loj数列分块入门

数列分块入门

• • 入门 1-区间加法-单点查询
  • 入门 2-区间加法-区间查询
  • 入门 3-区间加法-单点查询
  • 入门 4-区间加法-区间查询
  • 入门 5-区间开方-区间查询
  • 入门 6-单点插入-单点查询
  • 入门 7-区间乘法-区间加法-单点查询
  • 入门 8-区间修改-区间查询
  • 入门 9-区间查询众数

入门 1-区间加法-单点查询

ll n,a[maxn],lazy[maxn];
int main() {
	n = read;
	for(int i=1; i<=n; i++) a[i] = read;
	int blk = sqrt(n);
	for(int ii=1; ii<=n; ii++) {
		int op = read,l = read,r = read,c = read;
		if( op == 0) {
			for(int i=l; i<min(r+1,(l/blk+1)*blk); i++) {
				a[i] += c;
			}
			for(int i=l/blk+1; i<r/blk; i++) {
				lazy[i] += c;
			}
			if(l / blk != r / blk) {
				for(int i=r/blk*blk; i<=r; i++) a[i] += c;
			}
		} else {
			printf("%lld
",a[r] + lazy[r/blk]);
		}
	}
	return 0;
}
/**
4
1 2 2 3
0 1 3 1
1 0 1 0
0 1 2 2
1 0 2 0

2
5
**/

入门 2-区间加法-区间查询

const int maxn = 1e5 + 7;
ll n, a[maxn];
vector<ll> vet[maxn];
ll blk, lazy[maxn], b[maxn];
void reget(int id) {
    vet[id].clear();

    for (int i = (id - 1) * blk + 1; i <= min(n, id * blk); i++) {
        vet[id].push_back(a[i]);
    }

    sort(vet[id].begin(), vet[id].end());
}
void update(ll l, ll r, ll c) {
    for (int i = l; i <= min(b[l]*blk, r); i++)
        a[i] += c;

    reget(b[l]);

    if (b[l] != b[r]) {
        for (int i = (b[r] - 1) * blk + 1; i <= r; i++)
            a[i] += c;

        reget(b[r]);
    }

    for (int i = b[l] + 1; i <= b[r] - 1; i++) {
        lazy[i] += c;
    }
}
ll query(ll l, ll r, ll val) {
    ll ret = 0;

    for (int i = l; i <= min(b[l]*blk, r); i++) {
        if (a[i] + lazy[b[l]] < val)
            ++ ret;
    }

    if (b[l] != b[r]) {
        for (int i = (b[r] - 1) * blk + 1; i <= r; i++) {
            if (a[i] + lazy[b[r]] < val)
                ++ ret;
        }
    }

    for (int i = b[l] + 1; i <= b[r] - 1; i++) {
        int get = val - lazy[i];
        //      ret += upper_bound(vet[i].begin(),vet[i].end(),get) - lower_bound(vet[i].begin(),vet[i].end(),get);
        ret += lower_bound(vet[i].begin(), vet[i].end(), get) - vet[i].begin();
    }

    return ret;
}
int main() {
    n = read;

    for (int i = 1; i <= n; i++)
        a[i] = read;

    blk = sqrt(n);

    for (int i = 1; i <= n; i++) {
        b[i] = (i - 1) / blk + 1;
        vet[b[i]].push_back(a[i]);
    }

    for (int i = 1; i <= b[n]; i++)
        sort(vet[i].begin(), vet[i].end());

    for (int i = 1; i <= n; i++) {
        int op = read, l = read, r = read, c = read;

        if (op == 0)
            update(l, r, c);
        else
            printf("%lld
", query(l, r, c * c));
    }

    return 0;
}
/**
4
1 2 2 3
0 1 3 1
1 1 3 2
1 1 4 1
1 2 3 2

3
0
2
**/

入门 3-区间加法-单点查询

const int maxn = 1e5 + 7;
ll n, a[maxn];
vector<ll> vet[maxn];
ll blk, lazy[maxn], b[maxn];
void reget(int id) {
    vet[id].clear();

    for (int i = (id - 1) * blk + 1; i <= min(n, id * blk); i++) {
        vet[id].push_back(a[i]);
    }

    sort(vet[id].begin(), vet[id].end());
}
void update(ll l, ll r, ll c) {
    for (int i = l; i <= min(b[l]*blk, r); i++)
        a[i] += c;

    reget(b[l]);

    if (b[l] != b[r]) {
        for (int i = (b[r] - 1) * blk + 1; i <= r; i++)
            a[i] += c;

        reget(b[r]);
    }

    for (int i = b[l] + 1; i <= b[r] - 1; i++) {
        lazy[i] += c;
    }
}
ll query(ll l, ll r, ll val) {
    ll ret = -1;

