SPOJ GSS1 && GSS3 (无更新/更新单点，并询问区间最大连续和)

http://www.spoj.com/problems/GSS1/

题意：无更新询问区间最大连续和。

做法：线段树每个节点维护sum[rt],maxsum[rt],lsum[rt],rsum[rt]，分别区间和、区间最大和、区间左端最大和和区间右端最大和。

　　查询时按从左到右扫，维护ans为最大连续和，rans为到该段的右端最大连续和，扫到每一段时有：

　　ans = max(ans,maxsum[rt]);

　　ans = max(ans,rans+lsum[rt]);
　　rans = max(rsum[rt],rans+sum[rt]);

 /*
  *Author:       Zhaofa Fang
  *Created time: 2013-09-05-22.18 星期四
  */
 #include <cstdio>
 #include <cstdlib>
 #include <sstream>
 #include <iostream>
 #include <cmath>
 #include <cstring>
 #include <algorithm>
 #include <string>
 #include <utility>
 #include <vector>
 #include <queue>
 #include <map>
 #include <set>
 using namespace std;

 typedef long long ll;
 typedef pair<int,int> PII;
 #define DEBUG(x) cout<< #x << ':' << x << endl
 #define FOR(i,s,t) for(int i = (s);i <= (t);i++)
 #define FORD(i,s,t) for(int i = (s);i >= (t);i--)
 #define REP(i,n) for(int i=0;i<(n);i++)
 #define REPD(i,n) for(int i=(n-1);i>=0;i--)
 #define PII pair<int,int>
 #define PB push_back
 #define ft first
 #define sd second
 #define lowbit(x) (x&(-x))
 #define INF (1<<30)
 #define eps (1e-8)

 #define lson l , m , rt<<1
 #define rson m + 1 , r , rt<<1|1
 const int maxn = ;
 int sum[maxn<<],maxsum[maxn<<],lsum[maxn<<],rsum[maxn<<];
 int rans,ans;
 void pushUp(int l,int r,int rt){
     sum[rt] = sum[rt<<] + sum[rt<<|];
     maxsum[rt] = max(maxsum[rt<<],maxsum[rt<<|]);
     maxsum[rt] = max(maxsum[rt],rsum[rt<<]+lsum[rt<<|]);
     lsum[rt] = max(lsum[rt<<],sum[rt<<]+lsum[rt<<|]);
     rsum[rt] = max(rsum[rt<<|],sum[rt<<|]+rsum[rt<<]);
 }
 void build(int l,int r,int rt){
     if(l == r){
         scanf("%d",&sum[rt]);
         lsum[rt] = rsum[rt] = maxsum[rt] = sum[rt];
         return;
     }
     int m = (l + r) >> ;
     build(lson);
     build(rson);
     pushUp(l,r,rt);
 }
 void query(int L,int R,int l,int r,int rt){
     if(L <= l && r <= R){
         ans = max(ans,maxsum[rt]);
         ans = max(ans,rans+lsum[rt]);
         rans = max(rsum[rt],rans+sum[rt]);
         return;
     }
     int m = (l + r) >> ;
     if(L <= m)query(L,R,lson);
     if(m < R)query(L,R,rson);
 }
 int main(){
     //freopen("in","r",stdin);
     //freopen("out","w",stdout);
     int n;
     while(~scanf("%d",&n)){
         build(,n,);
         int Q;
         scanf("%d",&Q);
         while(Q--){
             int l,r;
             scanf("%d%d",&l,&r);
             ans = rans = -INF;
             query(l,r,,n,);
             printf("%d\n",ans);
         }
     }
     return ;
 }

http://www.spoj.com/problems/GSS3/

题意：更新单点，询问区间最大连续和。

做法：做法与GSS1差不多，多了个修改。

 /*
  *Author:       Zhaofa Fang
  *Created time: 2013-09-13-12.56 星期五
  */
 #include <cstdio>
 #include <cstdlib>
 #include <sstream>
 #include <iostream>
 #include <cmath>
 #include <cstring>
 #include <algorithm>
 #include <string>
 #include <utility>
 #include <vector>
 #include <queue>
 #include <map>
 #include <set>
 using namespace std;

 typedef long long ll;
 typedef pair<int,int> PII;
 #define DEBUG(x) cout<< #x << ':' << x << endl
 #define FOR(i,s,t) for(int i = (s);i <= (t);i++)
 #define FORD(i,s,t) for(int i = (s);i >= (t);i--)
 #define REP(i,n) for(int i=0;i<(n);i++)
 #define REPD(i,n) for(int i=(n-1);i>=0;i--)
 #define PII pair<int,int>
 #define PB push_back
 #define ft first
 #define sd second
 #define lowbit(x) (x&(-x))
 #define INF (1<<30)
 #define eps (1e-8)

 #define lson l , m , rt<<1
 #define rson m + 1 , r , rt<<1|1

 const int maxn = ;
 int sum[maxn<<],lsum[maxn<<],rsum[maxn<<],mx[maxn<<];

 void pushUp(int rt){
     sum[rt] = sum[rt<<] + sum[rt<<|];
     mx[rt] = max(mx[rt<<],mx[rt<<|]);
     mx[rt] = max(mx[rt],rsum[rt<<] + lsum[rt<<|]);

     lsum[rt] = max(lsum[rt<<],sum[rt<<] + lsum[rt<<|]);
     rsum[rt] = max(rsum[rt<<|],sum[rt<<|]+rsum[rt<<]);
 }
 void build(int l,int r,int rt){
     if(l == r){
         scanf("%d",&sum[rt]);
         mx[rt] = lsum[rt] = rsum[rt] = sum[rt];
         return ;
     }
     int m = (l + r) >> ;
     build(lson);
     build(rson);
     pushUp(rt);
 }
 void update(int k,int val,int l,int r,int rt){
     if(l == k && k == r){
         mx[rt] = lsum[rt] = rsum[rt] = sum[rt] = val;
         return;
     }
     int m = (l + r) >> ;
     if(k <= m)update(k,val,lson);
     else update(k,val,rson);
     pushUp(rt);
 }
 int ans,lans;
 void query(int L,int R,int l,int r,int rt){
     if(L <= l && r <= R){
         ans = max(ans,mx[rt]);
         ans = max(ans,lans+lsum[rt]);
         lans = max(lans+sum[rt],rsum[rt]);
         return;
     }
     int m = (l + r) >> ;
     if(L <= m)query(L,R,lson);
     if(m < R)query(L,R,rson);
 }
 int main(){
     //freopen("in","r",stdin);
     //freopen("out","w",stdout);
     int n;
     while(~scanf("%d",&n)){
         build(,n,);
         int Q;
         scanf("%d",&Q);
         while(Q--){
             int op,x,y;
             scanf("%d%d%d",&op,&x,&y);
             if(!op)update(x,y,,n,);
             else {
                 ans = lans = -INF;
                 query(x,y,,n,);
                 printf("%d\n",ans);
             }
         }
     }
     return ;
 }