Maximum Coins Heroes Can Collect


Explanation
The code is a Python solution to a problem where you are given three lists: heroes
, monsters
, and coins
. The goal is to find, for each hero, the maximum number of coins you can collect by defeating monsters that the hero can beat.
Details
Initialization:
mon_cost
sorts themonsters
andcoins
together. This way, you know how many coins each monster yields.ps
is a prefix sum array, whereps[i]
will contain the sum of coins for defeating the firsti
monsters.res
is the list that will hold the maximum coins that each hero can collect.
Calculate Prefix Sum for Monsters:
 Loop through
mon_cost
and fill theps
array. It will help in quickly finding the total coins for a range of monsters.
 Loop through
Find Maximum Coins for Each Hero:
 For each hero
h
, use binary search to find the strongest monster that the hero can beat.  Append the maximum coins corresponding to that monster to
res
.
 For each hero
Steps
Sort Monsters with Their Coin Value:
1
mon_cost = sorted(list(zip(monsters, coins)))
 Zips
monsters
andcoins
and sorts them based on monster strength.
 Zips
Calculate Prefix Sum for Monsters’ Coins:
1 2 3
ps = [0] for _, c in mon_cost: ps.append(ps[1] + c)
 Adds up coins as you loop through sorted
mon_cost
, storing them inps
.
 Adds up coins as you loop through sorted
Binary Search for Each Hero:
1 2 3 4 5 6 7 8
for h in heroes: l, r = 0, len(monsters)  1 while l <= r: m = (l + r) // 2 if mon_cost[m][0] > h: r = m  1 else: l = m + 1
 For each hero, this binary search finds the index
l
of the strongest monster they can defeat.
 For each hero, this binary search finds the index
Append Coins to Result:
1
res.append(ps[l])
 Using index
l
,ps[l]
gives us the maximum coins a hero can collect. We append it tores
.
 Using index
Return Result:
1
return res
 Return the
res
list, which contains the answer for each hero.
 Return the
Key Takeaways
 The use of sorting and prefix sum optimizes the problem.
 Binary search helps to find the range of monsters a hero can defeat quickly.
 Prefix sum allows for constanttime lookup to find the sum of coins a hero can collect.
This code is a good example of combining multiple techniques like sorting, prefix sum, and binary search to solve a problem efficiently.