HDU5187 zhx & amp; #39; s contest (count problem)

HDU5187 zhx & #39; s contest (count problem)

 

Question:

From 1 ~ N, how many sort

Make a1 ~ Ai can be monotonic or monotonic.

Ai ~ An is monotonically increasing or decreasing.

Obvious combination Problems

Select the number of I from n. The remaining number must meet the monotonic increasing or decreasing law, so the method is unique.

Ans = (C (N, 0) + C (N, 1) +... + C (N, N) = 2 ^ N;

But in this case, the monotonic increasing and monotonic decreasing are calculated twice, so we need to subtract 2.

Ans = 2 ^ n-2;

Note that n = 1, because n is relatively large, pay attention to multiplication Overflow

 

The Code is as follows:

 

#include 
 
  #include 
  
   #include 
   
    #include using namespace std;typedef long long LL;LL multi(LL a,LL b, LL c){    LL ans = 0;    while(b){        if(b&1){            ans= (ans+a)%c;            b--;        }        b>>=1;        a=(a+a)%c;    }    return ans;}LL quick_mod(LL a,LL b,LL c){    LL ans = 1;    while(b){        if(b&1){            ans = multi(ans,a,c);            b--;        }        b>>=1;        a=multi(a,a,c);    }    return ans ;}int main(){    LL n,p;    while(~scanf(%lld%lld,&n,&p)){        if(n==1){            printf(%d,1%p);            continue;        }        LL ans = 2;        ans = quick_mod(ans,n,p);        ans =(ans - 2 + p)%p;        printf(%I64d,ans);    }    return 0;}