【学习笔记】线段树优化建图

先开坑，有时间再说。

例题

CF786B Legacy

Code

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//线段树优化建图，从寒假一直咕到暑假 
//之前觉得难得不行，现在看还是挺好理解的 
#include<queue>
#include<cstdio>
#include<cstring>
#include<algorithm>

using namespace std;

const int MAXN = 2e6 + 10;
int n, m, s, cnt, root_in, root_out;
int head[MAXN];
long long dis[MAXN];
bool used[MAXN];
queue<int> q;

struct Edge{
    int to, next;
    long long dis;
}e[MAXN];

inline void Add(int u, int v, long long w){
    e[++cnt].to = v;
    e[cnt].dis = w;
    e[cnt].next = head[u];
    head[u] = cnt;
}

struct Segment_Tree{
    int tot;

    struct Tree{
        int lson, rson;
    }tr[MAXN];

    #define lson(x) tr[x].lson
    #define rson(x) tr[x].rson

    void Build_out(int &rt, int l, int r){
        if(l == r){
            rt = l;
            return;
        }

        rt = ++tot;
        int mid = (l + r) >> 1;
        Build_out(lson(rt), l, mid);
        Build_out(rson(rt), mid + 1, r);

        Add(rt, lson(rt), 0);
        Add(rt, rson(rt), 0);
    }

    void Build_in(int &rt, int l, int r){
        if(l == r){
            rt = l;
            return;
        }

        rt = ++tot;
        int mid = (l + r) >> 1;
        Build_in(lson(rt), l, mid);
        Build_in(rson(rt), mid + 1, r);

        Add(lson(rt), rt, 0);
        Add(rson(rt), rt, 0);
    }

    void Update_out(int rt, int l, int r, int L, int R, int u, int w){
        if(L >= l && R <= r){
            Add(u, rt, w);
            return;
        }

        int mid = (L + R) >> 1;
        if(l <= mid) Update_out(lson(rt), l, r, L, mid, u, w);
        if(r > mid) Update_out(rson(rt), l, r, mid + 1, R , u, w);
    }

    void Update_in(int rt, int l, int r, int L, int R, int v, int w){
        if(L >= l && R <= r){
            Add(rt, v, w);
            return;
        }

        int mid = (L + R) >> 1;
        if(l <= mid) Update_in(lson(rt), l, r, L, mid, v, w);
        if(r > mid) Update_in(rson(rt), l, r, mid + 1, R, v, w);
    }
}S;

void Spfa(int x){
    memset(used, 0, sizeof(used));
    memset(dis, 0x3f, sizeof(dis));

    dis[x] = 0;
    q.push(x);
    used[x] = true;

    while(!q.empty()){
        int k = q.front();
        q.pop();
        used[k] = false;

        for(register int i = head[k]; i; i = e[i].next){
            int v = e[i].to;

            if(dis[v] > dis[k] + e[i].dis){
                dis[v] = 1LL * dis[k] + e[i].dis;
                if(!used[v]){
                    q.push(v);
                    used[v] = true;
                }
            }
        }
    }
}

inline long long read(){
    long long x = 0, f = 1;
    char c = getchar();

    while(c < '0' || c > '9'){
        if(c == '-') f = -1;
        c = getchar();
    }
    while(c >= '0' && c <= '9'){
        x = (x << 1) + (x << 3) + (c ^ 48);
        c = getchar();
    }

    return x * f;
}

int main(){
    n = read(), m = read(), s = read();
    S.tot = n;
    S.Build_out(root_out, 1, n);
    S.Build_in(root_in, 1, n);
    for(register int i = 1; i <= m; i++){
        int opt;
        opt = read();

        if(opt == 1){
            int u, v, w;
            u = read(), v = read(), w = read();
            Add(u, v, w);
        }
        else if(opt == 2){
            int u, l, r, w;
            u = read(), l = read(), r = read(), w = read();
            S.Update_out(root_out, l, r, 1, n, u, w);
        }
        else{
            int v, l, r, w;
            v = read(), l = read(), r = read(), w = read();
            S.Update_in(root_in, l, r, 1, n, v, w);
        }
    }

