Codeforces 402D D. Upgrading Array (dp+ number theory)

Topic Links:

Codeforces 402D

Main topic:

Given a sequence, you can do an operation to remove a prefix from their gcd, there is a function f (x), f (1) = 0, f (x) = f (x/p) +1,f (x) = f (x/p)-1 (p is bad prime) ask ∑ i≤n F (a[I]) The maximum value

Topic Analysis:

• First, according to the recursive formula, we know that the result is that the F (x) of each number is the number of good primes in its mass factor minus the number of bad primes.
• Then we know that if the number of good primes in a gcd is less than the number of bad primes, then we can get better results if we get rid of them, so if we start with the last number, the number of GCD will not affect the previous number, because if the number of bad primes in this part of the factorization is more than the good primes, The preceding number must also be removed.
• So we are greedy of the reverse of doing just fine.
  

AC Code:

#include <iostream>#include <cstring>#include <cstdio>#include <algorithm>#include <map>#define MAX 5007#define M 100007using namespace STD;intN,m,a[max],b[max];intPrime[m],g[max]; map<int,bool>mpvoidInit () {memset(Prime,0,sizeof(prime)); prime[1] = prime[0] =1; for(inti =2; I*i < M; i++) {if(Prime[i])Continue; for(intj = i*i; J < M; j+= i) prime[j] =1; }}intGCD (intAintb) {returnB?GCD (b,a%b): A;}intMain () {init (); while( ~scanf("%d%d", &n, &m)) {mp.clear (); for(inti =0; I < n; i++)scanf("%d", &a[i]); for(inti =0; I < m; i++)scanf("%d", &b[i]); g[0] = a[0]; for(inti =0; I < m; i++) Mp[b[i] =true; for(inti = n1; I >=0; i--) {intx =0; for(intj =0; J <= I; j + +) x = gcd (x, a[j]);intxx = x;intnum1,num2; NUM1 = Num2 =0; for(intj =2; J*j <= x; J + +) {if(Prime[j])Continue;if(X%J)Continue;BOOLflag = Mp[j]; while(X%j = =0) {x/= J;if(flag) num1++;Elsenum2++; }            }if(X >1)             {if(Mp[x]) num1++;Elsenum2++; }if(Num1 > Num2) for(intj =0; J <= I;        J + +) A[j]/= xx; }intAns =0; for(inti =0; I < n; i++) {intx = A[i]; for(intj =2; J*j <= x; J + +) {if(Prime[j])Continue;if(X%J)Continue;BOOLflag = Mp[j]; while(X%j = =0) {x/= J;if(flag) ans--;Elseans++; }            }if(X >1)            {if(Mp[x]) ans--;Elseans++; }        }printf("%d\n", ans); }}

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Codeforces 402D D. Upgrading Array (dp+ number theory)