Nested Loops and Pattern Programs

Hello students, welcome to Kwickprep. How does a program print a triangle of stars, one star at a time? It needs a loop inside a loop. Today we learn nested loops, star, number and letter patterns, tracing by hand, and a prime number program.

First, a new term. A nested loop is a loop written inside another loop. Think of a school timetable, where the outer loop picks the day. For each day, the inner loop goes through every period, from first to last. So if there are three rows and four columns, the inner body runs three times four, which is twelve times.

Here the outer loop variable is row, and the inner loop variable is col, short for column. Range of one comma four gives one, two and three. Look at the indentation carefully. The inner print is inside both loops. The empty print is inside only the outer loop, so it ends each row.

Now let us watch the grid fill up. When row is one, col runs one, two, three, and then the line ends. When row is two, col starts again from one and runs to three. When row is three, the same thing happens once more. The inner loop always restarts and runs fully for every outer turn.

Here is the outer loop drawn as a flowchart. First, row is set to one. The diamond asks, is row less than or equal to three? If yes, the whole inner loop runs, row goes up by one, and we ask again. If no, the flow goes down and the program stops.

Pattern programs need two small print tricks. Normally print moves to a new line after printing. Writing end equals empty quotes keeps the cursor on the same line. A print with empty brackets prints nothing and just moves to the next line. The inner print builds the columns of one row. The outer print, after the inner loop, starts the next row.

Our first pattern is a star triangle. The outer loop variable row goes from one to four. The inner loop runs row times, so row one gets one star. Row two gets two stars, and row four gets four stars. The rule is simple: the row number decides how many stars.

Next, a number triangle. This time the inner loop prints the variable num, not a star. Range of one comma row plus one gives the numbers from one up to row. So row three prints one, two, three. Pause and predict. What would print if we wrote print of row instead of print of num? Every line would repeat its own row number, like three, three, three.

Now a letter pattern. Every character has a number code, and capital A has the code sixty five. The function chr turns a code back into its character. So chr of sixty five is A, and chr of sixty six is B. As pos, the position, goes zero, one, two, we print A, B and C.

To turn the triangle upside down, only the outer loop changes. Range of four, zero, minus one counts down four, three, two, one. It stops before zero. The inner loop is exactly the same as before. So the first row has four stars, and the last row has one.

Exams often ask you to predict the output of a nested loop. The safest way is a trace table, which is a table where you write each variable at every step. Here row goes one and two, and col also goes one and two. The program prints row times col each time. Let us trace it on the next slide.

Write one line in the table for every run of the inner body. First, row is one and col is one, so it prints one. Then row stays one and col becomes two, so it prints two. Now the inner loop is over, so row becomes two and col restarts at one. It prints two, and finally two times two prints four.

Our last program finds prime numbers. A prime number has exactly two factors, one and the number itself. Two, three, five and seven are prime. One is not prime, because it has only one factor, and nine is not prime because three divides it. To test a number, we try every number from two up to one less than it.

The outer loop picks each number, num, from two to nineteen. We first assume num is prime, so prime equals True. The inner loop tries every divisor, div, from two to num minus one. The percent sign gives the remainder, and double equals compares it with zero. If the remainder is zero, div divides num, so prime becomes False. After the inner loop, if prime is still True, we print num.

Some exams ask for nested loops in pseudocode. The arrow means store a value. Each for loop closes with the word next, followed by its own variable. The inner loop closes first, then the outer loop.

Watch out for four common mistakes. If the empty print goes inside the inner loop, every row breaks too early. If you forget end equals empty quotes, each star lands on its own line. If the inner loop reuses the outer variable name, the rows get mixed up. And remember, range always stops just before its end value.

Let us revise what we learned today. The inner loop runs fully for every turn of the outer loop. The outer loop makes rows, and the inner loop makes columns. End equals empty quotes stays on the line, and an empty print starts a new line. To predict output, trace the loops in a table. And to find primes, an inner loop tests every divisor. Try making a pyramid pattern yourself.