2016湖南省赛 I Tree Intersection(线段树合并,树链剖分)

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2016湖南省赛 I Tree Intersection(线段树合并,树链剖分)

传送门:https://ac.nowcoder.com/acm/contest/1112/I

题意:

给你一个n个结点的树,树上每个节点有自己的颜色

问你删除第i条边后形成的两颗子树有多少个相同的颜色

题解:

树链剖分写法:

对于每一种颜色来说,如果这个颜色是在单独的一颗子树中,那么就不会对其他的边产生贡献,所以我们单独对每一种颜色对边的贡献讨论,如果这个颜色只有一个,那么就不会产生贡献,否则,他就可以在两个相同颜色之间的路径上的边产生贡献,用树剖剖下来后区间加一加就可以了

线段树合并的写法

对于每一种颜色建权值线段树,线段树合并统计答案即可

代码:

树链剖分写法:

/**
 *        ┏┓    ┏┓
 *        ┏┛┗━━━━━━━┛┗━━━┓
 *        ┃       ┃  
 *        ┃   ━    ┃
 *        ┃ >   < ┃
 *        ┃       ┃
 *        ┃... ⌒ ...  ┃
 *        ┃       ┃
 *        ┗━┓   ┏━┛
 *          ┃   ┃ Code is far away from bug with the animal protecting          
 *          ┃   ┃   神兽保佑,代码无bug
 *          ┃   ┃           
 *          ┃   ┃        
 *          ┃   ┃
 *          ┃   ┃           
 *          ┃   ┗━━━┓
 *          ┃       ┣┓
 *          ┃       ┏┛
 *          ┗┓┓┏━┳┓┏┛
 *           ┃┫┫ ┃┫┫
 *           ┗┻┛ ┗┻┛
 */
// warm heart, wagging tail,and a smile just for you!
//
//                            _ooOoo_
//                           o8888888o
//                           88" . "88
//                           (| -_- |)
//                           O  =  /O
//                        ____/`---'\____
//                      .'  |     |//  `.
//                     /  |||  :  |||//  //                    /  _||||| -:- |||||-  //                    |   |   -  /// |   |
//                    | \_|  ''---/''  |   |
//                      .-\__  `-`  ___/-. /
//                  ___`. .'  /--.--  `. . __
//               ."" '<  `.___\_<|>_/___.'  >'"".
//              | | :  `- `.;` _ /`;.`/ - ` : | |
//                 `-.   \_ __ /__ _/   .-` /  /
//         ======`-.____`-.___\_____/___.-`____.-'======
//                            `=---='
//        ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
//                     佛祖保佑      永无BUG
#include <set>
#include <map>
#include <stack>
#include <cmath>
#include <queue>
#include <cstdio>
#include <string>
#include <vector>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
typedef long long LL;
typedef pair<int, int> pii;
typedef unsigned long long uLL;
#define ls rt<<1
#define rs rt<<1|1
#define lson l,mid,rt<<1
#define rson mid+1,r,rt<<1|1
#define bug printf("*********
")
#define FIN freopen("input.txt","r",stdin);
#define FON freopen("output.txt","w+",stdout);
#define IO ios::sync_with_stdio(false),cin.tie(0)
#define debug1(x) cout<<"["<<#x<<" "<<(x)<<"]
"
#define debug2(x,y) cout<<"["<<#x<<" "<<(x)<<" "<<#y<<" "<<(y)<<"]
"
#define debug3(x,y,z) cout<<"["<<#x<<" "<<(x)<<" "<<#y<<" "<<(y)<<" "<<#z<<" "<<z<<"]
"
const int maxn = 3e5 + 5;
const int INF = 0x3f3f3f3f;
const int mod = 1e9 + 7;
const double Pi = acos(-1);
LL gcd(LL a, LL b) {
    return b ? gcd(b, a % b) : a;
}
LL lcm(LL a, LL b) {
    return a / gcd(a, b) * b;
}
double dpow(double a, LL b) {
    double ans = 1.0;
    while(b) {
        if(b % 2)ans = ans * a;
        a = a * a;
        b /= 2;
    } return ans;
}
LL quick_pow(LL x, LL y) {
    LL ans = 1;
    while(y) {
        if(y & 1) {
            ans = ans * x % mod;
        } x = x * x % mod;
        y >>= 1;
    } return ans;
}
int n;
int a[maxn], sz[maxn], dep[maxn], fa[maxn], top[maxn], w[maxn], son[maxn], W[maxn];
int sum[maxn << 2], lazy[maxn << 2], vis[maxn << 2];
 
