rt){
if(L<=Tree[rt].l&&Tree[rt].r<=R){
return Tree[rt].maxx;
}
int ret=0;
int mid=(Tree[rt].l+Tree[rt].r)>>1;
if(L<=mid) ret=max(ret,query_ans(L,R,l,mid,rt<<1));
if(mid<R)  ret=max(ret,query_ans(L,R,mid+1,r,rt<<1|1));
return ret;
}
int main(){
int n,m,l,r;
while(~scanf("%d%d",&n,&m)){
for(int i=1; i<=n; i++) scanf("%d",&a[i]);
Build(1,n,1);
char op[10];
while(m--){
scanf("%s%d%d",op,&l,&r);
if(op[0]=='U') Update(l,r,1,n,1);
else           printf("%d\n",query_ans(l,r,1,n,1));
}
}
return 0;
}

【C POJ 3468 A Simple Problem with Integers】

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
#define ll long long
const int maxn = 100010;
struct node{
int l,r;
ll sum,lazy;
}Tree[maxn<<2];
int a[maxn];
void Push_Up(int rt){
Tree[rt].sum = Tree[rt<<1].sum+Tree[rt<<1|1].sum;
}
void Push_Down(int rt,int m){
if(Tree[rt].lazy!=0){
Tree[rt<<1].lazy+=Tree[rt].lazy;
Tree[rt<<1|1].lazy+=Tree[rt].lazy;
Tree[rt<<1].sum+=(m-(m>>1))*Tree[rt].lazy;
Tree[rt<<1|1].sum+=(m>>1)*Tree[rt].lazy;
Tree[rt].lazy=0;
}
}
void Build(int l,int r,int rt){
Tree[rt].l=l,Tree[rt].r=r,Tree[rt].lazy=0;
if(l==r){
Tree[rt].sum=a[l];
return ;
}
int mid=(l+r)>>1;
Build(l,mid,rt<<1);
Build(mid+1,r,rt<<1|1);
Push_Up(rt);
}
void Update(int L,int R,int c,int rt){
if(L<=Tree[rt].l&&Tree[rt].r<=R){
Tree[rt].lazy+=c;
Tree[rt].sum+=(ll)c*(Tree[rt].r-Tree[rt].l+1);
return ;
}
Push_Down(rt,Tree[rt].r-Tree[rt].l+1);
int mid=(Tree[rt].l+Tree[rt].r)>>1;
if(L<=mid) Update(L,R,c,rt<<1);
if(mid<R)  Update(L,R,c,rt<<1|1);
Push_Up(rt);
}
ll query_ans(int L,int R,int rt){
if(L<=Tree[rt].l&&Tree[rt].r<=R){
return Tree[rt].sum;
}
Push_Down(rt,Tree[rt].r-Tree[rt].l+1);
ll ret=0;
int mid=(Tree[rt].l+Tree[rt].r)>>1;
if(L<=mid) ret+=query_ans(L,R,rt<<1);
if(mid<R)  ret+=query_ans(L,R,rt<<1|1);
return ret;
}
int main(){
int n,m,l,r,c;
while(~scanf("%d%d",&n,&m)){
for(int i=1; i<=n; i++) scanf("%d",&a[i]);
Build(1,n,1);
char op[10];
while(m--){
scanf("%s",op);
if(op[0]=='Q'){
scanf("%d%d",&l,&r);
printf("%I64d\n",query_ans(l,r,1));
}else{
scanf("%d%d%d",&l,&r,&c);
Update(l,r,c,1);
}
}
}
return 0;
}

