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Infix to postfix conversion

Infix to postfix conversion. Use a loop to read the tokens one by one from a vector infixVect of tokens (strings) representing an infix expression. For each token do the following in the loop: When the token is an operand

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Infix to postfix conversion

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  1. Infix to postfix conversion Use a loop to read the tokens one by one from a vector infixVect of tokens (strings) representing an infix expression. For each token do the following in the loop: • When the token is an operand • Add it to the end of the vector postfixVect of token (strings) that is used to store the corresponding postfix expression • When the token is a left parenthesis “(” • Push_back the token x to the end of the vector stackVect of token (strings) that simulates a stack. • When the token is a right parenthesis “)” • Repeatedly pop_back a token y from stackVect and push_back that token y to postfixVect until “(“ is encountered in stackVect. Then pop_back “(“ from stackVect. • If stackVect is already empty before finding a “(“, that expression is not a valid expression. • When the token is an operator, see next slide.

  2. Infix to postfix conversion • When the token x is an operator • Write a loop that checks the following three conditions: • The stack stackVect is not empty • The token y currently in the end of stackVect is an operator. In other words, it is not not a lef parenthesis “(“ . • y is an operator of higer or equal precedence than that of x, • As long as the three conditions above are all true, in the loop above do the following in the body of the loop : • push_back the token y to postfixVect • pop_back the token y from stackVect • The loop above will stops as soon as any of the three conditions is not true. • After the loop, push_back the token x into stackVect.

  3. Infix to postfix conversion After the loop in slide 1 has processes all the tokens in infixVect and stop, use another loop to repeatedly do the following as long as the stack vector stackVect is not empty yet: • push_back the token on the top of the stack vector stackVect into postfixVect. • pop_back the stack vector to remove the top token y the stack.

  4. Infix to postfix conversion infixVect ( a + b - c ) * d – ( e + f ) postfixVect

  5. Infix to postfix conversion stackVect infixVect a + b - c ) * d – ( e + f ) postfixVect (

  6. Infix to postfix conversion stackVect infixVect + b - c ) * d – ( e + f ) postfixVect a (

  7. Infix to postfix conversion stackVect infixVect b - c ) * d – ( e + f ) postfixVect a + (

  8. Infix to postfix conversion stackVect infixVect - c ) * d – ( e + f ) postfixVect a b + (

  9. Infix to postfix conversion stackVect infixVect c ) * d – ( e + f ) postfixVect a b + - (

  10. Infix to postfix conversion stackVect infixVect ) * d – ( e + f ) postfixVect a b + c - (

  11. Infix to postfix conversion stackVect infixVect * d – ( e + f ) postfixVect a b + c -

  12. Infix to postfix conversion stackVect infixVect d – ( e + f ) postfixVect a b + c - *

  13. Infix to postfix conversion stackVect infixVect – ( e + f ) postfixVect a b + c - d *

  14. Infix to postfix conversion stackVect infixVect ( e + f ) postfixVect a b + c – d * -

  15. Infix to postfix conversion stackVect infixVect e + f ) postfixVect a b + c – d * ( -

  16. Infix to postfix conversion stackVect infixVect + f ) postfixVect a b + c – d * e ( -

  17. Infix to postfix conversion stackVect infixVect f ) postfixVect a b + c – d * e + ( -

  18. Infix to postfix conversion stackVect infixVect ) postfixVect a b + c – d * e f + ( -

  19. Infix to postfix conversion stackVect infixVect postfixVect a b + c – d * e f + -

  20. Infix to postfix conversion stackVect infixVect postfixVect a b + c – d * e f + -

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