    Spfa(s);

    for(register int i = 1; i <= n; i++){
        if(dis[i] == 4557430888798830399) printf("-1 ");
        else printf("%lld ", dis[i]);
    }

    return 0;
}

P6348 [PA2011]Journeys

Code

点击查看代码

#include<queue>
#include<cstdio>
#include<cstring>
#include<algorithm>

using namespace std;

const int MAXN = 8e6 + 10;
int n, m, p, cnt, tot, root_in, root_out;
int head[MAXN], dis[MAXN];
bool used[MAXN];

struct Edge{
    int to, next, dis;
}e[MAXN];

inline void Add(int u, int v, int w){
    e[++cnt].to = v;
    e[cnt].dis = w;
    e[cnt].next = head[u];
    head[u] = cnt;
}

struct Segment_Tree{
    struct Tree{
        int lson, rson;
    }tr[MAXN << 2];

    #define lson(x) tr[x].lson
    #define rson(x) tr[x].rson

    void Build_in(int &rt, int l, int r){
        if(l == r){
            rt = l;
            return;
        }

        rt = ++tot;
        int mid = (l + r) >> 1;
        Build_in(lson(rt), l, mid);
        Build_in(rson(rt), mid + 1, r);

        Add(rt, lson(rt), 0);
        Add(rt, rson(rt), 0);
    }

    void Build_out(int &rt, int l, int r){
        if(l == r){
            rt = l;
            return;
        }

        rt = ++tot;
        int mid = (l + r) >> 1;
        Build_out(lson(rt), l, mid);
        Build_out(rson(rt), mid + 1, r);

        Add(lson(rt), rt, 0);
        Add(rson(rt), rt, 0);
    }

    void Update_in(int rt, int l, int r, int L, int R, int u, int w){
        if(l <= L && r >= R){
            Add(u, rt, w);
            return;
        }

        int mid = (L + R) >> 1;
        if(l <= mid) Update_in(lson(rt), l, r, L, mid, u, w);
        if(r > mid) Update_in(rson(rt), l, r, mid + 1, R, u, w);
    }

    void Update_out(int rt, int l, int r, int L, int R, int v, int w){
        if(l <= L && r >= R){
            Add(rt, v, w);
            return;
        }

        int mid = (L + R) >> 1;
        if(l <= mid) Update_out(lson(rt), l, r, L, mid, v, w);
        if(r > mid) Update_out(rson(rt), l, r, mid + 1, R, v, w);
    }
}S;

struct Road{
    int pos;
    long long dis;

    bool operator < (const Road &a) const {
        return dis > a.dis;
    }
};

void Dijkstra(int x){
    priority_queue<Road> q;
    memset(used, 0, sizeof(used));
    memset(dis, 0x3f, sizeof(dis));
    
    dis[x] = 0;
    q.push((Road){x, dis[x]});

    while(!q.empty()){
        int k = q.top().pos;
        q.pop();

        if(used[k]) continue;
        used[k] = true;

        for(register int i = head[k]; i; i = e[i].next){
            int v = e[i].to;
            
            if(dis[v] > dis[k] + e[i].dis){
                dis[v] = dis[k] + e[i].dis;
                q.push((Road){v, dis[v]});
            }
        }
    }
}

inline int read(){
    int x = 0, f = 1;
    char c = getchar();

    while(c < '0' || c > '9'){
        if(c == '-') f = -1;
        c = getchar();
    }
    while(c >= '0' && c <= '9'){
        x = (x << 1) + (x << 3) + (c ^ 48);
        c = getchar();
    }

    return x * f;
}

int main(){
    n = read(), m = read(), p = read();
    tot = n;
    S.Build_in(root_in, 1, n);
    S.Build_out(root_out, 1, n);
    for(register int i = 1; i <= m; i++){
        int a, b, c, d;
        a = read(), b = read(), c = read(), d = read();
        
        int p1 = ++tot;
        S.Update_out(root_out, a, b, 1, n, p1, 1);
        S.Update_in(root_in, c, d, 1, n, p1, 1);

        int p2 = ++tot;
        S.Update_out(root_out, c, d, 1, n, p2, 1);
        S.Update_in(root_in, a, b, 1, n, p2, 1);
    }

    Dijkstra(p);

    for(register int i = 1; i <= n; i++)
        printf("%d\n", dis[i] / 2);

    return 0;
}