【D
POJ 2528
Mayor's posters】

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
const int maxn = 10010;
struct node{
int l,r,lazy;
}Tree[maxn<<4];
struct seg{
int l,r;
seg(){}
seg(int l,int r):l(l),r(r){}
}query[maxn];
int X[maxn<<2],ans;
bool Hash[maxn<<4];
void Push_Down(int rt){
if(Tree[rt].lazy!=-1){
Tree[rt<<1].lazy=Tree[rt<<1|1].lazy=Tree[rt].lazy;
Tree[rt].lazy=-1;
}
}
void Build(int l,int r,int rt){
Tree[rt].l=l,Tree[rt].r=r,Tree[rt].lazy=-1;
if(l==r) return ;
int m=(l+r)>>1;
Build(l,m,rt<<1);
Build(m+1,r,rt<<1|1);
}
void Update(int L,int R,int c,int rt){
if(L<=Tree[rt].l&&Tree[rt].r<=R){
Tree[rt].lazy=c;
return ;
}
Push_Down(rt);
int mid=(Tree[rt].l+Tree[rt].r)>>1;
if(L<=mid) Update(L,R,c,rt<<1);
if(mid<R)  Update(L,R,c,rt<<1|1);
}
void query_ans(int l,int r,int rt){
if(Tree[rt].lazy!=-1){
if(!Hash[Tree[rt].lazy]) ans++;
Hash[Tree[rt].lazy]=true;
return ;
}
if(l==r) return ;
int mid=(Tree[rt].l+Tree[rt].r)>>1;
query_ans(l,mid,rt<<1);
query_ans(mid+1,r,rt<<1|1);
}
int main(){
int tt,n,l,r;
int cnt,m;
scanf("%d",&tt);
while(tt--){
cnt=0;
scanf("%d",&n);
for(int i=0; i<n; i++){
scanf("%d%d",&l,&r);
query[i]=seg(l,r);
X[cnt++]=l,X[cnt++]=r;
}
//离散化之后做成线段树
sort(X,X+cnt);
m=1;
for(int i=1; i<cnt; i++)  if(X[i]!=X[i-1])   X[m++]=X[i];
for(int i=m-1; i>=1; i--) if(X[i]!=X[i-1]+1) X[m++]=X[i-1]+1;
sort(X,X+m);
Build(0,m,1);
for(int i=0; i<n; i++){
int l=lower_bound(X,X+m,query[i].l)-X;
int r=lower_bound(X,X+m,query[i].r)-X;
Update(l,r,i,1);
}
memset(Hash,false,sizeof(Hash));
ans=0;
query_ans(0,m,1);
printf("%d\n",ans);
}
return 0;
}

【E HDU 1698 Just a Hook 】

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
#define ll long long
const int maxn = 100010;
struct node{
int l,r;
ll sum,lazy;
}Tree[maxn<<2];
int a[maxn];
void Push_Up(int rt){
Tree[rt].sum = Tree[rt<<1].sum+Tree[rt<<1|1].sum;
}
void Push_Down(int rt,int m){
if(Tree[rt].lazy!=0){
Tree[rt<<1].lazy=Tree[rt].lazy;
Tree[rt<<1|1].lazy=Tree[rt].lazy;
Tree[rt<<1].sum=(m-(m>>1))*Tree[rt].lazy;
Tree[rt<<1|1].sum=(m>>1)*Tree[rt].lazy;
Tree[rt].lazy=0;
}
}
void Build(int l,int r,int rt){
Tree[rt].l=l,Tree[rt].r=r,Tree[rt].lazy=0;
if(l==r){
Tree[rt].sum=1;
return ;
}
int mid=(l+r)>>1;
Build(l,mid,rt<<1);
Build(mid+1,r,rt<<1|1);
Push_Up(rt);
}
void Update(int L,int R,int c,int rt){
if(L<=Tree[rt].l&&Tree[rt].r<=R){
Tree[rt].lazy=c;
Tree[rt].sum=(ll)c*(Tree[rt].r-Tree[rt].l+1);
return ;
}
Push_Down(rt,Tree[rt].r-Tree[rt].l+1);
int mid=(Tree[rt].l+Tree[rt].r)>>1;
if(L<=mid) Update(L,R,c,rt<<1);
if(mid<R)  Update(L,R,c,rt<<1|1);
Push_Up(rt);
}
ll query_ans(int L,int R,int rt){
if(L<=Tree[rt].l&&Tree[rt].r<=R){
return Tree[rt].sum;
}
Push_Down(rt,Tree[rt].r-Tree[rt].l+1);
ll ret=0;
int mid=(Tree[rt].l+Tree[rt].r)>>1;
if(L<=mid) ret+=query_ans(L,R,rt<<1);
if(mid<R)  ret+=query_ans(L,R,rt<<1|1);
return ret;
}
int main(){
int tt,n,q;
int l,r,c,ncase=1;
scanf("%d",&tt);
while(tt--){
scanf("%d",&n);
Build(1,n,1);
scanf("%d",&q);
while(q--){
scanf("%d%d%d",&l,&r,&c);
Update(l,r,c,1);
}
printf("Case %d: The total value of the hook is %I64d.\n",ncase++,Tree[1].sum);
}
return 0;
}

【PS】这几个题都是非常简单的，因此只上了我自己的代码，如果不懂可以看其他人的博客的解题思路。专题以后的题，持续更新。。。