Data Structures and Algorithms

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Presentation transcript:

Data Structures and Algorithms Prof. Ajit A. Diwan Prof. Ganesh Ramakrishnan Prof. Deepak B. Phatak Department of Computer Science and Engineering IIT Bombay Session: Application of Stacks and Evaluation of Expressions Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

Application of Stacks Handling Expressions Backtracking Infix to Postfix and vice versa Infix to Prefix and vice versa Evaluating Postfix/Prefix Expressions Backtracking Maze Chess Memory Management Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

Infix Expressions Used in arithmetic Operator is placed between the operands Parentheses are used to denote the priority of the operation Examples a + b (a + b) * (a - b) (a ^ b * (c + (d * e) - f ) ) / g Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

Postfix Expressions Mathematical Notation Operator is placed after all its operands No need of parentheses Easy to parse as compared to infix Examples Infix Expression Postfix Expressions a + b a b + (a + b) * (a - b) a b + a b - * (a ^ b * (b + (d * e) - f ) ) / g a b ^ c d e * + f - * g / Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

Evaluating Postfix Expressions Example 1 (a=5, b=3) Example 2(a=4, b=2, c=5, d=6, e=7, f=8, g=3) a b + a b - * 5 3 + 5 3 - * 8 2 * 16 (Answer) a b ^ c d e * + f - * g / 4 2 ^ 5 6 7 * + 8 - * 3 / 16 5 42 + 8 - * 3 / 16 47 8 - * 3 / 16 39 * 3 / 624 3 / 208 (Answer) Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

Prefix Expressions Mathematical Notation Operator is placed before all its operands No need of parentheses Easy to parse as compared to infix Examples Infix Expression Prefix Expressions a + b + a b (a + b) * (a - b) * + a b - a b (a ^ b * (c + (d * e) - f ) ) / g / * ^ a b - + * d e c f g Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

Evaluating Prefix Expressions Example 1 (a=5, b=3) Example 2(a=4, b=2, c=5, d=6, e=7, f=8, g=3) * + a b - a b - * + 5 3 - 5 3 * 8 2 16 (Answer) / * ^ a b - + * d e c f g / * ^ 4 2 - + * 6 7 5 8 3 / * 16 - + 42 5 8 3 / * 16 - 47 8 3 / * 16 39 3 / 624 3 208 (Answer) Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

References https://en.wikipedia.org/wiki/Stack_(abstract_data_type) https://en.wikipedia.org/wiki/Infix_notation https://en.wikipedia.org/wiki/Reverse_Polish_notation https://en.wikipedia.org/wiki/Polish_notation Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

Thank you Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay