线段树模板

1 线段树回答区间最大字段和

对前缀和序列用线段树做RMQ

#include <iostream>
#include <cstring>
#include <cstdio>

using namespace std;

/**
 * 待处理序列A从1到N
 * min对应的序列是前缀和序列右移一位
 */
const int  MaxN = 500000;
#define left  first
#define right second
long long A[MaxN];
struct Range:pair<int,int>{
    Range(int a=0,int b=0){
        left  = a;
        right = b;
    }
    long long sum() const {
        return A[right]-A[left-1];
    }
    bool operator < (const Range& rig) const {
        if(sum()<rig.sum()) return 1;
        if(sum()>rig.sum()) return 0;
        if(left >rig.left)  return 1;
        if(left <rig.left)  return 0;
        if(right>rig.right) return 1;
        if(right<rig.right) return 0;
        return 1;
    }
};

Range max(Range A,Range B){
    return A < B ? B : A;
}

struct node {
    Range range;
    int maxPos,minPos;
    node(int x=0){range.left=range.right=maxPos=minPos=x;}
    long max(){return A[maxPos];}
    long min(){return A[minPos-1];}
};
struct SegmentTree
{
    #define MaxSegmentLength 500000
    const int root;
    SegmentTree():root(1){}
    node data[4*MaxSegmentLength];
    void newNode(int p,int x){data[p]=node(x);}
    void maintain(int p){
        int lch= p*2,rch= p*2+1,t=0;
        data[p].range = max(data[rch].range,data[lch].range);
        Range MRange(data[lch].minPos,data[rch].maxPos);
        data[p].range = max(MRange,data[p].range);

        data[p].maxPos = (data[lch].max()>=data[rch].max())?
                            data[lch].maxPos:
                            data[rch].maxPos;
        data[p].minPos = (data[lch].min()<=data[rch].min())?
                            data[lch].minPos:
                            data[rch].minPos;
    }
    void build(int x,int y,int p){
        if (x==y)
            newNode(p,x);
        else {
            int mid=(x+y)/2;
            build(x    ,mid,p*2  );
            build(mid+1,y  ,p*2+1);
            maintain(p);
        }
    }
    int queryMax(int x,int y,int l,int r,int p)
    {
        //cout<<"QueryMax  ("<<x<<','<<y<<")  ["<<l<<','<<r<<"] @"<<p<<endl;
        if (x==l && y==r) return data[p].maxPos;
        int mid = (l+r)/2,LPos,RPos;
        //cout<<"        "<<l<<','<<mid<<'|'<<mid+1<<','<<r<<endl;
        if (y<=mid) return queryMax(x,y,l    ,mid,p*2  );
        if (x >mid) return queryMax(x,y,mid+1,r  ,p*2+1);
            LPos=queryMax(x    ,mid,l    ,mid,p*2);
            RPos=queryMax(mid+1,y  ,mid+1,r  ,p*2+1);
            //cout<<"     max(L,R)"<<LPos<<' '<<RPos<<endl;
            return A[LPos]>=A[RPos] ? LPos : RPos;
    }
    int queryMin(int x,int y,int l,int r,int p)
    {
        //cout<<"QueryMin  ("<<x<<','<<y<<")  ["<<l<<','<<r<<"] @"<<p<<endl;
        if (x==l && y==r) return data[p].minPos;
        int mid = (l+r)/2,LPos,RPos;
        //cout<<"        "<<l<<','<<mid<<'|'<<mid+1<<','<<r<<endl;
        if (y<=mid) return queryMin(x,y,l    ,mid,p*2  );
        if (x >mid) return queryMin(x,y,mid+1,r  ,p*2+1);
            LPos=queryMin(x    ,mid,l    ,mid,p*2);
            RPos=queryMin(mid+1,y  ,mid+1,r  ,p*2+1);
            //cout<<"     min(L,R)"<<LPos<<' '<<RPos<<endl;
            return A[LPos-1]<=A[RPos-1] ? LPos : RPos;
    }
    Range query(int x,int y,int l,int r,int p)
    {
        //cout<<"Query  ("<<x<<','<<y<<")  ["<<l<<','<<r<<"] @"<<p<<endl;
        if (x==l && y==r) return data[p].range;
        int mid = (l+r)/2 ;
        //cout<<"        "<<l<<','<<mid<<'|'<<mid+1<<','<<r<<endl;
        if (y<=mid) return query(x,y,l    ,mid,p*2  );
        if (x >mid) return query(x,y,mid+1,r  ,p*2+1);
            Range LRange,RRange,ans,MRange;
            LRange=query(x    ,mid,l    ,mid,p*2  );
            RRange=query(mid+1,y  ,mid+1,r  ,p*2+1);
            ans = max(LRange,RRange);
            //cout<<"     max(Query)"<<ans.sum()<<endl;
            int MaxPos=queryMax(mid+1,y  ,mid+1,r  ,p*2+1),
                MinPos=queryMin(x    ,mid,l    ,mid,p*2  );
            //cout<<"          MaxPos:"<<MaxPos<<"  "<<"MinPos:"<<MinPos<<endl;
            MRange = Range(MinPos,MaxPos);
            ans = max(MRange,ans);
            /*
            if(A[MaxPos]-A[MinPos-1]>ans.sum()){
                ans.left  = MinPos;
                ans.right = MaxPos;
            }
            */
            //cout<<"      max(max-min)"<<ans.sum()<<endl;
            return ans;
    }
    #undef MaxSegmentLength
};