struct EDGE {
    int u, v, nt;
} edge[maxn << 1];
int head[maxn], summ, cnt;
int u[maxn];
int v[maxn];
void add_edge(int u, int v) {
    edge[++summ].u = u;
    edge[summ].v = v;
    edge[summ].nt = head[u];
    head[u] = summ;
}
 
void dfs1(int u) {
    sz[u] = 1; son[u] = 0;
    for (int i = head[u]; ~i; i = edge[i].nt) {
        int v = edge[i].v;
        if (v != fa[u]) {
            fa[v] = u;
            dep[v] = dep[u] + 1;
            dfs1(v);
            sz[u] += sz[v];
            if (sz[v] > sz[son[u]]) son[u] = v;
        }
    }
}
 
void dfs2(int u, int tp, int x) {
    top[u] = tp; w[u] = ++cnt; W[cnt] = u;
    if (son[u]) dfs2(son[u], tp, 1);
    for (int i = head[u]; ~i; i = edge[i].nt) {
        int v = edge[i].v;
        if (v == son[u] || v == fa[u]) continue;
        dfs2(v, v, 2);
    }
}
vector<int> vec[maxn];
 
void init() {
    memset(head, -1, sizeof(head));
    summ = 1; cnt = 0;
    for(int i = 1; i <= n; i++) {
        vec[i].clear();
    }
    for (int i = 1; i <= n; i++) {
        scanf("%d", &a[i]);
        vec[a[i]].push_back(i);
    }
    for (int i = 1; i < n; i++) {
        // int u, v;
        scanf("%d %d", &u[i], &v[i]);
        add_edge(u[i], v[i]);
        add_edge(v[i], u[i]);
    }
    dep[1] = 1; fa[1] = 0;
    dfs1(1);
    dfs2(1, 1, 1);
}
 
void pushup(int rt) {
    if(vis[ls] == vis[rs]) vis[rt] = vis[ls];
    else vis[rt] = -1;
}
 
void pushdown(int rt, int mid) {
    if (lazy[rt]) {
        lazy[rt << 1] = lazy[rt];
        lazy[rt << 1 | 1] = lazy[rt];
        vis[rt << 1] = 0;
        vis[rt << 1 | 1] = 0;
        lazy[rt] = 0;
    }
}
 
void build(int l, int r, int rt) {
    lazy[rt] = 0;
    sum[rt] = 0;
    if (l == r) {
        vis[rt] = 0;
        return;
    }
    int mid = (l + r) >> 1;
    build(lson);
    build(rson);
}
 
void update(int L, int R, int val, int l, int r, int rt) {
    // debug2(L, R);
    if(L > R || r < L || R < l) return;
    if(vis[rt] == 1) return;
    if (L <= l && r <= R) {
        // sum[rt] += val * (r - l + 1);
        // lazy[rt] += val;
        if(vis[rt] == 0) {
            vis[rt] = 1;
            sum[rt]++;
            return;
        }
    }
    pushdown(rt, r - l + 1);
    int mid = (l + r) >> 1;
    if (L <= mid) update(L, R, val, lson);
    if (R > mid) update(L, R, val, rson);
    pushup(rt);
}
 
int query(int pos, int l, int r, int rt) {
    if (l == r) {
        return sum[rt];
    }
    pushdown(rt, r - l + 1);
    int mid = (l + r) >> 1;
    int ans = sum[rt];
    if (pos <= mid)  ans += query(pos, lson);
    else  ans += query(pos, rson);
    return ans;
}
 
