title: how to insert new value into max heap and apply max_delete to heap
body: <p><em>Problem 1</em></p>
  
  <pre><code>                     98
                      /  \
                     /    \
                   67      89
                  / \     /  \
                 /   \   /    \
               38   42  54    89
              / \
             /   \
            17   25
  </code></pre>
  
  <p>i want to insert 97 into max heap [98,67,89,38,42,54,89,17,25] (represented in list).</p>
  
  <p>As per me, resulting heap is [98,97,89,38,67,54,89,17,25,42]</p>
  
  <pre><code>                     98
                      /  \
                     /    \
                   97      89
                  / \     /  \
                 /   \   /    \
               38    67  54    89
              / \     |
             /   \    |
            17   25   42
  </code></pre>
  
  <p><em>Problem 2</em> </p>
  
  <p>i want to apply delete_max() twice to the heap [100,97,93,38,67,54,93,17,25,42]. </p>
  
  <pre><code>                    100
                      /  \
                     /    \
                   97      93
                  / \     /  \
                 /   \   /    \
               38    67  54    93
              / \     |
             /   \    |
            17   25   42
  </code></pre>
  
  <p>As per me heap after two deletemax operations,resulting heap is [93,67,93,38,42,54,25,17]</p>
  
  <pre><code>                     93
                      /  \
                     /    \
                   67      93
                  / \     /  \
                 /   \   /    \
               38    42  54    25
              /     
             /      
            17      
  </code></pre>
  
  <p><strong>I want to conform, is I am doing insertion and max_delete correctly for heap and above answer is correct?</strong>
  If not correct, then please guide me. </p>