Algorithm for subdividing an array into “semi-equal”, uniform sub-arrays

Question

Given an array with N elements, I am looking for M (M < N) successive sub-arrays with equal lengths or with lengths that differ by mostly 1. For example, if N = 12 and M

Answer 1

If your language has integer division that truncates, an easy way to compute the size of section i is via (N*i+N)/M - (N*i)/M. For example, the python program

  N=100;M=12
  for i in range(M): print (N*i+N)/M - (N*i)/M

outputs the numbers 8 8 9 8 8 9 8 8 9 8 8 9. With N=12;M=5 it outputs 2 2 3 2 3. With N=12;M=3 it outputs 4 4 4.

If your section numbers are 1-based rather than 0-based, the expression is instead (N*i)/M - (N*i-N)/M.

Answer 2

Space-filling-curves and fractals subdivide the plane and reduce the complexity. There is for example z-curve, hilbert curve, morton curve.