Waterfilling problems subjected to peak power constraints are solved, which are known as cave-filling problems (CFP). The proposed algorithm finds both the optimum number of positive powers and the number of resources that are assigned the peak power before finding the specific powers to be assigned. The proposed solution is non-iterative and results in a computational complexity, which is of the order of M, O(M), where M is the total number of resources, which is significantly lower than that of the existing algorithms given by an order of M2, O(M2), under the same memory requirement and sorted parameters. The algorithm is then generalized both to weighted CFP (WCFP) and WCFP requiring the minimum power. These extensions also result in a computational complexity of the order of M, O(M). Finally, simulation results corroborating the analysis are presented. © 2016 IEEE.