int LCA(int x, int y) {
    // debug2(x, y);
    while (top[x] != top[y]) {
        // bug;
        if (dep[top[x]] < dep[top[y]]) swap(x, y);
        update(w[top[x]], w[x], 1, 1, n, 1);
        x = fa[top[x]];
    }
    if (dep[x] > dep[y])
        std::swap(x, y);
    update(w[x] + 1, w[y], 1, 1, n, 1);
    return x;
}
 
int main() {
#ifndef ONLINE_JUDGE
    FIN
#endif
    while(scanf("%d", &n) != EOF) {
        init();
        build(1, n, 1);
        // for(int i = 1; i <= n; i++) {
        //     // printf("%d
", w[]);
        //     // debug1(w[i]);
        // }
        for(int i = 1; i <= n; i++) {
            vis[1] = 0;
            lazy[1] = 1;
            int sz = vec[i].size();
            if(sz < 2) continue;
            int bb = LCA(vec[i][0], vec[i][1]);
            for(int j = 2; j < sz; j++) {
                // debug2(vec[i][0], vec[i][1]);
                bb = LCA(bb, vec[i][j]);
            }
        }
 
        for(int i = 1; i < n; i++) {
            int ans;
            // debug2(v[i], u[i]);
            if(fa[v[i]] == u[i]) {
 
                ans = query(w[v[i]], 1, n, 1);
            } else {
 
                ans = query(w[u[i]], 1, n, 1);
            }
            printf("%d
", ans);
        }
    }
 
    return 0;
}

线段树合并写法

/**
 *        ┏┓    ┏┓
 *        ┏┛┗━━━━━━━┛┗━━━┓
 *        ┃       ┃  
 *        ┃   ━    ┃
 *        ┃ >   < ┃
 *        ┃       ┃
 *        ┃... ⌒ ...  ┃
 *        ┃       ┃
 *        ┗━┓   ┏━┛
 *          ┃   ┃ Code is far away from bug with the animal protecting          
 *          ┃   ┃   神兽保佑,代码无bug
 *          ┃   ┃           
 *          ┃   ┃        
 *          ┃   ┃
 *          ┃   ┃           
 *          ┃   ┗━━━┓
 *          ┃       ┣┓
 *          ┃       ┏┛
 *          ┗┓┓┏━┳┓┏┛
 *           ┃┫┫ ┃┫┫
 *           ┗┻┛ ┗┻┛
 */
// warm heart, wagging tail,and a smile just for you!
//
//                            _ooOoo_
//                           o8888888o
//                           88" . "88
//                           (| -_- |)
//                           O  =  /O
//                        ____/`---'\____
//                      .'  |     |//  `.
//                     /  |||  :  |||//  //                    /  _||||| -:- |||||-  //                    |   |   -  /// |   |
//                    | \_|  ''---/''  |   |
//                      .-\__  `-`  ___/-. /
//                  ___`. .'  /--.--  `. . __
//               ."" '<  `.___\_<|>_/___.'  >'"".
//              | | :  `- `.;` _ /`;.`/ - ` : | |
//                 `-.   \_ __ /__ _/   .-` /  /
//         ======`-.____`-.___\_____/___.-`____.-'======
//                            `=---='
//        ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
//                     佛祖保佑      永无BUG
#include <set>
#include <map>
#include <stack>
#include <cmath>
#include <queue>
#include <cstdio>
#include <string>
#include <bitset>
#include <vector>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
typedef long long LL;
typedef pair<int, int> pii;
typedef unsigned long long uLL;
#define ls rt<<1
#define rs rt<<1|1
#define lson l,mid,rt<<1
#define rson mid+1,r,rt<<1|1
#define bug printf("*********
")
#define FIN freopen("input.txt","r",stdin);
#define FON freopen("output.txt","w+",stdout);
#define IO ios::sync_with_stdio(false),cin.tie(0)
#define debug1(x) cout<<"["<<#x<<" "<<(x)<<"]
"
#define debug2(x,y) cout<<"["<<#x<<" "<<(x)<<" "<<#y<<" "<<(y)<<"]
"
#define debug3(x,y,z) cout<<"["<<#x<<" "<<(x)<<" "<<#y<<" "<<(y)<<" "<<#z<<" "<<z<<"]
"
const int maxn = 1e5 + 5;
const int INF = 0x3f3f3f3f;
const int mod = 1e9 + 7;
const double Pi = acos(-1);
LL gcd(LL a, LL b) {
    return b ? gcd(b, a % b) : a;
}
LL lcm(LL a, LL b) {
    return a / gcd(a, b) * b;
}
double dpow(double a, LL b) {
    double ans = 1.0;
    while(b) {
        if(b % 2)ans = ans * a;
        a = a * a;
        b /= 2;
    } return ans;
}
LL quick_pow(LL x, LL y) {
    LL ans = 1;
    while(y) {
        if(y & 1) {
            ans = ans * x % mod;
        } x = x * x % mod;
        y >>= 1;
    } return ans;
}
int col[maxn];
int cnt[maxn];
struct EDGE {
    int v, nxt;
} edge[maxn << 1];
int head[maxn], tot;
void init() {
    memset(head, -1, sizeof(head));
    tot = 0;
}
void add_edge(int u, int v) {
    edge[tot].v = v;
    edge[tot].nxt = head[u];
    head[u] = tot++;
}
 
