Codility Peaks v2

This is the second solution for Codility task, named Peaks.

The idea is simple:
I collect all the "peaks", and meanwhile I notice prefix sum of peak encounters.
I go through possible sizes of division as long, as I find that one, that has at least one peak in every "block" aka division.
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public int solution(int[] A) {
      int r = 0;              // result
      final int N = A.length; // size of input table
      int[] P = new int[N/2]; // peaks
      int pInd = -1;          // last index of peaks table
      int[] S = new int[N];   // sumprefix of peak count
     
      for(int i = 1; i < N-1; i++){
        if(A[i] > A[i-1] && A[i] > A[i+1]){
          P[++pInd] = i;      // remember peak index
          S[i] = S[i-1]+1;    // remember amount of peaks till this idx
        } else {
          S[i] = S[i-1];
        }
      }
      if(pInd == -1) return 0;   // no peaks
      if(pInd ==  0) return 1;   // one peak means one block
     
      S[N-1] = S[N-2];        // filling the last value of S
     
      int minSize = max(N - P[pInd], P[0]+1); // first and last block has to have a peak
      for(int size = minSize; size <=N; size++){
        boolean noPeak = false;
        if(N % size == 0){
          int blocksAmount = N/size;
          for(int blockNb = 1; blockNb < blocksAmount; blockNb++){
            if( !(S[(blockNb+1)*size -1] > S[blockNb*size -1]) ){
              noPeak = true;
              break;
            }
          } // end of loop for blocks
          if (!noPeak) {
            r = N / size;
            break;
          }
        }
      } // end of loop for sizes
     
      return r;
    }

Codility - Peaks

This is the first solution of the peaks task form Codility platform:

Idea is to determine min and max size of possible block, then go through peaks and increase minimum size of the block if some peak is "out of the division". Additionally there is a list of forbidden value of sizes to avoid situation that increasing minimum size on one peak would negatively interfere with any of previous peaks.

It's very long in implementation, but intuitive, very fast && maybe original. Faster than widely published version with checking all the peaks in a loop of consecutive size of the block, if one don't use prefix sum for counting blocks. Of course 100% in Codility test.

Here is a code:


public int solution(int[] A) {
    int r;
    final int N = A.length;
    int[] B = new int[N]; // space between peaks +1
    int[] P = new int[N]; // peaks idxs
    int iP;               // max index of values in table P
    int max_bl, min_bl;
    List<Integer> list_impossible_min = new ArrayList<>();
    int[] min_max_ip = new int[3]; // temporary storage for variables

    // detemine B, P, iP, max_bl, min_bl
    getMinMaxBl(A, B, P, min_max_ip);
    min_bl = min_max_ip[0];
    max_bl = min_max_ip[1];
    iP     = min_max_ip[2];
   
    if(iP == -1){       // no peaks
      return 0;
    } else if(iP == 0){ // one peak
      return 1;
    }

    // applaying last block size
    int last_bl = N-1 -P[iP] + 1;
   
    if( last_bl > min_bl){
      min_bl = last_bl;}
    if(last_bl > B[P[iP]]){
      B[P[iP]] = last_bl;}

    // applying condition of possible divide
    while ((N % min_bl) != 0) {
      min_bl++;}
    while ((N % max_bl) != 0) {
      max_bl++;}


    for (int i = 1; i <= iP; i++) {
      int idx_peak = P[i];
      if (B[idx_peak] > min_bl) {   
        int pp = P[i-1]; // previous peak
       
        int a = (idx_peak + 1) / min_bl;
        int b = a * min_bl;
        if (b != (idx_peak + 1)) { // border of division is in between peaks
          if (b - pp > min_bl) {   // border of division is too far from pp

            // seraching for first possible new min_bl
            for (int j = min_bl + 1; j <= max_bl; j++) {
              a = (idx_peak + 1) / j;
              b = a * j;

              if (list_impossible_min.isEmpty() || !list_impossible_min.contains(j)) {
                if (N % j == 0 && (b - pp <= j)) {
                  min_bl = j;
                  break;
                }
              }
            }
          }
        }
        for (int j = min_bl + 1; j <= B[idx_peak]; j++) {
          a = (idx_peak + 1) / j;
          b = a * j;

          if (N % j != 0 || ((pp + j < idx_peak) && ( b*a-pp > j))) {
            if (pp + j < idx_peak) {
              if (list_impossible_min.isEmpty() || !list_impossible_min.contains(j)) {
                list_impossible_min.add(j);
              }
            }
          }
        }
      }
    }
    r = N / min_bl;

    return r;
  }

  private void getMinMaxBl(int[] A, int[] B, int[] P, int[] min_max_ip) {
    int N = A.length;
    int f_peak = -1, l_peak = -1;
    int iP = -1, min_bl = 0, max_bl = 0;

    // detemine max_bl, min_bl
    // first min_bl & max_bl
    for (int i = 1; i < N - 1; i++) {
      if (peak(A, i)) {
        max_bl = i+1;
        min_bl = i+1;
        f_peak = i;
        l_peak = i;
        B[i]   = i+1;
        P[++iP] = i;
        break;
      }
    }
    if(f_peak > 0){
      for(int i = f_peak+2; i < N-1; i++){
        int t_max_block;
        int t_min_block;
        if (peak(A, i)) {
          t_max_block = i - l_peak; // covers cells max empty space + 1 for peak
          t_min_block = (t_max_block + 1)/2; // covers two peaks + space between
          if((t_max_block+1)%2 != 0){
            t_min_block++;
          }
          min_bl = max(min_bl, t_min_block);
          max_bl = max(max_bl, t_max_block);
          B[i]   = t_max_block;
          l_peak = i;
          P[++iP] = i;
        }
      }
    }
    min_max_ip[0] = min_bl;
    min_max_ip[1] = max_bl;
    min_max_ip[2] = iP;
  }

  boolean peak(int[] A, int i) {
    return A[i] > A[i - 1] && A[i] > A[i + 1];
  }