# Lec 05 - Loops Slides: {% embed url="" %} Lecture Slides {% endembed %} ## Loops ### `for` loop The `for` loop in C has the following syntax: {% code lineNumbers="true" %} ```c for (; ; ) { } ``` {% endcode %} ### `while` loop The `while` loop looks like this: {% code lineNumbers="true" %} ```c while () { } ``` {% endcode %} Note that there is no restriction `` must execute after `` in a `while` loop. But in a `for` loop, `` is **always** executed **after** ``. ### `do-while` loop The `do-while` loop looks similar to the `while` loop, except that the **body of the loop is guaranteed to be executed at least once**. {% code lineNumbers="true" %} ```c do { } while (); ``` {% endcode %} Similar to the `while` loop, the `` component and `` componenet in the loop do not have to be in order. {% hint style="info" %} When doing paper questions about the loop, **always think about whether it will become an infinite loop or not**. {% endhint %} ## Loop Invariant A *loop invariant* is an assertion that is true before the loop, after each iteration of the loop, and after the loop. **Argue that an invariant is true** * it is true before entering the loop. * it is true at the end of the first iteration of the loop * if it is true at the end of the $$k$$-th iteration of the loop, then it is true at the end of the $$k+1$$-th iteration. * it is true when we exit the loop. Loop invariant, however, is not unique. We can write down infinitely many loop invariants. A good invariant, however, will lead us to an assertion that we want to see (e.g., relating `product` to `n`). We can derive other invariants in our code (such as `{ n != 0 }` below) that do not contribute to the reasoning of the behavior of our loop. *Such invariants should be avoided*. {% hint style="info" %} In the past year final papers, you may see that the *loop invariant* doesn't need to contain exact expression, it can contain some formative words, like "m is the minimum element in the list", etc. {% endhint %}