第一周 8.29 - 9.4

Posted 2020-08-04

开学了>_<

8.29

Round B APAC Test 2017

B. Sherlock and Watson Gym Secrets

昨天下午做了下 g 家的笔试..真的好菜啊..差好远..好好补下题叭

给出 n,A,B,k ，使得( i^A + j^B) % k == 0 的 i ，j 有多少对(i != j , 1 <= i <= n , 1 <= j <= n)

可以按照 模 k 的余数分类

然后 将 两边的余数 组合起来

cnt[x] * cnt[k-x] (0 <= x <= k-1)，再将 i = j 的统计出来 减掉

好多地方都要取模..找好久错

 1 #include <cstdio>
 2 #include <cstring>
 3 #include <iostream>
 4 #include <algorithm>
 5 using namespace std;
 6 typedef long long LL;
 7 const LL mod = 1e9+7;
 8 const int maxn = 1e6+5;
 9 LL A,B,k,n;
10 LL ca[maxn],cb[maxn],cc[maxn];
11 LL cnt[maxn];
12 
13 LL qpow(LL a, LL b,LL MOD)
14 {
15     LL ret = 1LL;
16     while(b)
17     {
18         if(b & 1) ret = ret * a % MOD;
19         a = a * a % MOD;
20         b >>= 1;
21     }
22     return ret;
23 }
24 
25 void solve(){
26     LL tot = n/k;
27     LL yu = n%k;
28     for(int i = 1;i <= k;i++){
29         cnt[i%k] = tot;
30         if(i <= yu) cnt[i%k]++;
31         cnt[i%k] = (cnt[i%k]+mod) % mod;
32     }
33     for(int i = 1;i <= min(n,k);i++){
34         int l = qpow(i,A,k) % k;
35         int r = qpow(i,B,k) % k;
36         ca[l] = (ca[l] + cnt[i%k]) % mod;
37         cb[r] = (cb[r] + cnt[i%k]) % mod;
38         if((l+r) % k == 0){
39             cc[i%k] = (cc[i%k]+cnt[i%k]) % mod;
40         }
41     }
42     
43     /*for(int i = 0;i <= k;i++){
44         printf("cnt[%d] = %I64d ca[%d] = %I64d cb[%d] = %I64d cc[%d] = %I64d\\n",i,cnt[i],i,ca[i],i,cb[i],i,cc[i]);
45     }*/
46 
47     LL ans = 0;
48     for(int i = 0;i < k;i++){
49         int l = i;l = l%k;
50         int r = k-i;r = r%k;
51         LL tmp = (ca[l]*cb[r])%mod;
52         ans = (ans+tmp) % mod;
53         ans = (ans-cc[i%k]+mod) % mod;
54     }
55     printf("%I64d\\n",ans);
56 }
57 
58 int main(){
59     int T,kase = 0;
60     freopen("B-large-practice.in","r",stdin);
61     freopen("output.out","w",stdout);
62     scanf("%d",&T);
63     while(T--){
64         scanf("%I64d %I64d %I64d %I64d",&A,&B,&n,&k);
65         printf("Case #%d: ",++kase);
66         memset(ca,0LL,sizeof(ca));
67         memset(cb,0LL,sizeof(cb));
68         memset(cc,0LL,sizeof(cc));
69         memset(cnt,0LL,sizeof(cnt));
70         solve();
71     }
72     return 0;
73 }

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