    for (int i = l; i <= min(b[l]*blk, r); i++) {
        if (a[i] + lazy[b[l]] < val)
            ret = max(ret, a[i] + lazy[b[l]]);
    }

    if (b[l] != b[r]) {
        for (int i = (b[r] - 1) * blk + 1; i <= r; i++) {
            if (a[i] + lazy[b[r]] < val)
                ret = max(ret, a[i] + lazy[b[r]]);
        }
    }

    for (int i = b[l] + 1; i <= b[r] - 1; i++) {
        ll get = val - lazy[i];
        vector<ll>::iterator l = lower_bound(vet[i].begin(), vet[i].end(), get);

        if (l == vet[i].begin())
            continue;

        l --;
        ret = max(ret, *l + lazy[i]);
    }

    return ret;
}
int main() {
    n = read;

    for (int i = 1; i <= n; i++)
        a[i] = read;

    blk = sqrt(n);

    for (int i = 1; i <= n; i++) {
        b[i] = (i - 1) / blk + 1;
        vet[b[i]].push_back(a[i]);
    }

    for (int i = 1; i <= b[n]; i++)
        sort(vet[i].begin(), vet[i].end());

    for (int i = 1; i <= n; i++) {
        int op = read, l = read, r = read, c = read;

        if (op == 0)
            update(l, r, c);
        else
            printf("%lld
", query(l, r, c));

        //      debug(i);
    }

    return 0;
}
/**
4
1 2 2 3
0 1 3 1
1 1 4 4
0 1 2 2
1 1 2 4

3
-1
**/

入门 4-区间加法-区间查询

ll n,a[maxn];
ll blk,lazy[maxn],b[maxn],sum[maxn];
void update(ll l,ll r,ll c) {
	for(int i=l; i<=min(b[l]*blk,r); i++) a[i] += c,sum[b[l]] += c;
	if(b[l] != b[r]) {
		for(int i=(b[r] - 1) * blk+1; i<=r; i++) a[i] += c,sum[b[r]] += c;
	}
	for(int i=b[l]+1; i<=b[r] - 1; i++) {
		lazy[i] += c;
	}
}
ll query(ll l,ll r,ll val) {
	ll ret = 0;
	for(int i=l; i<=min(b[l]*blk,r); i++) {
		ret += a[i] + lazy[b[l]];
		ret %= (val + 1);
	}
	if(b[l] != b[r]) {
		for(int i=(b[r]-1)*blk+1; i<=r; i++) {
			ret += a[i] + lazy[b[r]];
			ret %= (val + 1);
		}
	}
	for(int i=b[l]+1; i<=b[r]-1; i++) {
		ll add = lazy[i] * blk % (val + 1);
		ret += (sum[i] + add) % (val + 1);
		ret %= (val + 1);
	}
	return ret;
}
int main() {
	n = read;
	for(int i=1; i<=n; i++) a[i] = read;
	blk = sqrt(n);
	for(int i=1; i<=n; i++) {
		b[i] = (i - 1) / blk + 1;
		sum[b[i]] += a[i];
	}
	for(int i=1; i<=n; i++) {
		int op = read,l = read,r = read,c = read;
		if(op == 0) update(l,r,c);
		else printf("%lld
",query(l,r,c));
	}
	return 0;
}
/**
4
1 2 2 3
0 1 3 1
1 1 4 4
0 1 2 2
1 1 2 4

1
4
**/

入门 5-区间开方-区间查询

ll n,a[maxn];
ll blk,lazy[maxn],b[maxn],sum[maxn];
bool vis[maxn];
bool check(int id) {
	if(vis[id]) return true;
	for(int i=(id-1)*blk+1; i<=min(n,blk*id); i++) {
		if(a[i] > 1) return false;
	}
	return vis[id] = 1;
}
void update(ll l,ll r) {
	if(!check(b[l])) {
		for(int i=l; i<=min(b[l]*blk,r); i++) {
			sum[b[l]] -= a[i];
			a[i] = sqrt(a[i]);
			sum[b[l]] += a[i];
		}
	}
	if(b[l] != b[r] && !check(b[r])) {
		for(int i=(b[r]-1)*blk+1; i<=r; i++) {
			sum[b[r]] -= a[i];
			a[i] = sqrt(a[i]);
			sum[b[r]] += a[i];
		}
	}
	for(int i=b[l]+1; i<=b[r]-1; i++) {
		if(!check(i)) {
			sum[i] = 0;
			for(int j=(i-1)*blk+1; j<=i*blk; j++) {
				a[j] = sqrt(a[j]);
				sum[i] += a[j];
			}
		}
	}
}
ll query(ll l,ll r) {
	ll ret = 0;
	for(int i=l; i<=min(b[l]*blk,r); i++) {
		ret += a[i];
	}
	if(b[l] != b[r]) {
		for(int i=(b[r]-1)*blk+1; i<=r; i++) {
			ret += a[i];
		}
	}
	for(int i=b[l]+1; i<=b[r]-1; i++) {
		ret += sum[i];
	}
	return ret;
}
int main() {
	n = read;
	for(int i=1; i<=n; i++) a[i] = read;
	blk = sqrt(n);
	for(int i=1; i<=n; i++) {
		b[i] = (i - 1) / blk + 1;
		sum[b[i]] += a[i];
	}
	for(int i=1; i<=n; i++) {
		int op = read,l = read,r = read,c = read;
		if(op == 0) update(l,r);
		else printf("%lld
",query(l,r));
	}
	return 0;
}
/**
4
1 2 2 3
0 1 3 1
1 1 4 4
0 1 2 2
1 1 2 4

