Educational Codeforces Round 24 E. Card Game Again[数论][线段树]

题目：http://codeforces.com/contest/818/problem/E

题意：有多少种情况使得对数组剔除前缀x项和后缀y项后，中间的项乘积能被k整除

题解：直接记录区间乘积数字过大，利用取余的分配律 (a%x)*(b%x)==(a*b)%x，暴力枚举x，二分寻找最大的y，线段树保存区间取模值。

  1 #define _CRT_SECURE_NO_DEPRECATE
  2 #pragma comment(linker, "/STACK:102400000,102400000")
  3 #include<iostream>  
  4 #include<cstdio>  
  5 #include<fstream>  
  6 #include<iomanip>
  7 #include<algorithm>  
  8 #include<cmath>  
  9 #include<deque>  
 10 #include<vector>  
 11 #include<assert.h>
 12 #include<bitset>
 13 #include<queue>  
 14 #include<string>  
 15 #include<cstring>  
 16 #include<map>  
 17 #include<stack>  
 18 #include<set>
 19 #include<functional>
 20 #define pii pair<int, int>
 21 #define mod 1000000007
 22 #define mp make_pair
 23 #define pi acos(-1)
 24 #define eps 0.00000001
 25 #define mst(a,i) memset(a,i,sizeof(a))
 26 #define all(n) n.begin(),n.end()
 27 #define lson(x) ((x<<1))  
 28 #define rson(x) ((x<<1)|1) 
 29 #define inf 0x3f3f3f3f
 30 typedef long long ll;
 31 typedef unsigned long long ull;
 32 using namespace std;
 33 
 34 const int maxn = 1e5 + 5;
 35 int ori[maxn];
 36 ll md;
 37 class t {
 38 public:
 39     int l, r;
 40     ll value;
 41     t() { l = 0, r = 0; }
 42 }tree[maxn * 4 + 5];
 43 
 44 void build(int l, int r, int u)
 45 {
 46     tree[u].l = l;
 47     tree[u].r = r;
 48     if (l == r)
 49     {
 50         tree[u].value = ori[l] % md;
 51         return;
 52     }
 53     int mid = (l + r) >> 1;
 54     build(l, mid, lson(u));
 55     build(mid + 1, r, rson(u));
 56     tree[u].value = (tree[lson(u)].value* tree[rson(u)].value) % md;
 57 }
 58 
 59 ll query(int l, int r, int u)
 60 {
 61     if (l > r)return 0;
 62     if (tree[u].l >= l&&tree[u].r <= r)return tree[u].value;
 63     int mid = (tree[u].l + tree[u].r) >> 1;
 64     ll ret = 1;
 65     if (l <= mid)ret *= query(l, r, lson(u));
 66     if (r > mid)ret *= query(l, r, rson(u));
 67     return ret%md;
 68 }
 69 
 70 inline ll check(int l, int r)
 71 {
 72     return query(l, r, 1);
 73 }
 74 
 75 int main()
 76 {
 77     ios::sync_with_stdio(false);
 78     cin.tie(0); cout.tie(0);
 79     int i, j, k, m, n;
 80     cin >> n >> md;
 81     for (int i = 1; i <= n; ++i)
 82         cin >> ori[i];
 83     build(1, n, 1);
 84     ll ans = 0;
 85 
 86     for (int i = 1; i <= n; ++i)
 87     {
 88         int l = i, r = n;
 89         while (r - l > 1)
 90         {
 91             int mid = (l + r) >> 1;
 92             if (check(i, mid))l = mid;
 93             else r = mid;
 94         }
 95         if (!check(i, l))
 96             ans += n - l + 1;
 97         else if(!check(i, r)) ans += n - r + 1;
 98     }
 99     cout << ans;
100     return 0;
101 }

 

posted @ 2017-09-21 13:27  Meternal  阅读(158)  评论(0)  编辑  收藏  举报