<h2 id="heading-on2">o(n^2)</h2>
<pre><code class="lang-python">def quad_find(s, n):
 slen = len(s)

 for i in range(slen):
 for j in range(slen-1):
 if s[i] + s[j+1] == n:
 return (i, j+1)

 return None
</code></pre>
In the provided Python function, 's' represents a list and 'n' represents the target value.
<h2 id="heading-on">o(n)</h2>
<pre><code class="lang-python">def linear_find(s, n): 
 dict = {}

 for i in range(len(s)):
 if s[i] in dict:
 return (i, dict[s[i]]) # s[i] contains the other index
 else:
 complement = n - s[i]
 dict[complement] = i

 return None
</code></pre>
In our <code>linear_find</code> function, we commence by initializing an empty dictionary, which plays a critical role as a hashmap. This hashmap is used to store indices of 'complementary' elements—these are elements which, when added to another, would equal the target sum 'n'.

## o(n^2)

```python
def quad_find(s, n):
    slen = len(s)

    for i in range(slen):
        for j in range(slen-1):
            if s[i] + s[j+1] == n:
                return (i, j+1)

    return None
```

In the provided Python function, 's' represents a list and 'n' represents the target value.

## o(n)

```python
def linear_find(s, n):    
    dict = {}

    for i in range(len(s)):
        if s[i] in dict:
            return (i, dict[s[i]])    # s[i] contains the other index
        else:
            complement = n - s[i]
            dict[complement] = i
    
    return None
```

In our `linear_find` function, we commence by initializing an empty dictionary, which plays a critical role as a hashmap. This hashmap is used to store indices of 'complementary' elements—these are elements which, when added to another, would equal the target sum 'n'.

looking for two indices whose value add to target n

o(n^2)

o(n)