Step by Step solution about How to resolve the algorithm Catalan numbers/Pascal's triangle step by step in the Go programming language

This code snippet in Go is a program that calculates the number of ways a given number of objects can be arranged in a row. It uses dynamic programming to calculate the number of arrangements for each number of objects up to a specified maximum.

The code first declares a constant n which specifies the maximum number of objects to be arranged. It then declares an array t of size n + 2, where t[i] will store the number of arrangements for i objects.

The main loop of the program iterates from 1 to n, and for each value of i, it calculates the number of arrangements for i objects.

To do this, it first iterates from i down to 1, and for each value of j, it adds the number of arrangements for j-1 objects to the number of arrangements for j objects. This is because the number of arrangements for j objects is equal to the number of arrangements for j-1 objects, plus the number of arrangements for j objects where the last object is placed in the first position.

After the first loop, the number of arrangements for i objects is stored in t[i+1].

The second loop then iterates from i + 1 down to 1, and for each value of j, it adds the number of arrangements for j-1 objects to the number of arrangements for j objects. This is because the number of arrangements for j objects is equal to the number of arrangements for j-1 objects, plus the number of arrangements for j objects where the first object is placed in the last position.

After the second loop, the number of arrangements for i objects is stored in t[i+1].

The program then prints the number of arrangements for each value of i up to n.

Here is an example of the output of the program for n = 15:

1 : 1
2 : 2
3 : 5
4 : 14
5 : 42
6 : 132
7 : 429
8 : 1430
9 : 4862
10 : 16796
11 : 58786
12 : 208012
13 : 742900
14 : 2674440
15 : 9694845

package main

import "fmt"

func main() {
    const n = 15
    t := [n + 2]uint64{0, 1}
    for i := 1; i <= n; i++ {
        for j := i; j > 1; j-- {
            t[j] += t[j-1]
        }
        t[i+1] = t[i]
        for j := i + 1; j > 1; j-- {
            t[j] += t[j-1]
        }
        fmt.Printf("%2d : %d\n", i, t[i+1]-t[i])
    }
}