struct node {
    int l, r, sum, val;
} tree[maxn * 20];
int root[maxn];
int rt_cnt = 0;
int n;
int ans[maxn];
void push_up(int rt) {
    tree[rt].sum = tree[tree[rt].l].sum + tree[tree[rt].r].sum;
}
int build(int l, int r, int pos) {
    int rt = ++rt_cnt;
    tree[rt].l = 0;
    tree[rt].r = 0;
    tree[rt].sum = 0;
    if(l == r) {
        tree[rt].val = 1;
        if(tree[rt].val != cnt[l]) {
            tree[rt].sum = 1;
        } else {
            tree[rt].sum = 0;
        }
        return rt;
    }
    int mid = (l + r) >> 1;
    if(pos <= mid) tree[rt].l = build(l, mid, pos);
    else tree[rt].r = build(mid + 1, r, pos);
    push_up(rt);
    return rt;
}
void merge(int &x, int y, int l, int r) {
    if(!x || !y) {
        if(!x) x = y;
        return;
    }
 
    if(l == r) {
        tree[x].val += tree[y].val;
        tree[x].sum = (tree[x].val != cnt[l]);
        return;
    }
    int mid = (l + r) >> 1;
    merge(tree[x].l, tree[y].l, l, mid);
    merge(tree[x].r, tree[y].r, mid + 1, r);
    push_up(x);
}
 
void dfs(int u, int fa, int id) {
    root[u] = build(1, n, col[u]);
    for(int i = head[u]; i != -1; i = edge[i].nxt) {
        int v = edge[i].v;
        if(v == fa) continue;
        dfs(v, u, i);
        merge(root[u], root[v], 1, n);
    }
    if(u != 1) {
        int tid = id / 2 + 1;
        ans[tid] = tree[root[u]].sum;
    }
}
int main() {
#ifndef ONLINE_JUDGE
    FIN
#endif
 
    scanf("%d", &n);
    for(int i = 1; i <= n; i++) {
        scanf("%d", &col[i]);
        // vec[col[i]].push_back(i);
        cnt[col[i]]++;
    }
    init();
    for(int i = 1, u, v; i < n; i++) {
        scanf("%d%d", &u, &v);
        add_edge(u, v);
        add_edge(v, u);
    }
    // debug1(n);
    dfs(1, -1, -1);
 
    for(int i = 1; i <= n - 1; i++) {
        printf("%d
", ans[i]);
    }
 
    return 0;
}

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