# Program to find maximum sum obtained of any permutation in Python

PythonServer Side ProgrammingProgramming

Suppose we have an array nums, and another array called requests where requests[i] = [start_i, end_i], this represents the ith request asks for the sum of nums[start_i] + nums[start_i+1] + ... + nums[end_i-1] + nums[end_i]. We have to find the maximum total sum of all requests among all permutations of nums. The answer may be very large, so return it modulo 10^9+7.

So, if the input is like nums = [10,20,30,40,50] requests = [[1,3],[0,1]], then the output will be 190, because if we arrange like [30,50,40,20,10] we get: from requests[0] : nums[1] + nums[2] + nums[3] = 50 + 40 + 20 = 110, and from requests[1] : nums[0] + nums[1] = 30 + 50 = 80, so total sum 110+80 = 190.

To solve this, we will follow these steps:

• A := a new list
• for each request (s, e) in requests, do
• insert pair (s, 0) at the end of A
• insert pair (e, 1) at the end of A
• sort the list A
• fr := an empty map
• cnt := 0
• n := size of A
• i := 0
• while i < n, do
• r := 1
• while i < n - 1 and A[i+1] is same as A[i], do
• r := r + 1
• i := i + 1
• cnt := cnt + r
• if cnt - r > 0, then
• insert (pre, p-1) at the end of fr[cnt-r]
• pre := p
• otherwise when flag is same as 1, then
• cnt := cnt - r
• insert (pre, p) at the end of fr[cnt+r]
• pre := p+1
• i := i + 1
• sort the list nums in reverse order
• ks := a new list from list of all keys of fr
• sort the list ks in reverse order
• ans := 0
• m := 10^9 + 7
• i := 0
• for each k in ks, do
• for each pair (s, e) in fr[k], do
• d := e - s + 1
• ans := ans + (sum of all elements of nums[from index i to i+d-1]) * k
• ans := ans mod m
• i := i + d
• return ans

## Example

Let us see the following implementation to get better understanding −

from collections import defaultdict
def solve(nums, requests):
A = []
for s, e in requests:
A.append((s, 0))
A.append((e, 1))
A.sort()
fr = defaultdict(list)
cnt = 0

n = len(A)
i = 0
while i < n:
r = 1
while i < n - 1 and A[i+1] == A[i]:
r += 1
i += 1
p, flag = A[i]
if flag == 0:
cnt += r
if cnt - r > 0:
fr[cnt-r].append((pre, p-1))
pre = p
elif flag == 1:
cnt -= r
fr[cnt+r].append((pre, p))
pre = p+1
i += 1

nums.sort(reverse=True)
ks = list(fr.keys())
ks.sort(reverse=True)
ans = 0
m = 10**9 + 7
i = 0
for k in ks:
for s, e in fr[k]:
d = e - s + 1
ans += sum(nums[i:i+d]) * k
ans %= m
i += d
return ans

nums = [10,20,30,40,50]
requests = [[1,3],[0,1]]
print(solve(nums, requests))

## Input

[10,20,30,40,50],[[1,3],[0,1]]

## Output

190
Published on 04-Oct-2021 09:39:59