USACO: Section 1.4 -- PROB Arithmetic Progressions
Source Code
Lesson Learned:
1. Just as the sorting, searching algorithms, the sequence search(O(N)) < binary search(O(logN)) < bitmap algorithm(O(1)).
2. To boost performance a program, the most possible bottleneck is the nested loops. For deep nested loops, the time is: d1*d2*d3...(di stands for the loop count of level i). So, we should optimize at different levels to boost the whole nested loops performance.
For example, we first caculate the MaxB(using fomular a+(N-1)*b <=p^2+q^2 ) for variable "b" in level1; then, we pre-calculate the possible value array for variable "a" in level2("a" must be in the square array set. Note: this greatly cuts level2 loop count). Then, we check if the a+(N-1)*b exceeds the max square value to filter even more level2 values(This at least cuts the level2 loop by half). Finally, in the level3, we use the bitmap search for optimization.
Lesson Learned:
1. Just as the sorting, searching algorithms, the sequence search(O(N)) < binary search(O(logN)) < bitmap algorithm(O(1)).
2. To boost performance a program, the most possible bottleneck is the nested loops. For deep nested loops, the time is: d1*d2*d3...(di stands for the loop count of level i). So, we should optimize at different levels to boost the whole nested loops performance.
For example, we first caculate the MaxB(using fomular a+(N-1)*b <=p^2+q^2 ) for variable "b" in level1; then, we pre-calculate the possible value array for variable "a" in level2("a" must be in the square array set. Note: this greatly cuts level2 loop count). Then, we check if the a+(N-1)*b exceeds the max square value to filter even more level2 values(This at least cuts the level2 loop by half). Finally, in the level3, we use the bitmap search for optimization.
