UVa 12063 (DP) Zeros and Ones

Test instructions

Find the number of binary numbers with an equal length of n, 0, and 1 numbers, no leading 0, and a multiple of K.

Analysis:

This problem should be done with dynamic planning.

Set DP (zeros, ones, MoD) to have zeros 0,ones 1, divided by the remainder of K is the number of binary numbers of the MoD, then the state transition equation is:

DP (zeros + 1, ones, (mod>>1)% k) + = DP (zeros, ones, MoD)

DP (zeros, ones + 1, ((mod>>1) +1)% k) + = DP (zeros, ones, MoD)

Using the memory search and recursive way to write again, recursion than the memory of the search faster than half the time.

1#include <cstdio>2#include <cstring>3 4 intN, K;5 Long Longd[ *][ *][ the];6 7 Long LongdpintZeros,intOnesintMoD)8 {9     if(zeros + ones > N | | zeros > n/2|| Ones > n/2)return 0;Ten     if(D[zeros][ones][mod]! =-1)returnD[zeros][ones][mod]; One     returnD[ZEROS][ONES][MOD] = DP (zeros+1, Ones, (mod<<1)%k) + DP (Zeros, ones+1, (((mod<<1)%k) +1)%k); A } -  - intMain () the { -     //freopen ("In.txt", "R", stdin); -  -     intT; +scanf"%d", &T); -      for(intKase =1; Kase <= T; ++Kase) +     { Ascanf"%d%d", &n, &k); at  -         if(n%2==1|| K = =0) {printf ("Case %d:0\n", Kase);Continue; } -  -memset (D,-1,sizeof(d)); -d[n/2][n/2][0] =1; -printf"Case %d:%lld\n", Kase, DP (0,1,1)); in  -     } to  +     return 0; -}

Memory Search

1#include <cstdio>2#include <cstring>3 4 intN, K;5 Long Longdp[ *][ *][ the];6 7 intMain ()8 {9     //freopen ("In.txt", "R", stdin);Ten  One     intT; Ascanf"%d", &T); -      for(intKase =1; Kase <= T; ++Kase) -     { thescanf"%d%d", &n, &k); -  -         if(n%2==1|| K = =0) {printf ("Case %d:0\n", Kase);Continue; } -  +N/=2; -Memset (DP,0,sizeof(DP)); +  Adp[0][1][1%K] =1; at          for(inti =0; I <= N; i++) -              for(intj =0; J <= N; J + +) -                  for(intm =0; M < K; m++) -                 { -dp[i+1][j][(m<<1)%k] + =Dp[i][j][m]; -dp[i][j+1[(m<<1)+1)%k] + =Dp[i][j][m]; in                 } -  toprintf"Case %d:%lld\n", Kase, dp[n][n][0]); +  -     } the  *     return 0; $}

Recursive

UVa 12063 (DP) Zeros and Ones