# Write a loop invariant code

### Loop invariant geeksforgeeks

Termination - The code will terminate after has reached the last element in the array, which means the sorted subarray has expanded to encompass the entire array. Loop Invariant In computer science, you could prove it formally with a loop invariant, where you state that a desired property is maintained in your loop. The children of node i are numbered higher than i. This function was presented in the previous example. The combination of the loop invariant and the termination condition gives that smallestSoFar is the index of the smallest value in the array. Each time through the loop increased numSorted by one. It might also work to think about the first few iterations, i. It was like getting a secret superpower: suddenly I could write code that used to be impossible. You're the one mentioning such representation. Note that [a,b means all integers from a to b, including a, but not including b.

It might also work to think about the first few iterations, i. Since we are running a loop, we are gaining information step by step.

When doing so we can assume that the invariant holds at the beginning of the loop. That's it.

### Write a loop invariant code

An element gets inserted into the array only when it is greater than the element to its left. The list below is not meant to be complete, and also one strategy might work better for you then another. In the outer loop, array is sorted for first i elements. We can assume that the invariant holds before the loop, i. Each time through the loop increased numSorted by one. The loop invariant is in terms of numSorted, the number of elements already sorted from the array, The smallest numSorted values are sorted in descending order in locations [n-numSorted,n , and the rest are in locations [0,n-numSorted. Check that each time through the loop, assuming the Loop Invariant true going into the loop, it is true going out of the loop; Check that headway towards termination is being made.

Pivot element is placed at its correct position. Before we look at how to handle them, lets remind ourselves, why they together constitute a proof. To make things more confusing: for the for-loops that we are considering, it is always obvious that they terminate, but it can happen that you have for instance a while-loop for which this is not so obvious.

The point of Loop Invariants is the promise that the invariant will be restored before repeating the loop body each time. About Termination: We have formulated a loop invariant, that -if true after stepping out of the loop- gives us a statement with which we can prove correctness.

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