Algorithms and Flowcharts

• Algorithm: A finite, well-defined, step-by-step sequence of clear, unambiguous instructions designed to solve a specific computational problem or perform a task.
• Five Essential Characteristics (Donald Knuth):
1. Finiteness: The algorithm must terminate after a finite number of executed steps.
2. Definiteness: Every individual instruction must be clear, precise, and completely unambiguous (no double meanings).
3. Input: Must accept zero or more valid input data values.
4. Output: Must produce at least one defined, correct output result.
5. Effectiveness: Every operation must be feasible and simple enough to be performed mechanically in a finite amount of time.

• (a) Start / Stop: Oval (or Rounded Rectangle) (Terminal symbol).
• (b) Input / Output: Parallelogram (READ A, PRINT Sum).
• (c) Arithmetic Calculations: Rectangle (Processing box, e.g., Sum = A + B).
• (d) Testing a Condition: Diamond (Rhombus) (Decision box, e.g., Is A > B?).

• Step 1: Start.
• Step 2: Input/Read the integer $N$.
• Step 3: Calculate the remainder $R$ when $N$ is divided by $2$ ($R = N \pmod 2$).
• Step 4: If $R == 0$, then:
• Print "$N$ is an Even Number" and goto Step 6.
• Step 5: Else:
• Print "$N$ is an Odd Number".
• Step 6: Stop.

1. Sequential Structure: Instructions are executed sequentially in a strict linear top-to-bottom order, where each step executes exactly once without any jumping or branching.
   2. Selection (Conditional / Branching) Structure: Evaluates a logical condition to decide between alternative paths of execution: IF (Condition) THEN [Action 1] ELSE [Action 2].
   3. Iterative (Looping / Repetition) Structure: Repeats a block of instructions multiple times as long as a specified condition remains true (e.g., printing numbers 1 to 100). When the condition becomes false, the loop terminates.

• Infinite Loop: A logical programming error where a looping structure repeats continuously and endlessly without ever terminating, because the exit condition is never satisfied (e.g., forgetting to increment a counter variable $i$).
• Prevention:
1. Ensure that the loop counter variable is properly updated (incremented or decremented) in every iteration.
2. Verify that the loop test condition will mathematically become False after a finite number of cycles.

• Connector Symbol: Used to connect different parts of a complex flowchart without drawing long, confusing, criss-crossing flowlines that clutter the diagram.
• On-Page Connector: Represented by a small Circle ($\\bigcirc$); used to connect two points of a flowchart lying on the same sheet of paper.
• Off-Page Connector: Represented by a Pentagon (or shield shape); used to link the end of a flowchart on one page to its continuation on a subsequent page.

• Step 1: Start.
• Step 2: Input values of Principal ($P$), Rate ($R$), and Time ($T$).
• Step 3: Calculate Simple Interest: $SI = (P \times R \times T) / 100$.
• Step 4: Calculate Total Amount: $A = P + SI$.
• Step 5: Display/Print $SI$ and $A$.
• Step 6: Stop.

1. Visual Clarity: A flowchart provides an intuitive, high-level bird's-eye view of the overall logic and decision pathways of the program.
   2. Effective Debugging: Logical flaws, missing conditions, and infinite loops can be spotted and corrected easily on paper before writing complex syntax.
   3. Language-Independent Blueprint: It serves as a universal blueprint that can be translated into any programming language (Python, Java, C++).
   4. Documentation: Facilitates clear communication among team developers.