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up vote 0 down vote favorite

Can anyone help to convert this to a recursion function?

def max_vel(t):
    vel = 0   
    thr = 10
    c = -0.1
    for i in range(t):
        fric = c * vel
        acc = thr + fric
        vel = vel + acc
        print fric, acc, vel
    print vel
    return vel
print max_vel(154)
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11  
Why? Iterative functions are generally better, and in python this is especially true. You avoid the recursion limit and a lot of function call overhead. By the way: in your function you are mixing computation and input/output. This is bad design. The two things should be separated to increase code re-usability. –  Bakuriu Jun 5 '13 at 5:27
    
Thanks, my aim is to grip the thought/design process for implementing recursion, so this is just a demo code. –  01dfaithfull Jun 5 '13 at 6:22
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2 Answers

up vote 0 down vote accepted

To solve a problem with a recursion, it is needed to state that problem in recursion manner. That means to define it in self similar way.

In this case there are variables: time, acceleration and velocity. So, main problem has to be defined with sub-problems with same variables. There are 2 (quite similar) problems we can use:

  • what is acceleration and velocity after t seconds from start.
  • if we have given acceleration and velocity, what will be acceleration and velocity after t seconds.

With that there are two (similar) recursion solutions:

def start_av(t):
  if t == 0: return 0, 0
  acc, vel = start_av(t-1)
  thr = 10
  c = -0.1
  fric = c*vel
  acc = thr + fric
  return (acc, vel + acc)

def given_av(t, acc=0, vel=0):
  if t == 0: return acc, vel
  thr = 10
  c = -0.1
  fric = c*vel
  acc = thr + fric
  return given_av(t-1, acc, vel + acc)    

print start_av(10)
print given_av(10)
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up vote 0 down vote

A rather simple way:

def max_vel(t, vel=[0], thr=10):
    c = -0.1
    if t > 0:
        fric = c * vel[0]
        acc = thr + fric
        vel[0] = vel[0] + acc
        print fric, acc, vel
        max_vel(t - 1, vel, thr)
    return vel[0]

Here you just decrement t, since this is the the number of iterations. c never changes, so it is not passed in the recursion. Now I use vel as a list of 1 element because in Python lists are mutable: this allows vel content to be updated by recursion calls.

share|improve this answer
    
your function doesn't return anything –  oleg Jun 5 '13 at 7:40
    
Good remark... Updated ! –  Emmanuel Jun 5 '13 at 10:29
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