6
2
**/

入门 6-单点插入-单点查询

typedef pair<int,int> PII;
ll n,a[maxn];
ll blk,lazy[maxn],b[maxn],sum[maxn],tot;
vector<int> vet[maxn];
void reBuild() {
	int p = 0;
	for(int i=1; i<=tot; i++) {
		for(int val : vet[i]) {
			a[++p] = val;
		}
		vet[i].clear();
	}
	blk = sqrt(p);
	tot = ceil(1.0 * p / blk);
	for(int i=1; i<=p; i++) {
		b[i] = (i - 1) / blk + 1;
		vet[b[i]].push_back(a[i]);
	}
}
PII query(ll r) {
	for(int i=1; i<=tot; i++) {
		if(r > vet[i].size()) r -= vet[i].size();
		else return {i,r-1};
	}
}
void insert(ll l,ll r) {
	PII t = query(l);
	vet[t.first].insert(vet[t.first].begin() + t.second,r);
	if(vet[t.first].size() > 10 * blk) reBuild();
}
int main() {
	n = read;
	for(int i=1; i<=n; i++) a[i] = read;
	blk = sqrt(n);
	tot = ceil(1.0*n / blk);
	for(int i=1; i<=n; i++) {
		b[i] = (i - 1) / blk + 1;
		vet[b[i]].push_back(a[i]);
	}
	for(int i=1; i<=n; i++) {
		int op = read,l = read,r = read,c = read;
		if(op == 0) insert(l,r);
		else {
			PII t = query(r);
			printf("%d
",vet[t.first][t.second]);
		}
	}
	return 0;
}
/**
4
1 2 2 3
0 1 3 1
1 1 4 4
0 1 2 2
1 1 2 4

2
3
**/

入门 7-区间乘法-区间加法-单点查询

const int maxn = 1e5 + 7;
const int mod = 10007;
ll n,a[maxn];
ll blk,add[maxn],b[maxn],sum[maxn],mul[maxn];
void pushDown(int id) {
	for(int i=(id-1) * blk + 1; i<=min(id * blk,n); i++) {
		a[i] = (a[i] * mul[id] % mod + add[id] + mod) % mod;
	}
	mul[id] = 1;
	add[id] = 0;
}
void add_mul(int l,int r,ll val,int op) {
	pushDown(b[l]);
	for(int i=l; i<=min(b[l]*blk,1LL*r); i++) {
		if(op) a[i] = (a[i] * val) % mod;
		else a[i] = (a[i] + val) % mod;
	}
	if(b[l] != b[r]) {
		pushDown(b[r]);
		for(int i=(b[r]-1)*blk + 1; i<=r; i++) {
			if(op) a[i] = (a[i] * val) % mod;
			else a[i] = (a[i] + val) % mod;
		}
	}
	for(int i=b[l]+1; i<=b[r]-1; i++) {
		if(op) mul[i] = (mul[i] * val) % mod,add[i] = (add[i] * val) % mod;
		else add[i] = (add[i] + val) % mod;
	}
}
ll query(int r) {
	ll ret = 0;
	ret = (a[r] * mul[b[r]] % mod + add[b[r]]) % mod;
	return ret;
}
int main() {
	n = read;
	for(int i=1; i<=n; i++) a[i] = read;
	blk = sqrt(n);
	for(int i=1; i<=n; i++) {
		b[i] = (i - 1) / blk + 1;
		mul[b[i]] = 1;
		add[b[i]] = 0;
	}
	for(int i=1; i<=n; i++) {
		int op = read,l = read,r = read,c = read;
		if(op == 2) {
			printf("%lld
",query(r));
		} else {
			add_mul(l,r,c,op);
		}
	}
	return 0;
}
/**
7
1 2 2 3 9 3 2
0 1 3 1
2 1 3 1
1 1 4 4
0 1 7 2
1 2 6 4
1 1 6 5
2 2 6 4

