# Building Expression tree from Prefix Expression

Given a character array a[] representing a prefix expression. The task is to build an Expression Tree for the expression and then print the infix and postfix expression of the built tree.

Examples:

Input: a[] = “*+ab-cd”
Output: The Infix expression is:
a + b * c – d
The Postfix expression is:
a b + c d – *

Input: a[] = “+ab”
Output: The Infix expression is:
a + b
The Postfix expression is:
a b +

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: If the character is an operand i.e. X then it’ll be the leaf node of the required tree as all the operands are at the leaf in an expression tree. Else if the character is an operator and of the form OP X Y then it’ll be an internal node with left child as the expressionTree(X) and right child as the expressionTree(Y) which can be solved using a recursive function.

Below is the implementation of the above approach:

 // C program to construct an expression tree  // from prefix expression #include #include    // Represents a node of the required tree typedef struct node {     char data;     struct node *left, *right; } node;    // Function to recursively build the expression tree char* add(node** p, char* a) {        // If its the end of the expression     if (*a == '\0')         return '\0';        while (1) {         char* q = "null";         if (*p == NULL) {                // Create a node with *a as the data and             // both the children set to null             node* nn = (node*)malloc(sizeof(node));             nn->data = *a;             nn->left = NULL;             nn->right = NULL;             *p = nn;         }         else {                // If the character is an operand             if (*a >= 'a' && *a <= 'z') {                 return a;             }                // Build the left sub-tree             q = add(&(*p)->left, a + 1);                // Build the right sub-tree             q = add(&(*p)->right, q + 1);                return q;         }     } }    // Function to print the infix expression for the tree void inr(node* p) // recursion {     if (p == NULL) {         return;     }     else {         inr(p->left);         printf("%c ", p->data);         inr(p->right);     } }    // Function to print the postfix expression for the tree void postr(node* p) {     if (p == NULL) {         return;     }     else {         postr(p->left);         postr(p->right);         printf("%c ", p->data);     } }    // Driver code int main() {     node* s = NULL;     char a[] = "*+ab-cd";     add(&s, a);     printf("The Infix expression is:\n ");     inr(s);     printf("\n");     printf("The Postfix expression is:\n ");     postr(s);     return 0; }

Output:

The Infix expression is:
a + b * c - d
The Postfix expression is:
a b + c d - *

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