HDU

HDU - 5381

首先我们可以观察出从一个点开始的连续gcd最多只有log个， 因为gcd每次最少除2, 

然后我们暴力莫队转移就好啦。

#include<bits/stdc++.h>
#define LL long long
#define LD long double
#define ull unsigned long long
#define fi first
#define se second
#define mk make_pair
#define PLL pair<LL, LL>
#define PLI pair<LL, int>
#define PII pair<int, int>
#define SZ(x) ((int)x.size())
#define ALL(x) (x).begin(), (x).end()
#define fio ios::sync_with_stdio(false); cin.tie(0);

using namespace std;

const int N = 1e4 + 7;
const int inf = 0x3f3f3f3f;
const LL INF = 0x3f3f3f3f3f3f3f3f;
const int mod = 1e9 + 7;
const double eps = 1e-8;
const double PI = acos(-1);

template<class T, class S> inline void add(T &a, S b) {a += b; if(a >= mod) a -= mod;}
template<class T, class S> inline void sub(T &a, S b) {a -= b; if(a < 0) a += mod;}
template<class T, class S> inline bool chkmax(T &a, S b) {return a < b ? a = b, true : false;}
template<class T, class S> inline bool chkmin(T &a, S b) {return a > b ? a = b, true : false;}

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

const int B = 130;

int Log[N];
struct ST {
    int dp[N][15]; int ty;
    void build(int n, int b[]) {
        for(int i = -(Log[0] = -1); i < N; i++)
            Log[i] = Log[i - 1] + ((i & (i - 1)) == 0);
        for(int i = 1; i <= n; i++) dp[i][0] = b[i];
        for(int j = 1; j <= Log[n]; j++)
            for(int i = 1; i + (1 << j) - 1 <= n; i++)
                dp[i][j] = __gcd(dp[i][j - 1], dp[i + (1 << (j - 1))][j - 1]);
    }
    inline int query(int x, int y) {
        if(x > y) return 0;
        int k = Log[y - x + 1];
        return __gcd(dp[x][k], dp[y - (1 << k) + 1][k]);
    }
} rmq;

int n, q, a[N];
LL ans[N];
LL tmp[N];

vector<int> LP[N], RP[N];
vector<int> LV[N], RV[N];

struct Qus {
    int L, R, id;
    bool operator < (const Qus &rhs) const {
        if(L / B == rhs.L / B) return R < rhs.R;
        return L < rhs.L;
    }
} qus[N];

void init() {
    for(int i = 1; i <= n; i++) {
        LP[i].clear();
        RP[i].clear();
        LV[i].clear();
        RV[i].clear();
    }
}

int main() {
    int T; scanf("%d", &T);
    while(T--) {
        scanf("%d", &n);
        init();
        for(int i = 1; i <= n; i++) {
            scanf("%d", &a[i]);
        }

        rmq.build(n, a);

        for(int i = 1; i <= n; i++) {
            int p = i, low, high, mid, gcd, ret;
            while(p <= n) {
                ret = p;
                gcd = rmq.query(i, p);
                RP[i].push_back(p);
                RV[i].push_back(gcd);
                low = p, high = n;
                while(low <= high) {
                    mid = low + high >> 1;
                    if(rmq.query(i, mid) == gcd) ret = mid, low = mid + 1;
                    else high = mid - 1;
                }
                p = ret + 1;
            }
            RP[i].push_back(n + 1);
            RV[i].push_back(0);
        }
        for(int i = 1; i <= n; i++) {
            int p = i, low, high, mid, gcd, ret;
            while(p >= 1) {
                ret = p;
                gcd = rmq.query(p, i);
                LP[i].push_back(p);
                LV[i].push_back(gcd);
                low = 1, high = p;
                while(low <= high) {
                    mid = low + high >> 1;
                    if(rmq.query(mid, i) == gcd) ret = mid, high = mid - 1;
                    else low = mid + 1;
                }
                p = ret - 1;
            }
            LP[i].push_back(0);
            LV[i].push_back(0);
        }
        scanf("%d", &q);
        for(int i = 1; i <= q; i++) {
            scanf("%d%d", &qus[i].L, &qus[i].R);
            qus[i].id = i;
        }

        sort(qus + 1, qus + 1 + q);

        int l = 1, r = 0;
        LL now = 0;
        for(int i = 1; i <= q; i++) {
            int L = qus[i].L, R = qus[i].R, id = qus[i].id;
            while(r < R) {
                r++;
                for(int i = 0; i < SZ(LP[r]) - 1; i++) {
                    if(LP[r][i + 1] >= l) {
                        now += 1LL * LV[r][i] * (LP[r][i] - LP[r][i + 1]);
                    }
                    else {
                        now += 1LL * LV[r][i] * (LP[r][i] - l + 1);
                        break;
                    }
                }
            }
            while(l > L) {
                l--;
                for(int i = 0; i < SZ(RP[l]) - 1; i++) {
                    if(RP[l][i + 1] <= r) {
                        now += 1LL * RV[l][i] * (RP[l][i + 1] - RP[l][i]);
                    }
                    else {
                        now += 1LL * RV[l][i] * (r - RP[l][i] + 1);
                        break;
                    }
                }
            }
            while(r > R) {
                for(int i = 0; i < SZ(LP[r]) - 1; i++) {
                    if(LP[r][i + 1] >= l) {
                        now -= 1LL * LV[r][i] * (LP[r][i] - LP[r][i + 1]);
                    }
                    else {
                        now -= 1LL * LV[r][i] * (LP[r][i] - l + 1);
                        break;
                    }
                }
                r--;
            }
            while(l < L) {
                for(int i = 0; i < SZ(RP[l]) - 1; i++) {
                    if(RP[l][i + 1] <= r) {
                        now -= 1LL * RV[l][i] * (RP[l][i + 1] - RP[l][i]);
                    }
                    else {
                        now -= 1LL * RV[l][i] * (r - RP[l][i] + 1);
                        break;
                    }
                }
                l++;
            }
            ans[id] = now;
        }
        for(int i = 1; i <= q; i++) {
            printf("%lld
", ans[i]);
        }
    }
    return 0;
}

/*
*/