data structures using we then go up the tree with ptr initially pointing to node in each iteration of the while loopval[ptris compared with the value of its parent par howeverif either ptr is the root or key[ptr>key[par]then the binomial tree is heap-ordered otherwisenode ptr violates heap-orderingso its key is exchanged with that of its parent we set ptr par and par parent[ptrto move up one level in the tree and continue the process the binomial-heap_decrease_val procedure takes (log ntime as the maximum depth of node is log nso the while loop will iterate at most log times deleting node binomial-heap_delete-node(hxonce we have understood the binomial-heap_ decrease_val procedureit becomes easy to delete step binomial-heap_decrease_val(hx-* node ' value from the binomial heap in step min-extract_binomial-heap(ho(log ntime to start with the algorithmwe set step end the value of to assuming that there is no node in the heap that has value less than *the figure algorithm to delete node from algorithm to delete node from binomial heap bionomial heap can be given as shown in fig the binomial-heap_delete-node procedure sets the value of to *which is unique minimum value in the entire binomial heap the binomial-heap_decrease_val algorithm bubbles this key upto root and then this root is removed from the heap by making call to the min-extract_binomialheap procedure the binomial-heap_delete-node procedure takes (log ntime example solution delete the node with the value from the binomial heap (step par ptr - head [ (step (step ptr - par ptr - head [ ptr - par head [ (step head [hhead [ head [ (step - (contd