#coinflips2.py

import random

flips = int(input("Input the number of flips to do: "))
display_flips = input("Do you want to display the flips? (y or n) ")

heads = tails = 0
heads_ahead = tails_ahead = 0
is_head_run = is_tail_run = True    #counterintuitive
head_run = tail_run = 0
head_runs = []
tail_runs = []
max_head_run = max_tail_run = 0
max_head_run_start = max_tail_run_start = -1
max_heads_ahead = max_tails_ahead = 0
max_heads_ahead_place = max_tails_ahead_place = -1
side_changes = 0
lead_changes = 0

for flipNum in range(flips):
    if random.choice(['H','T']) == 'H':     #randomly H or T
        if display_flips == 'y':
            print('H',end="")
        heads += 1
        head_run += 1
        if is_tail_run:  #tail run ends
            side_changes += 1
            is_head_run = True
            is_tail_run = False
            if tail_run > max_tail_run:
                max_tail_run = tail_run
                max_tail_run_start = (heads+tails) - tail_run
            if tails > 0:  #bypass first at start
                tail_runs.append(tail_run)
            tail_run = 0
        
        if (heads-tails) > max_heads_ahead:
            max_heads_ahead = heads-tails
            max_heads_ahead_place = heads+tails

        if heads == tails + 1:  #this H moves Heads into the lead
            lead_changes += 1
            
    else:
        if display_flips == 'y':
            print('T',end="")
        tails += 1
        tail_run += 1
        if is_head_run:
            side_changes += 1
            is_tail_run = True
            is_head_run = False
            if head_run > max_head_run:
                max_head_run = head_run
                max_head_run_start = (heads+tails) - head_run 
            if heads > 0:  #bypass first at start
                head_runs.append(head_run)
            head_run = 0

        if (tails-heads) > max_tails_ahead:
            max_tails_ahead = tails-heads
            max_tails_ahead_place = heads+tails

        if tails== heads + 1:  #this T moves Tails into the lead
            lead_changes += 1


#if last run is the max
if is_tail_run:
    if tail_run > max_tail_run:
        max_tail_run = tail_run
        max_tail_run_start = (heads+tails) - tail_run + 1
    tail_runs.append(tail_run)
else:
    if head_run > max_head_run:
        max_head_run = head_run
        max_head_run_start = (heads+tails) - head_run + 1
    head_runs.append(head_run)
    
print()        
print("Number of heads:", heads, " %", (heads/flips*100),\
      "  Number of tails:", tails, " %", (tails/flips*100))
print("Changes of sides:", side_changes)
print("Changes of lead:", lead_changes)

print("Head runs:",head_runs)  #comment out if doing many flips
print("Longest run of heads:",max_head_run,"starting at flip #",max_head_run_start)
print(" Average run of heads:",sum(head_runs)/len(head_runs))
print("Tail runs:",tail_runs)
print("Longest run of tails:",max_tail_run,"starting at flip #",max_tail_run_start)
print(" Average run of tails:",sum(tail_runs)/len(tail_runs))

if max_heads_ahead > 0:
    print("Max heads ahead gap:",max_heads_ahead,"at flip #",max_heads_ahead_place)
else:
    print("Heads never ahead")
if max_tails_ahead > 0:
    print("Max tails ahead gap:",max_tails_ahead,"at flip #",max_tails_ahead_place)
else:
    print("Tails never ahead")

# average run is about 2
# 1, 2, 3, 4, ...each runlength is about half as frequent as the previous length
#   about half being length 1.  Thus, #side changes is about half the flips.