[algorithm] Differences between time complexity and space complexity?

Sometimes yes they are related, and sometimes no they are not related, actually we sometimes use more space to get faster algorithms as in dynamic programming https://www.codechef.com/wiki/tutorial-dynamic-programming dynamic programming uses memoization or bottom-up, the first technique use the memory to remember the repeated solutions so the algorithm needs not to recompute it rather just get them from a list of solutions. and the bottom-up approach start with the small solutions and build upon to reach the final solution. Here two simple examples, one shows relation between time and space, and the other show no relation: suppose we want to find the summation of all integers from 1 to a given n integer: code1:

sum=0
for i=1 to n
   sum=sum+1
print sum

This code used only 6 bytes from memory i=>2,n=>2 and sum=>2 bytes therefore time complexity is O(n), while space complexity is O(1) code2:

array a[n]
a[1]=1
for i=2 to n
    a[i]=a[i-1]+i
print a[n]

This code used at least n*2 bytes from the memory for the array therefore space complexity is O(n) and time complexity is also O(n)

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