What is the ruling regarding clothes or trousers that have been affected by madhy, without precisely identifying the spot of contamination, and with difficulty in purifying it immediately?

If you are certain that your clothes have been stained by madhy (pre-seminal fluid) or other impurities, and it is not merely a doubt, then you must wash the part of your clothing that has been defiled so that your prayer is valid, because purity from impurities is a condition for the validity of prayer. If the location of the impurity on the garment is hidden from you, then the entire garment must be washed.