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Computer notes - Expression Tree

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Algorithm to convert postfix expression into an expression tree. We already have an expression to convert an infix expression to postfix. Read a symbol from the postfix expression. If symbol is an operand, put it in a one node tree and push it on a stack

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Class No.23 Data Structures http://ecomputernotes.com
Expression Tree ,[object Object],http://ecomputernotes.com a c + b g * + + d * * e f
Expression Tree ,[object Object],http://ecomputernotes.com a c + b g * + + d * * e f
Expression Tree ,[object Object],http://ecomputernotes.com a c + b g * + + d * * e f
Expression Tree ,[object Object],http://ecomputernotes.com a c + b g * + + d * * e f
Enforcing Parenthesis ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],http://ecomputernotes.com
Expression Tree ,[object Object],http://ecomputernotes.com a c + b g * + + d * * e f
Expression Tree ,[object Object],http://ecomputernotes.com a c + b g * + + d * * e f
Constructing Expression Tree ,[object Object],[object Object],[object Object],[object Object],[object Object],http://ecomputernotes.com
Constructing Expression Tree ,[object Object],stack http://ecomputernotes.com
Constructing Expression Tree ,[object Object],Stack is growing left to right If symbol is an operand, put it in a one node tree and push it on a stack. top http://ecomputernotes.com b a
Constructing Expression Tree ,[object Object],Stack is growing left to right If symbol is an operator, pop two trees from the stack, form a new tree with operator as the root and T 1 and T 2 as left and right subtrees and push this tree on the stack. http://ecomputernotes.com b a +
Constructing Expression Tree ,[object Object],http://ecomputernotes.com b a + d c e
Constructing Expression Tree ,[object Object],http://ecomputernotes.com b a + c e d +
Constructing Expression Tree ,[object Object],http://ecomputernotes.com b a + c e d + *
Constructing Expression Tree ,[object Object],http://ecomputernotes.com b a + c e d + * *
Other Uses of Binary Trees Huffman Encoding http://ecomputernotes.com
Huffman Encoding ,[object Object],[object Object],[object Object],[object Object],[object Object],http://ecomputernotes.com
Huffman Encoding ,[object Object],[object Object],[object Object],[object Object],http://ecomputernotes.com http://ecomputernotes.com
Huffman Encoding ,[object Object],[object Object],[object Object],[object Object]
Huffman Encoding ,[object Object],[object Object],[object Object]
Huffman Encoding ,[object Object],[object Object],[object Object]
Huffman Encoding ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Huffman Encoding v 1 y 1 SP 3 r 5 h 1 e 5 g 1 b 1 NL 1 s 2 n 2 i 2 d 2 t 3 2 2 is equal to sum of the frequencies of the two children nodes. a 3
Huffman Encoding v 1 y 1 SP 3 r 5 h 1 e 5 g 1 b 1 NL 1 s 2 n 2 i 2 d 2 t 3 2 2 There a number of ways to combine nodes. We have chosen just one such way. a 3
Huffman Encoding v 1 y 1 SP 3 r 5 h 1 e 5 g 1 b 1 NL 1 s 2 n 2 i 2 d 2 t 3 2 2 2 a 3
Huffman Encoding v 1 y 1 SP 3 r 5 h 1 e 5 g 1 b 1 NL 1 s 2 n 2 i 2 d 2 t 3 2 2 2 4 4 a 3
Huffman Encoding v 1 y 1 SP 3 r 5 h 1 e 5 g 1 b 1 NL 1 s 2 n 2 i 2 d 2 t 3 2 2 2 5 4 4 4 6 a 3
Huffman Encoding v 1 y 1 SP 3 r 5 h 1 e 5 g 1 b 1 NL 1 s 2 n 2 i 2 d 2 t 3 2 2 2 5 4 4 4 8 6 9 10 a 3
Huffman Encoding v 1 y 1 SP 3 r 5 h 1 e 5 g 1 b 1 NL 1 s 2 n 2 i 2 d 2 t 3 2 2 2 5 4 4 4 8 6 14 9 19 10 a 3
Huffman Encoding v 1 y 1 SP 3 r 5 h 1 e 5 g 1 b 1 NL 1 s 2 n 2 i 2 d 2 t 3 a 3 2 2 2 5 4 4 4 8 6 14 9 19 10 33

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Computer notes - Expression Tree

  • 1. Class No.23 Data Structures http://ecomputernotes.com
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  • 17. Other Uses of Binary Trees Huffman Encoding http://ecomputernotes.com
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  • 24. Huffman Encoding v 1 y 1 SP 3 r 5 h 1 e 5 g 1 b 1 NL 1 s 2 n 2 i 2 d 2 t 3 2 2 is equal to sum of the frequencies of the two children nodes. a 3
  • 25. Huffman Encoding v 1 y 1 SP 3 r 5 h 1 e 5 g 1 b 1 NL 1 s 2 n 2 i 2 d 2 t 3 2 2 There a number of ways to combine nodes. We have chosen just one such way. a 3
  • 26. Huffman Encoding v 1 y 1 SP 3 r 5 h 1 e 5 g 1 b 1 NL 1 s 2 n 2 i 2 d 2 t 3 2 2 2 a 3
  • 27. Huffman Encoding v 1 y 1 SP 3 r 5 h 1 e 5 g 1 b 1 NL 1 s 2 n 2 i 2 d 2 t 3 2 2 2 4 4 a 3
  • 28. Huffman Encoding v 1 y 1 SP 3 r 5 h 1 e 5 g 1 b 1 NL 1 s 2 n 2 i 2 d 2 t 3 2 2 2 5 4 4 4 6 a 3
  • 29. Huffman Encoding v 1 y 1 SP 3 r 5 h 1 e 5 g 1 b 1 NL 1 s 2 n 2 i 2 d 2 t 3 2 2 2 5 4 4 4 8 6 9 10 a 3
  • 30. Huffman Encoding v 1 y 1 SP 3 r 5 h 1 e 5 g 1 b 1 NL 1 s 2 n 2 i 2 d 2 t 3 2 2 2 5 4 4 4 8 6 14 9 19 10 a 3
  • 31. Huffman Encoding v 1 y 1 SP 3 r 5 h 1 e 5 g 1 b 1 NL 1 s 2 n 2 i 2 d 2 t 3 a 3 2 2 2 5 4 4 4 8 6 14 9 19 10 33

Editor's Notes

  1. Start of lecture 25.
  2. Start of Lecture 26
  3. End of lecture 25.