AVL Tree Insertion
Write a C Program to implement AVL Tree Insertion. Here’s simple Program to implement AVL Tree Insertion in C Programming Language.
What is AVL Tree ?
AVL tree is a self-balancing Binary Search Tree (BST) where the difference between heights of left and right subtrees cannot be more than one for all nodes.
Why AVL Trees?
Most of the BST operations (e.g., search, max, min, insert, delete.. etc) take O(h) time where h is the height of the BST. The cost of these operations may become O(n) for a skewed Binary tree.
If we make sure that height of the tree remains O(Logn) after every insertion and deletion, then we can guarantee an upper bound of O(Logn) for all these operations. The height of an AVL tree is always O(Logn) where n is the number of nodes in the tree
Below is the source code for C Program to implement AVL Tree Insertion which is successfully compiled and run on Windows System to produce desired output as shown below :
SOURCE CODE : :
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/* C Program to implement AVL Tree Insertion */ #include <stdio.h> #include <stdlib.h> #define FALSE 0 #define TRUE 1 struct node { struct node *lchild; int info; struct node *rchild; int balance; }; void inorder(struct node *ptr); struct node *RotateLeft(struct node *pptr); struct node *RotateRight(struct node *pptr); struct node *insert(struct node *pptr, int ikey); struct node *insert_left_check(struct node *pptr, int *ptaller); struct node *insert_right_check(struct node *pptr, int *ptaller); struct node *insert_LeftBalance(struct node *pptr); struct node *insert_RightBalance(struct node *pptr); void display(struct node *ptr,int level); int main() { int choice,key; struct node *root = NULL; while(1) { printf("\n"); printf("1.Insert\n"); printf("2.Display\n"); printf("3.Quit\n"); printf("\nEnter your choice : "); scanf("%d",&choice); switch(choice) { case 1: printf("\nEnter the key to be inserted : "); scanf("%d",&key); root = insert(root,key); break; case 2: printf("\n"); display(root,0); printf("\n"); break; case 3: exit(1); default: printf("Wrong choice\n"); }/*End of switch */ }/*End of while */ return 0; }/*End of main()*/ struct node *insert(struct node *pptr, int ikey) { static int taller; if(pptr==NULL) /*Base case*/ { pptr = (struct node *) malloc(sizeof(struct node)); pptr->info = ikey; pptr->lchild = NULL; pptr->rchild = NULL; pptr->balance = 0; taller = TRUE; } else if(ikey < pptr->info) /*Insertion in left subtree*/ { pptr->lchild = insert(pptr->lchild, ikey); if(taller==TRUE) pptr = insert_left_check( pptr, &taller ); } else if(ikey > pptr->info) /*Insertion in right subtree */ { pptr->rchild = insert(pptr->rchild, ikey); if(taller==TRUE) pptr = insert_right_check(pptr, &taller); } else /*Base Case*/ { printf("Duplicate key\n"); taller = FALSE; } return pptr; }/*End of insert( )*/ struct node *insert_left_check(struct node *pptr, int *ptaller ) { switch(pptr->balance) { case 0: /* Case L_A : was balanced */ pptr->balance = 1; /* now left heavy */ break; case -1: /* Case L_B: was right heavy */ pptr->balance = 0; /* now balanced */ *ptaller = FALSE; break; case 1: /* Case L_C: was left heavy */ pptr = insert_LeftBalance(pptr); /* Left Balancing */ *ptaller = FALSE; } return pptr; }/*End of insert_left_check( )*/ struct node *insert_right_check(struct node *pptr, int *ptaller ) { switch(pptr->balance) { case 0: /* Case R_A : was balanced */ pptr->balance = -1; /* now right heavy */ break; case 1: /* Case R_B : was left heavy */ pptr->balance = 0; /* now balanced */ *ptaller = FALSE; break; case -1: /* Case R_C: Right heavy */ pptr = insert_RightBalance(pptr); /* Right Balancing */ *ptaller = FALSE; } return pptr; }/*End of insert_right_check( )*/ struct node *insert_LeftBalance(struct node *pptr) { struct node *aptr, *bptr; aptr = pptr->lchild; if(aptr->balance == 1) /* Case L_C1 : Insertion in AL */ { pptr->balance = 0; aptr->balance = 0; pptr = RotateRight(pptr); } else /* Case L_C2 : Insertion in AR */ { bptr = aptr->rchild; switch(bptr->balance) { case -1: /* Case L_C2a : Insertion in BR */ pptr->balance = 0; aptr->balance = 1; break; case 1: /* Case L_C2b : Insertion in BL */ pptr->balance = -1; aptr->balance = 0; break; case 0: /* Case L_C2c : B is the newly inserted node */ pptr->balance = 0; aptr->balance = 0; } bptr->balance = 0; pptr->lchild = RotateLeft(aptr); pptr = RotateRight(pptr); } return pptr; }/*End of insert_LeftBalance( )*/ struct node *insert_RightBalance(struct node *pptr) { struct node *aptr, *bptr; aptr = pptr->rchild; if(aptr->balance == -1) /* Case R_C1 : Insertion in AR */ { pptr->balance = 0; aptr->balance = 0; pptr = RotateLeft(pptr); } else /* Case R_C2 : Insertion in AL */ { bptr = aptr->lchild; switch(bptr->balance) { case -1: /* Case R_C2a : Insertion in BR */ pptr->balance = 1; aptr->balance = 0; break; case 1: /* Case R_C2b : Insertion in BL */ pptr->balance = 0; aptr->balance = -1; break; case 0: /* Case R_C2c : B is the newly inserted node */ pptr->balance = 0; aptr->balance = 0; } bptr->balance = 0; pptr->rchild = RotateRight(aptr); pptr = RotateLeft(pptr); } return pptr; }/*End of insert_RightBalance( )*/ struct node *RotateLeft(struct node *pptr) { struct node *aptr; aptr = pptr->rchild; /*A is right child of P*/ pptr->rchild = aptr->lchild; /*Left child of A becomes right child of P */ aptr->lchild = pptr; /*P becomes left child of A*/ return aptr; /*A is the new root of the subtree initially rooted at P*/ }/*End of RotateLeft( )*/ struct node *RotateRight(struct node *pptr) { struct node *aptr; aptr = pptr->lchild; /*A is left child of P */ pptr->lchild = aptr->rchild; /*Right child of A becomes left child of P*/ aptr->rchild = pptr; /*P becomes right child of A*/ return aptr; /*A is the new root of the subtree initially rooted at P*/ }/*End of RotateRight( )*/ void display(struct node *ptr,int level) { int i; if(ptr == NULL )/*Base Case*/ return; else { display(ptr->rchild, level+1); printf("\n"); for (i=0; i<level; i++) printf(" "); printf("%d", ptr->info); display(ptr->lchild, level+1); } }/*End of display()*/ |
OUTPUT : :
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/* C Program to implement AVL Tree Insertion */ Enter your choice : 1 Enter the key to be inserted : 6 1.Insert 2.Display 3.Quit Enter your choice : 2 8 7 6 1.Insert 2.Display 3.Quit Enter your choice : 1 Enter the key to be inserted : 5 1.Insert 2.Display 3.Quit Enter your choice : 1 Enter the key to be inserted : 4 1.Insert 2.Display 3.Quit Enter your choice : 2 8 7 6 5 4 1.Insert 2.Display 3.Quit Enter your choice : 1 Enter the key to be inserted : 3 1.Insert 2.Display 3.Quit Enter your choice : 1 Enter the key to be inserted : 2 1.Insert 2.Display 3.Quit Enter your choice : 1 Enter the key to be inserted : 1 1.Insert 2.Display 3.Quit Enter your choice : 2 8 7 6 5 4 3 2 1 1.Insert 2.Display 3.Quit Enter your choice : 1 Enter the key to be inserted : 0 1.Insert 2.Display 3.Quit Enter your choice : 2 8 7 6 5 4 3 2 1 0 1.Insert 2.Display 3.Quit Enter your choice : 1 Enter the key to be inserted : 9 1.Insert 2.Display 3.Quit Enter your choice : 2 9 8 7 6 5 4 3 2 1 0 1.Insert 2.Display 3.Quit Enter your choice : 3 Process returned 1 |
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