线段树

Posted 2020-08-07 SteveDevin

1.数组大小为Max << 2;
 
2.初始化
#define lson l , m , rt << 1
#define rson m + 1 , r , rt << 1 | 1
 
3.建树
 void build(int l, int r, int rt) {
    if (l == r) {
        scanf("%d", &sum[rt]);
        return ;
    }
    int m = (l + r) >> 1;
    build(lson);
    build(rson);
    PushUP(rt);
}
 
4.更新节点
void update(int p, int add, int l, int r, int rt) {
    if (l == r) {
        sum[rt] += add;
        return ;
    }
    int m = (l + r) >> 1;
    if (p <= m) update(p , add , lson);
    else update(p , add , rson);
    PushUP(rt);
}
 
5.区间求和
int query(int L, int R, int l, int r, int rt) {
    if (L <= l && r <= R) {
        return sum[rt];
    }
    int m = (l + r) >> 1;
    int ret = 0;
    if (L <= m) ret += query(L , R , lson);
    if (R > m) ret += query(L , R , rson);
    return ret;
}
 
6.延迟更新
void pushDown(int m, int rt)
{
    if(!col[rt]) return ;
    
    col[rt << 1] = col[rt << 1 | 1] = col[rt];
    col[rt] = 0;
    
    mag[rt << 1] = col[rt << 1] * (m - (m >> 1));
    mag[rt << 1 | 1] = col[rt << 1 | 1] * (m >> 1); 
}

 
7.成段更新
void pushDown(int m, int rt)
{
    if(!col[rt]) return ;
    
    col[rt << 1] = col[rt << 1 | 1] = col[rt];
    col[rt] = 0;
    
    mag[rt << 1] = col[rt << 1] * (m - (m >> 1));
    mag[rt << 1 | 1] = col[rt << 1 | 1] * (m >> 1); 
}

8.放个程序：upc3453
#include <iostream>
#include <cstring>
#include <cstdio>
#include <algorithm>
using namespace std;

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

const int Maxn = 100000 + 2;
long long mag[Maxn << 2];
long long col[Maxn << 2];

inline void pushUp(int rt)
{
    mag[rt] = mag[rt << 1] + mag[rt << 1 | 1];
}

void build(int l, int r, int rt)
{
    col[rt] = 0;
    if(l == r) { mag[rt] = 0; return ; }
    
    int m = (l + r) >> 1;
    build(lson);
    build(rson);
    pushUp(rt);
}

inline void pushDown(int m, int rt)
{
    if(!col[rt]) return ;
    
    col[rt << 1] = col[rt << 1 | 1] = col[rt];
    col[rt] = 0;
    
    mag[rt << 1] = (long long) col[rt << 1] * (m - (m >> 1));
    mag[rt << 1 | 1] = (long long) col[rt << 1 | 1] * (m >> 1); 
}

inline void update(int x, int L, int R, int l, int r, int rt)
{
    if(L <= l && R >= r) 
    {
        col[rt] = x; 
        mag[rt] = (long long)(r - l + 1) * x;
        return ;
    }
    
    int m = (l + r) >> 1;
    pushDown(r - l + 1, rt);
    if(L <= m) update(x, L, R, lson);
    if(R > m) update(x, L, R, rson);
    pushUp(rt);
}

int main()
{
    int N;
    scanf("%d", &N);
    for(int t = 1; t <= N; t++)
    {
        int n, m;
        scanf("%d%d", &n, &m);
        build(1, n, 1);
        
        for(int i = 1; i <= m; i++)
        {
            int a, b, c;
            scanf("%d%d%d", &a, &b, &c);
            update(a, b, c, 1, n, 1);
        }
        printf("%lld\n", mag[1]);
    }
    return 0;
} 

9.二维线段树POJ2155

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <algorithm>
using namespace std;
#define lson l , m , rt << 1 
#define rson m + 1 , r , rt << 1 | 1
bool seg[4010][4010];
int n,m,T,ans;
void buildy(int i,int l,int r,int rt)
{
    seg[i][rt] = 0;
    if(l == r) return ;
    int m = (l + r) >> 1;
    buildy(i,lson);
    buildy(i,rson);
}
void buildx(int l,int r,int rt)
{
    buildy(rt,1,n,1);
    if(l == r) return ;
    int m = (l + r) >> 1;
    buildx(lson);
    buildx(rson);
}
void updatey(int i,int L,int R,int l,int r,int rt)
{
    if(L <= l && r <= R)
    {
        seg[i][rt]^= 1;
        return ;
    }
    int m = (l + r) >> 1;
    if(m >= L)
    updatey(i,L,R,lson);
    if(m < R)
    updatey(i,L,R,rson);    
}
void updatex(int L,int R,int y1,int y2,int l,int r,int rt)
{
    if(L <= l && r <= R)
    {
        updatey(rt,y1,y2,1,n,1);
        return ;
    }
    int m = (l + r) >> 1;
    if(L <= m) updatex(L,R,y1,y2,lson);
    if(R > m)  updatex(L,R,y1,y2,rson);
}
void queryy(int i,int y,int l,int r,int rt)
{
    ans^= seg[i][rt];
    if(l == r)
    return ; 
    int m = (l + r) >> 1;
    if(y <= m) queryy(i,y,lson);
    else  queryy(i,y,rson);
}
void queryx(int x,int y,int l,int r,int rt)
{
    queryy(rt,y,1,n,1);
    if(l == r)
    return ;
    int m = (l + r) >> 1;
    if(x <= m) queryx(x,y,lson);
    else queryx(x,y,rson);
}
int main()
{
    scanf("%d",&T);
    while(T--)
    {
        scanf("%d%d",&n,&m);
        buildx(1,n,1);
        for(int i = 0 ; i < m ; i++)
        {
            char s[2];
            scanf("%s",s);
            if(s[0] == ‘C‘)
            {
                int x1,x2,y1,y2;
                scanf("%d%d%d%d",&x1,&y1,&x2,&y2);
                updatex(x1,x2,y1,y2,1,n,1);
            }
            else
            {
                ans = 0;
                int x,y;
                scanf("%d%d",&x,&y);
                queryx(x,y,1,n,1);
                printf("%d\n",ans);
            }
        }
        if(T)
        printf("\n");
    }
    return 0;
} 



注意： 
    比较符号、对象
    区间更新，注意染色边界