Approach
Written by Isaiah Iliffe from CSESoc
This question likely requires some problem solving on paper before starting to code.
Firstly, if two adjacent given percentages are out of order, then obviously it is impossible to satisfy the requirements.
Otherwise, after trying a few cases, you might think about when it is still impossible to make everything add to . In the final sample case, we see that the lowest possible sum we could achieve while respecting the non-decreasing requirement is , by going from right to left and setting each unknown percentage to whatever is on its immediate right (or 1 if there is nothing on its right), since this keeps each value as low as possible.
Similarly, we can achieve the highest possible sum by going from left to right and setting each unknown percentage to whatever is on its left (or 100 if there is nothing on its left).
It's clear that if the highest possible sum is less than 100, or if the lowest possible sum is more than 100, then there is no valid assignment. Interestingly, if neither of these is true, it turns out that there must be a valid assignment!
This is because we can gradually change a solution with highest possible sum to a solution with lowest possible sum by going from right to left and decreasing unknown percentages whereever possible. It's not hard to why this is true, and if we only decrease percentages by one at a time, then we must hit a sum of 100 somewhere along the way.
For a more compact description of the whole procedure, see the sample code.