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115 pts) Consider binary trees where each node contains an integer Here is an example of a binary tree 15 . The root node of the whole tree above is the node at the root with integer 3. The left subtree of the root rode 3 is the tree with root rode 4 that has chid nodes. The right tree of the root nodes the tree with node Integer and two children with integers of 7 and 8. Write an algorithm such that its input is a binary treet and a numberx.it has no output, and it has a side effect of setting the integer at every node oft to bex Uhin the problem decomposition method to design the algorithem. You are not allowed to use loops. Make a problem decomposition and their decomposibly condition explication your dipormes. Your digorts must follow the format discussed in class in your algorithm, no other functions are allowed except the following function child its input is any tree and output is the left subtree of the root of function child its input is any troet and output is the right subtree of the root oft function empty its input is any tree and output is the tree is empty, there are no nodes) and also otherwise function set its input is a tree and a numbers, it has no output, and its side effect is to set the integer at the root node of tobox Hintatree can usually be decomposed as three parts its root, its left tree and its right tree