DynamicSegmentTree

最近尝试了一下动态开点线段树，英文直译就是Dynamic Open Point Segment Tree，太SB了。

就跟之前的主席树写法差不多。

if(!x || x == y) {
    x = ++tot;
}

if(!o) {
    o = ++tot;
}

实际上当普通线段树用就行了......

例题：洛谷P1908 逆序对

我们可以不离散化，使用动态开点，直接在1e9上开值域线段树。吸氧后堪堪A掉。

// luogu-judger-enable-o2
#include <cstdio>

typedef long long LL;
const int N = 500010;

int sum[N * 20], tot, ls[N * 20], rs[N * 20], a[N], root;

void add(int L, int R, int l, int r, int &o) {
    if(!o) {
        o = ++tot;
    }
    if(L <= l && r <= R) {
        sum[o]++;
        return;
    }
    int mid = (l + r) >> 1;
    if(L <= mid) {
        add(L, R, l, mid, ls[o]);
    }
    if(mid < R) {
        add(L, R, mid + 1, r, rs[o]);
    }
    sum[o] = sum[ls[o]] + sum[rs[o]];
    return;
}

int ask(int L, int R, int l, int r, int o) {
    if(!o) {
        return 0;
    }
    if(L <= l && r <= R) {
        return sum[o];
    }
    int mid = (l + r) >> 1;
    int ans = 0;
    if(L <= mid) {
        ans += ask(L, R, l, mid, ls[o]);
    }
    if(mid < R) {
        ans += ask(L, R, mid + 1, r, rs[o]);
    }
    return ans;
}

int main() {
    //printf("%d", sizeof(sum) / 1024 / 1024 * 3);
    int n, m = 1e9;
    
    scanf("%d", &n);
    for(int i = 1; i <= n; i++) {
        scanf("%d", &a[i]);
    }
    
    LL ans = 0;
    for(int i = 1; i <= n; i++) {
        ans += ask(a[i] + 1, m, 1, m, 1);
        add(a[i], a[i], 1, m, root);
    }
    printf("%lld", ans);
    return 0;
}

例题：洛谷P2471 降雨量

这个题的难点TM在于分类讨论......大毒瘤。

对于未知的位置，我们用一个bool数组维护就行了。

询问的时候查x，y，(x,y)三段，然后暴力讨论.....

#include <cstdio>
#include <algorithm>

const int N = 50010, E = 1e9 + 1;

int root, large[N * 50], tot, ls[N * 50], rs[N * 50];
bool maybe, sure[N * 50];

void change(int p, int v, int l, int r, int &o) {
    //printf("change : %d %d %d %d 
", p, v, l, r);
    //getchar();
    if(!o) {
        o = ++tot;
    }
    if(l == r) {
        large[o] = v;
        sure[o] = 1;
        return;
    }
    int mid = l + (r - l) / 2;
    if(p <= mid) {
        change(p, v, l, mid, ls[o]);
    }
    else {
        change(p, v, mid + 1, r, rs[o]);
    }
    large[o] = std::max(large[ls[o]], large[rs[o]]);
    sure[o] = sure[ls[o]] & sure[rs[o]];
    return;
}

int ask(int L, int R, int l, int r, int o) {
    //printf("%d %d %d %d 
", L, R, l, r);
    if(!o) {
        maybe = 1;
        return 0;
    }
    if(L <= l && r <= R) {
        if(!sure[o]) {
            maybe = 1;
        }
        return large[o];
    }
    int mid = l + (r - l) / 2;
    int ans = 0;
    if(L <= mid) {
        ans = std::max(ans, ask(L, R, l, mid, ls[o]));
    }
    if(mid < R) {
        ans = std::max(ans, ask(L, R, mid + 1, r, rs[o]));
    }
    return ans;
}

int main() {
    int n, limit = E << 1, x, y;
    scanf("%d", &n);
    for(int i = 1; i <= n; i++) {
        scanf("%d%d", &x, &y);
        change(x + E, y, 1, limit, root);
    }
    scanf("%d", &n);
    while(n--) {
        scanf("%d%d", &y, &x);
        if(y == x) {
            printf("true
");
            continue;
        }
        int c = ask(y + E, y + E, 1, limit, root);
        int cc = maybe;
        maybe = 0;
        int d = ask(x + E, x + E, 1, limit, root);
        int dd = maybe;
        maybe = 0;
        //printf("%d %d %d %d 
", c, cc, d, dd);    false -> maybe 
        if(y + 1 == x) {
            if(cc || dd){
                printf("maybe
");
            }
            else {
                if(c >= d) {
                    printf("true
");
                }
                else {
                    printf("false
");
                }
            }
            continue;
        }
        int e = ask(y + 1 + E, x - 1 + E, 1, limit, root);
        int ee = maybe;
        maybe = 0;
        //printf("%d %d 
", e, ee);
        if(dd) {
            if(cc) {
                printf("maybe
");
            }
            else {
                if(e >= c) {
                    printf("false
");
                }
                else {
                    printf("maybe
");
                }
            }
            continue;
        }
        if(cc) {
            if(e >= d) {
                printf("false
");
            }
            else {
                printf("maybe
");
            }
            continue;
        }
        if(ee) {
            if(e >= d || c < d) {
                printf("false
");
            }
            else {
                printf("maybe
");
            }
            continue;
        }
        if(e >= d || c < d) {
            printf("false
");
        }
        else {
            printf("true
");
        }
    }
    
    return 0;
}