• loj#6031. 「雅礼集训 2017 Day1」字符串(SAM 广义SAM 数据分治)


    题意

    链接

    Sol

    (10^5)次询问每次询问(10^5)个区间。。这种题第一感觉就是根号/数据分治的模型。

    (K)是个定值这个很关键。

    考虑(K)比较小的情况,可以直接暴力建SAM,(n^2)枚举(w)的子串算出现次数。询问用个(n^2)的vector记录一下每次在vector里二分就好。

    (K)比较大的情况我没想到什么好的做法,网上的做法复杂度也不是很好。。

    然后写了个广义SAM + 暴力跳parent就过了。。

    不过这题思想还是很好的

    #include<bits/stdc++.h> 
    #define Pair pair<int, int>
    #define MP(x, y) make_pair(x, y)
    #define fi first
    #define se second
    #define LL long long 
    #define ull unsigned long long 
    #define Fin(x) {freopen(#x".in","r",stdin);}
    #define Fout(x) {freopen(#x".out","w",stdout);}
    using namespace std;
    const int MAXN = 4e5 + 10, INF = 1e9 + 1, mod = 1e9 + 7;
    const double eps = 1e-9, pi = acos(-1);
    template <typename A, typename B> inline bool chmin(A &a, B b){if(a > b) {a = b; return 1;} return 0;}
    template <typename A, typename B> inline bool chmax(A &a, B b){if(a < b) {a = b; return 1;} return 0;}
    template <typename A, typename B> inline LL add(A x, B y) {if(x + y < 0) return x + y + mod; return x + y >= mod ? x + y - mod : x + y;}
    template <typename A, typename B> inline void add2(A &x, B y) {if(x + y < 0) x = x + y + mod; else x = (x + y >= mod ? x + y - mod : x + y);}
    template <typename A, typename B> inline LL mul(A x, B y) {return 1ll * x * y % mod;}
    template <typename A, typename B> inline void mul2(A &x, B y) {x = (1ll * x * y % mod + mod) % mod;}
    inline int read() {
        char c = getchar(); int x = 0, f = 1;
        while(c < '0' || c > '9') {if(c == '-') f = -1; c = getchar();}
        while(c >= '0' && c <= '9') x = x * 10 + c - '0', c = getchar();
        return x * f;
    }
    int N, M, Q, K;
    char s[MAXN], w[MAXN];
    string q[MAXN];
    int l[MAXN], r[MAXN], a[MAXN], b[MAXN], pos[MAXN];
    vector<int> line[1001][1001], v[MAXN];
    int ch[MAXN][26], siz[MAXN], len[MAXN], fa[MAXN], las = 1, root = 1, tot = 1;
    void insert(int x, int opt) {
    	int now = ++tot, pre = las; las = now; len[now] = len[pre] + 1; siz[now] = opt; 
    	for(; pre && !ch[pre][x]; pre = fa[pre]) ch[pre][x] = now;
    	if(!pre) fa[now] = root; 
    	else {
    		int q = ch[pre][x];
    		if(len[pre] + 1 == len[q]) fa[now] = q;
    		else {
    			int nq = ++tot; len[nq] = len[pre] + 1; fa[nq] = fa[q];
    			memcpy(ch[nq], ch[q], sizeof(ch[q]));
    			fa[now] = fa[q] = nq;
    			for(; pre && ch[pre][x] == q; pre = fa[pre]) ch[pre][x] = nq;
    		}
    	}
    }
    void dfs(int x) {
    	for(auto &to : v[x]) {
    		dfs(to);
    		siz[x] += siz[to];
    	}
    }
    int Query(vector<int> &q, int a, int b) {
    	return (upper_bound(q.begin(), q.end(), b) - lower_bound(q.begin(), q.end(), a));
    }
    LL solve1(int a, int b) {
    	LL ret = 0;
    	for(int i = 1; i <= K; i++) {
    		int now = root;
    		for(int j = i; j <= K; j++) {
    			int x = w[j] - 'a'; now = ch[now][x];
    			if(!now) break;
    			else ret += 1ll * siz[now] * Query(line[i][j], a, b);
    		}
    	}
    	return ret;
    }
    void Build() {
    	for(int i = 1; i <= tot; i++) v[fa[i]].push_back(i);
    	dfs(root);
    }
    signed main() {
    //	freopen("string9.in", "r", stdin);	freopen("b.out", "w", stdout);
    	N = read(); M = read(); Q = read(); K = read(); 
    	scanf("%s", s + 1);
    	for(int i = 1; i <= N; i++) insert(s[i] - 'a', 1);
    	if(K <= 1000) {
    		Build();
    		for(int i = 1; i <= M; i++) l[i] = read() + 1, r[i] = read() + 1, line[l[i]][r[i]].push_back(i);
    		for(int i = 1; i <= Q; i++) {
    			scanf("%s", w + 1); int a = read() + 1, b = read() + 1;
    			cout <<  solve1(a, b) << '
    ';
    		}
    	} 
    	else {
    		for(int i = 1; i <= M; i++) l[i] = read() + 1, r[i] = read() + 1;
    		for(int i = 1; i <= Q; i++) {
    			cin >> q[i]; a[i] = read() + 1, b[i] = read() + 1;
    			las = 1;
    			for(auto &x : q[i]) insert(x - 'a', 0);
    		}
    		Build();
    		for(int i = 1; i <= Q; i++) {
    			memset(pos, 0, sizeof(pos));
    			int now = root;
    			for(int j = 0; j < q[i].length(); j++) {
    				int x = q[i][j] - 'a'; now = ch[now][x];
    				if(!now) break;
    				else pos[j + 1] = now;
    			}
    			LL ans = 0;
    			for(int j = a[i]; j <= b[i]; j++) {
    				int cur = pos[r[j]];
    				while(len[fa[cur]] >= r[j] - l[j] + 1) cur = fa[cur];//这里可以卡掉
    				ans += siz[cur];
    			}
    			cout << ans << '
    ';
    		}
    	}
    	return 0;
    }
    
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  • 原文地址:https://www.cnblogs.com/zwfymqz/p/10531477.html
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