3
100
**/

入门 8-区间修改-区间查询

ll n,a[maxn];
ll blk,add[maxn],b[maxn],upd[maxn];
void reset(int id) {
	if(upd[id] == -1) return ;
	for(int i=(id-1) * blk+1; i<=min(id*blk,n); i++) {
		a[i] = upd[id];
	}
	upd[id] = -1;
}
ll getSet(int l,int r,ll val) {
	ll ans = 0;
	reset(b[l]);
	for(int i=l; i<=min(b[l]*blk,1LL*r); i++) {
		ans += a[i] == val;
		a[i] = val;
	}

	if(b[l] != b[r]) {
		reset(b[r]);
		for(int i=(b[r]-1)*blk + 1; i<=r; i++) {
			ans += a[i] == val;
			a[i] = val;
		}
	}
	for(int i=b[l]+1; i<=b[r]-1; i++) {
		if(upd[i] == -1) {
			for(int j=(i-1)*blk+1; j<=i*blk; j++) {
				ans += a[j] == val;
			}
		} else ans += upd[i] == val?blk:0;
		upd[i] = val;
	}
	return ans;
}
int main() {
	n = read;
	for(int i=1; i<=n; i++) a[i] = read;
	blk = sqrt(n);
	for(int i=1; i<=n; i++) {
		b[i] = (i - 1) / blk + 1;
		upd[b[i]] = -1;
	}
	for(int i=1; i<=n; i++) {
		int l = read,r = read,c = read;
		ll ans = getSet(l,r,c);
		printf("%lld
",ans);
	}
	return 0;
}
/**
4
1 2 2 4
1 3 1
1 4 4
1 2 2
1 4 2

1
1
0
2
**/

入门 9-区间查询众数

#define Clear(x,val) memset(x,val,sizeof x)
ll n,a[maxn],ans[2007][2007],b[maxn],blk,cnt[maxn],num;
vector<int> vet[maxn];
map<int,int> vis,val;
void get(int id) {
	Clear(cnt,0);
	int mx = 0,res = 0;
	for(int i=(id-1) * blk + 1; i<=n; i++) {
		int to = b[i];///cur is the b[i]-th blk
		++ cnt[a[i]];/// the amt ++
		if(cnt[a[i]] > mx || (cnt[a[i]] == mx && val[a[i]] < val[res])) {
			res = a[i];/// set the cur mx value
			mx = cnt[a[i]];
		}
		ans[id][to] = res;/// from blk id -> blk to  the ans = res
	}
}
int getNum(int l,int r,int x) {
	int ret = 0;
	ret = upper_bound(vet[x].begin(),vet[x].end(),r) - lower_bound(vet[x].begin(),vet[x].end(),l);/// amount of x
	return ret;
}
ll query(int l,int r) {
	ll ret = ans[b[l] + 1][b[r] - 1];// center blks
	int mx = getNum(l,r,ret);// get the amount of this
	for(int i=l; i<=min(r*1LL,b[l]*blk); i++) {
		int amt = getNum(l,r,a[i]);
		if(amt > mx || (amt == mx && val[a[i]] < val[ret])) { ///val[ret]
			ret = a[i];
			mx = amt;
		}
	}
	if(b[l] != b[r]) {
		for(int i = (b[r] - 1) * blk + 1; i<=r; i++) {
			int amt = getNum(l,r,a[i]);
			if(amt > mx || (amt == mx && val[a[i]] < val[ret])) {
				ret = a[i];
				mx = amt;
			}
		}
	}
	return val[ret];
}
int main() {
	n = read;
	blk = sqrt(n);
	blk = 80;
	for(int i=1; i<=n; i++) {
		a[i] = read;
		b[i] = (i - 1) / blk + 1;
		if(!vis[a[i]]) {
			vis[a[i]] = ++ num;
			val[num] = a[i];///¶ÔÓ¦ÏÂ
		}
		a[i] = vis[a[i]];
		vet[a[i]].push_back(i);
	}
	for(int i=1; i<=b[n]; i++) get(i); /// get the i-th blk
	for(int i=1; i<=n; i++) {
		int l = read,r = read;
		if(l > r) swap(l,r);
		ll ans = query(l,r);
		printf("%lld
",ans);
	}
	return 0;
}
/**
4
1 2 2 4
1 2
1 4
2 4
3 4

1
2
2
2
**/

七夕快乐