SegmentTree Tree;

int main()
{
    int n,m,CaseNum=0;A[0]=0;
    while(scanf("%d%d",&n,&m)!=EOF){
        for(int i=1;i<=n;i++) scanf("%lld",A+i);
        for(int i=2;i<=n;i++) A[i]+=A[i-1];

        Tree.build(1,n,Tree.root);
        printf("Case %d:
",++CaseNum);

        for(int i=0;i<m;i++){
            int a,b;
            scanf("%d%d",&a,&b);
            Range ans = Tree.query(a,b,1,n,Tree.root);
            printf("%d %d
",ans.left,ans.right);
        }
    }
    /*
    int N,delta;
    cin>>N;
    for(int i=1;i<=N;i++) cin>>A[i];
    //delta=A[1];
    //A[1]=A[0]=0;
    for(int i=2;i<=N;i++)
        A[i]+=A[i-1];//-delta;
    //for(int i=1;i<=N;i++)cout<<A[i]<<' ';
    //cout<<endl;
    Tree.build(1,N,Tree.root);
    int a,b;
    while(cin>>a>>b){
        Range ans = Tree.query(a,b,1,N,Tree.root);
        cout<<ans.left<<' '<<ans.right<<endl;
        //cout<<ans.left<<','<<ans.right<<endl<<endl;
    }
    */
    return 0;
}
//10
// 1  2  3  4  5  6  7  8  9  10
// 4  5  6  2  9  0 -1 13  9 -10
// 4  9 15 17 26 26 25 38 47  37
// 0  1  2 -2  5 -4 -5  9  5 -14

2 支持单点修改的线段树维护RMQ

#include <iostream>
#include <cstring>
#include <cstdio>

using namespace std;

/**
 * 待处理序列A从1到N
 */
const int  MaxN = 200000+10;
#define left  first
#define right second
long long A[MaxN];
struct node {
    long long max;
    node(long long x=0):max(x){};
};
struct SegmentTree
{
    #define MaxSegmentLength 200010
    const int root;
    SegmentTree():root(1){}
    node data[4*MaxSegmentLength];
    void newNode(int p,int x){data[p]=node(A[x]);}
    void maintain(int p){
        int lch= p*2,rch= p*2+1;
        data[p].max=max(data[lch].max,data[rch].max);
    }
    void build(int x,int y,int p){
        if (x==y)
            newNode(p,x);
        else {
            int mid=(x+y)/2;
            build(x    ,mid,p*2  );
            build(mid+1,y  ,p*2+1);
            maintain(p);
        }
    }
    long long query(int x,int y,int l,int r,int p)
    {
        //cout<<"QueryMax  ("<<x<<','<<y<<")  ["<<l<<','<<r<<"] @"<<p<<endl;
        if (x==l && y==r) return data[p].max;
        int mid = (l+r)/2,LPos,RPos;
        //cout<<"        "<<l<<','<<mid<<'|'<<mid+1<<','<<r<<endl;
        if (y<=mid) return query(x,y,l    ,mid,p*2  );
        if (x >mid) return query(x,y,mid+1,r  ,p*2+1);
            //cout<<"     max(L,R)"<<LPos<<' '<<RPos<<endl;
            return max(query(x,mid,l,mid,p*2),query(mid+1,y,mid+1,r,p*2+1));
    }
    long long update(int key,long long value,int l,int r,int p)
    {
        if (key==l && key==r) {
            data[p].max=max(value,data[p].max);
            return data[p].max;
        }
        else{
            int mid = (l+r)/2;
            //cout<<"        "<<l<<','<<mid<<'|'<<mid+1<<','<<r<<endl;
            if (key<=mid)  update(key,value,l    ,mid,p*2  );
            if (key >mid)  update(key,value,mid+1,r  ,p*2+1);
            maintain(p);
            return data[p].max;
                //cout<<"     max(L,R)"<<LPos<<' '<<RPos<<endl;

        }
    }
    #undef MaxSegmentLength
};

SegmentTree Tree;

int main()
{
    int n,m;A[0]=0;
    while(scanf("%d%d",&n,&m)!=EOF){
        for(int i=1;i<=n;i++) scanf("%lld",A+i);

        Tree.build(1,n,Tree.root);

        for(int i=0;i<m;i++){
            char flag,t;
            long long a,b;
            scanf("%c%c%lld%lld",&t,&flag,&a,&b);
            switch(flag){
                case 'Q':{
                    cout<<Tree.query(a,b,1,n,Tree.root)<<endl;
                    break;
                }
                case 'U':{
                    Tree.update(a,b,1,n,Tree.root);
                    break;
                }
            }
        }
    }
    return 0;
}