（预处理+莫队算法）HDU - 5381 The sum of gcd

  1 #include <iostream>
  2 #include <cstdio>
  3 #include <algorithm>
  4 #include <cmath>
  5 #include <cstring>
  6 #include <set>
  7 #include <vector>
  8 #include <queue>
  9 #include <map>
 10 #include <list>
 11 #include <bitset>
 12 #include <string>
 13 #include <cctype>
 14 #include <cstdlib>
 15 
 16 using namespace std;
 17 
 18 typedef long long ll;
 19 typedef unsigned long long ull;
 20 #define inf (0x3f3f3f3f)
 21 #define lnf (0x3f3f3f3f3f3f3f3f)
 22 #define eps (1e-8)
 23 #define fi first
 24 #define se second
 25 typedef pair<ll, ll> pll;
 26 
 27 int sgn(double a) {
 28     return a < -eps ? -1 : a < eps ? 0 : 1;
 29 }
 30 
 31 const int maxn = 50010;
 32 struct Q {
 33     int l, r, index;
 34 };
 35 Q query[maxn];
 36 int t, n, q;
 37 int a[maxn];
 38 int b[maxn];
 39 const int bk = 250;
 40 long long res;
 41 long long ans[maxn];
 42 int f[maxn][20];
 43 
 44 void rmq_init() {
 45     for(int i = 1; i <= n; i++)
 46         f[i][0] = a[i];
 47     int k = floor(log((double)n) / log(2.0));
 48     for(int j = 1; j <= k; j++)
 49         for(int i = n; i >= 1; i--) {
 50             if(i + (1 << (j - 1)) <= n)
 51                 f[i][j] = __gcd(f[i][j - 1], f[i + (1 << (j - 1))][j - 1]);
 52         }
 53 }
 54 
 55 int rmq(int i, int j) {
 56     int k = floor(log((double)(j - i + 1)) / log(2.0));
 57     return __gcd(f[i][k], f[j - (1 << k) + 1][k]);
 58 }
 59 
 60 bool cmp (Q a, Q b) {
 61     if(a.l / bk == b.l / bk)return a.r < b.r;
 62     else return a.l / bk < b.l / bk;
 63 }
 64 
 65 
 66 vector<pll> pre[maxn];
 67 vector<pll> suf[maxn];
 68 
 69 
 70 int search2(int zl, int l, int b) {
 71     int left = l, right = n;
 72     int w = l + 1;
 73     while(left <= right) {
 74         int mid = (left + right) >> 1;
 75         int pp = rmq(zl, mid);
 76         if(pp == b) {
 77             left = mid + 1;
 78             w = mid;
 79         } else {
 80             right = mid - 1;
 81         }
 82     }
 83     return w;
 84 }
 85 
 86 int search3(int zl, int l, int b) {
 87     int left = l, right = n;
 88     int w = l + 1;
 89     while(left <= right) {
 90         int mid = (left + right) >> 1;
 91         int pp = rmq(n - mid + 1, n - zl + 1);
 92         if(pp == b) {
 93             left = mid + 1;
 94             w = mid;
 95         } else {
 96             right = mid - 1;
 97         }
 98     }
 99     return w;
100 }
101 
102 void Pfinit() {
103     for(int i = 1; i <= n; i++) {
104         pre[i].clear();
105         for(int s = i - 1; s < n;) {
106             int d = search2(i, s + 1, rmq(i, s + 1));
107             pre[i].push_back(make_pair(d - s, rmq(i, s + 1)));
108             s = d;
109         }
110     }
111     for(int i = 1; i <= n; i++) {
112         b[i] = a[n - i + 1];
113     }
114     for(int i = 1; i <= n; i++) {
115         suf[n - i + 1].clear();
116         for(int s = i - 1; s < n;) {
117             int d = search3(i, s + 1, rmq(n - s, n - i + 1));
118             suf[n - i + 1].push_back(make_pair(d - s, rmq(n - s, n - i + 1)));
119             s = d;
120         }
121     }
122 
123 }
124 
125 
126 void add_left( int s, int x, int v) {
127     int num = s - x + 1;
128     for(int i = 0; i < pre[x].size(); i++) {
129         if(pre[x][i].fi >= num) {
130             res += num * pre[x][i].se * v;
131             break;
132         } else {
133             res += pre[x][i].fi * pre[x][i].se * v;
134             num -= pre[x][i].fi;
135         }
136     }
137 }
138 
139 
140 void add_right(int s, int x, int v) {
141     int num = x - s + 1;
142     for(int i = 0; i < suf[x].size(); i++) {
143         if(suf[x][i].fi >= num) {
144             res += num * suf[x][i].se * v;
145             break;
146         } else {
147             res += suf[x][i].fi * suf[x][i].se * v;
148             num -= suf[x][i].fi;
149         }
150     }
151 }
152 
153 int main() {
154     scanf("%d", &t);
155     while(t--) {
156         res = 0;
157         scanf("%d", &n);
158         for(int i = 1; i <= n; i++) {
159             scanf("%d", &a[i]);
160         }
161         rmq_init();
162         Pfinit();
163         scanf("%d", &q);
164         for(int i = 0; i < q; i++) {
165             scanf("%d%d", &query[i].l, &query[i].r);
166             query[i].index = i;
167         }
168         sort(query, query + q, cmp);
169         int pl = 1, pr = 0;
170         for (int i = 0; i < q; i++) {
171             int index = query[i].index;
172             if (pr < query[i].r) {
173                 for (int j = pr + 1; j <= query[i].r; j++) {
174                     add_right(pl, j, 1);
175                 }
176 
177             } else {
178                 for (int j = pr; j > query[i].r; j--) {
179                     add_right(pl, j, -1);
180                 }
181             }
182             pr = query[i].r;
183             if (pl < query[i].l) {
184                 for (int j = pl; j < query[i].l; j++) {
185                     add_left(pr, j, -1);
186                 }
187             } else {
188                 for (int j = pl - 1; j >= query[i].l; j--) {
189                     add_left(pr, j, 1);
190                 }
191             }
192             pl = query[i].l;
193             ans[index] = res;
194         }
195         for(int i = 0; i < q; i++) {
196             printf("%lld\n", ans[i]);
197         }
198     }
199     return 0;
200 }