Playlist (Codeforces 1140C)
Tags: Others, data structures

You have a playlist consisting of $$$n$$$ songs. The $$$i$$$-th song is characterized by two numbers $$$t_i$$$ and $$$b_i$$$ — its length and beauty respectively. The pleasure of listening to set of songs is equal to the total length of the songs in the set multiplied by the minimum beauty among them. For example, the pleasure of listening to a set of $$$3$$$ songs having lengths $$$[5, 7, 4]$$$ and beauty values $$$[11, 14, 6]$$$ is equal to $$$(5 + 7 + 4) \cdot 6 = 96$$$.You need to choose at most $$$k$$$ songs from your playlist, so the pleasure of listening to the set of these songs them is maximum possible.

Input: The first line contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le k \le n \le 3 \cdot 10^5$$$) – the number of songs in the playlist and the maximum number of songs you can choose, respectively.Each of the next $$$n$$$ lines contains two integers $$$t_i$$$ and $$$b_i$$$ ($$$1 \le t_i, b_i \le 10^6$$$) — the length and beauty of $$$i$$$-th song.

Output: Print one integer — the maximum pleasure you can get.

Note: In the first test case we can choose songs $$${1, 3, 4}$$$, so the total pleasure is $$$(4 + 3 + 6) \cdot 6 = 78$$$.In the second test case we can choose song $$$3$$$. The total pleasure will be equal to $$$100 \cdot 100 = 10000$$$.

Sample Inputs:
4 3
4 7
15 1
3 6
6 8

5 3
12 31
112 4
100 100
13 55
55 50

Sample Outputs:
78

10000

Solution (Python):
from heapq import heappush, heappop
import sys
input = sys.stdin.readline

def solve():
    (n, k) = map(int, input().split())
    a = [[] for _ in range(n)]
    (ans, s) = (0, 0)
    for i in range(n):
        a[i].extend(list(map(int, input().split())))
    h = []
    a.sort(key=lambda x: -x[1])
    for i in range(n):
        if len(h) == k:
            s -= heappop(h)
        s += a[i][0]
        ans = max(ans, s * a[i][1])
        heappush(h, a[i][0])
    print(ans)
if __name__ == '__main__':
    solve()

Solution (Python):
import heapq
(n, k) = map(int, input().split())
a = []
for i in range(n):
    (second, first) = map(int, input().split())
    a.append((first, second))
a.sort(reverse=True)
res = 0
sum_val = 0
max_heap = []
for i in range(n):
    heapq.heappush(max_heap, a[i][1])
    sum_val += a[i][1]
    if len(max_heap) > k:
        sum_val -= heapq.heappop(max_heap)
    res = max(res, sum_val * a[i][0])
print(res)

Solution (Python):
from heapq import heappush, heappop
import sys
(n, k) = map(int, input().split())
songs = sorted(map(lambda x: (int(x[1]), int(x[0])), map(str.split, sys.stdin)), reverse=True)
ans = 0
total_current_duration = 0
heap = []
for (beauty, duration) in songs:
    total_current_duration += duration
    heappush(heap, duration)
    if len(heap) > k:
        total_current_duration -= heappop(heap)
    ans = max(ans, total_current_duration * beauty)
print(ans)