function insert(heap &H,key k)

   integer i;

   H.n=H.n+1;    // number of elements increases
   H.a[n]=k;        // insert element

   i=H.n;
   while (i>1)    // root not yet reached   
   do
      if (H.a[i]>H.a[i/2]) // heap property violated ?
      then temp=H.a[i];         // yes, exchange nodes
           H.a[i]=H.a[i/2];
           H.a[i/2]=temp;
           i=i/2;         // go up in direction of root
      else i=1;                 // exit while loop
      fi
   od

function delete_maximum(heap &H)

   integer i;

   H.a[1]=H.a[H.n]; // max now deleted
   H.n=H.n-1;    // number of elements decreases

   i=1;
   while (2*i<=H.n) // has at least a left child
   do
      child_left=2*i;     // index of left child
      child_right=2*i+1;  // index of right child
      if (child_right<=H.n)   // does right child exist?
      then                       // yes, then find max of both children
         if (H.a[child_left]>H.a[child_right])
         then child_max=child_left;
         else child_max=child_right;
         fi
      else child_max=child_left; // no, maximum is left child
      fi
      if (H.a[i]<H.a[child_max]) // heap property violated?
      then temp=H.a[i];         // yes, exchange nodes
           H.a[i]=H.a[child_max];
           H.a[child_max]=temp;
           i=child_max;         // go down in direction of leaf
      else i=H.n+1;          // exit while loop
      fi
   od
end

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