Find $n’th$ perfect number , where perfect number is a positive integer whose sum of digits is $10$

For example $ 46$ is a perfect number , since $ 4+6=10$ . If $ n=1$ , answer is $ 19$ . If $ n=2$ , answer is $ 28$ . If $ n=3$ , answer is $ 37$ and so on .We need to make a program which takes $ n$ and outputs $ n’th$ perfect number.

How to solve this problem for large $ n$ , for example $ n$ close to $ 10^{18}$ ? we can’t use brute force method since input can be so large .Can we solve it using DP or binary search ?

Source of the problem : Perfect Number

Note: In given problem statement (in link) $ n$ is not large and thus can be solved using brute force.But i am curious to solve it for large $ n$ .

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While riding a mount summoned by Find Steed, when does the caster choose whether the mount is controlled or independent?

Other Q&As on RPG.SE have discussed the by-now-familiar rules for mounted combat, including the differences between controlled and independent mounts. See, e.g., When can you choose to control a mount? Mounts summoned via find steed, however, are a special case. Per this 2018 guidance from Jeremy Crawford,

when you ride the mount [summoned via find steed] in combat, you decide whether it follows the rules for a controlled or an independent mount.

What remains unclear, however, is precisely when a caster who is already mounted on the summoned steed may, or must, make that choice. For example, it could be:

  • When the DM calls for initiative rolls.
  • Only on the caster’s first turn.
  • Only the mount’s first turn.
  • On any turn the caster takes.
  • On any turn the mount takes.
  • On any turn whatsoever.

Some of these options would require the caster to choose only once and stick with it. Others would conceivably let the caster change her mind each round, or even multiple times each round. Which (if any) is the correct way to handle mount control using find steed?

How to find the distances between two adjacent maxima in a solution from NDSolve

I try to find a general approach to plot the time evolution of horizontal distances from maximum to maximum in a solution of PDE. The solution u[x,t] normally have multiple maximum and minimum in space x, which move in space x and evolve in time t.

Here is a simple example, in which the maxima and minima are periodic. But in my real problem they are not periodic and the distances between different pairs of adjacent max are different at a given t, also the distances between two adjacent max can change with t.

sol = NDSolve[{D[u[x, t], t] + u[x, t] D[u[x, t], x] + D[u[x, t], x, x] +  0.4*D[u[x, t], {x, 3}] + D[u[x, t], {x, 4}] == 0, u[-4 \[Pi], t] == u[4 \[Pi], t], u[x, 0] == 0.1*Sin[x]}, u, {t, 0, 20}, {x, -4 \[Pi], 4 \[Pi]}]  Plot3D[Evaluate[u[x, t] /. First[sol]], {t, 0, 10}, {x, -4 Pi, 4 Pi}, PlotRange -> All, PlotPoints -> 100] 

enter image description here

I have tried to use Table[FindMaximum[Evaluate[u[x, t] /. First[sol]], {x, x0}][[2, 1, 2]], {t,0,tend,0.01}] with an initial position x0 to find a local maximum. But I don’t know how to find two adjacent maxima simultaneously in order to plot the time evolution of their distance.

Find minimum pair number based on selection algorithm

If we have n balls in a red box (each ball is assigned a different number from 1 to n) and n balls in a green box (again each ball is assigned a different number from 1 to n). Lets say we have a player that chooses randomly a ball from each box and throws it on the floor. If we can predict exactly the time when a pair (red ball and green ball) given their numbers will be chosen (ex. input: red ball 5, green ball 6 output: 5sec ) , can we find the pair that will be chosen first in O(n) time?

The predictions costs: O(1) for each pair we input. We can predict as many pairs as we want

I have thought the simple solution: Predict every pair and then choose the minimum time, but that would cost $ O(n^{2})$ . I cannot optimize this further

How to find SSL root cert that made connection to the database in PostgreSQL?

When we connect to postgreSQL via ssl-mode=verify-full how will I make sure if the certificate I passed is used while making the connection?

With ssl_is_used(); shows only true or false. Is there any other extension or pg_catalog views that shows the root cert used in making connection to the DB ?

Find Integer Values Occurring more than Half of the Time [on hold]

I need help finding an algorithm.

I have been tasked with identifying the integer that accounts for more than half of the values in a given array. Additionally, I have been asked to submit versions of such an algorithm that differ in their complexity. I have initialized a short, test-case array, but am unsure of how to iterate over it in a way that will identify and print a value that accounts for more than half of array a[]’s elements.

What algorithms would identify such an element? It would be nice to include an optimal algorithm, and since I am asked for an algorithm with a different time complexity as well, it would be good to include one non-optimal algorithm.