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 = 50011;
int sum[maxn<<2],maxsum[maxn<<2],lsum[maxn<<2],rsum[maxn<<2];
int rans,ans;
void pushUp(int l,int r,int rt){
    sum[rt] = sum[rt<<1] + sum[rt<<1|1];
    maxsum[rt] = max(maxsum[rt<<1],maxsum[rt<<1|1]);
    maxsum[rt] = max(maxsum[rt],rsum[rt<<1]+lsum[rt<<1|1]);
    lsum[rt] = max(lsum[rt<<1],sum[rt<<1]+lsum[rt<<1|1]);
    rsum[rt] = max(rsum[rt<<1|1],sum[rt<<1|1]+rsum[rt<<1]);
}
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) >> 1;
    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) >> 1;
    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(1,n,1);
        int Q;
        scanf("%d",&Q);
        while(Q--){
            int l,r;
            scanf("%d%d",&l,&r);
            ans = rans = -INF;
            query(l,r,1,n,1);
            printf("%d
",ans);
        }
    }
    return 0;
}

 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 = 50011;
int sum[maxn<<2],lsum[maxn<<2],rsum[maxn<<2],mx[maxn<<2];

void pushUp(int rt){
    sum[rt] = sum[rt<<1] + sum[rt<<1|1];
    mx[rt] = max(mx[rt<<1],mx[rt<<1|1]);
    mx[rt] = max(mx[rt],rsum[rt<<1] + lsum[rt<<1|1]);

    lsum[rt] = max(lsum[rt<<1],sum[rt<<1] + lsum[rt<<1|1]);
    rsum[rt] = max(rsum[rt<<1|1],sum[rt<<1|1]+rsum[rt<<1]);
}
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) >> 1;
    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) >> 1;
    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) >> 1;
    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(1,n,1);
        int Q;
        scanf("%d",&Q);
        while(Q--){
            int op,x,y;
            scanf("%d%d%d",&op,&x,&y);
            if(!op)update(x,y,1,n,1);
            else {
                ans = lans = -INF;
                query(x,y,1,n,1);
                printf("%d
",ans);
            }
        }
    }
    return 0;
}