leetcode_gym/_problems/countOnesInArray.md

layout, title

layout	title
page	Count Ones (In Array)

{% highlight text %}

''' https://leetcode.com/problems/counting-bits/

Problem:

Given num, return array which contains numOnes
Ie, input = 2, return [0,1,1]

Do it in O(n) time, and not O(n*numBits)

Solution: dynamic programming (build table bottom up)

d[i] = d[i//2] + (i%2)

ex:
d[3] = d[3//2] + 3%2
     = d[1] + 1
     = 2
d[6] = d[6//2] + 6%2
     = d[3] + 0
     = 2 + 0
     = 2
d[7] = d[7//2] + 7%2
     = d[3] + 1
     = 2 + 1 = 3

https://leetcode.com/problems/counting-bits/discuss/626777/Easy-DP-Explanation-%3A-Python-Solution

'''

{% endhighlight %}

{% highlight python %}

def countOnes(num):

if num==0: return [0]
if num==1: return [0,1]


dp=[0,1]

for i in range(2, num+1):
    # dp[i] = dp[i//2] + (i%2)
    dp.append( dp[i//2] + (i%2) )

return dp

print(countOnes(2))

{% endhighlight %}