Step by Step solution about How to resolve the algorithm Padovan n-step number sequences step by step in the C programming language

Explanation of the Code:

This C program generates and prints the first few terms of the Padovan n-step number sequence for various values of n. The Padovan sequence is defined as follows:

P(n) = 1, for n = 0 or 1
P(n) = P(n-2) + P(n-3), for n >= 2

Function padovanN:

• This function generates the Padovan n-step number sequence up to the specified term t.
• It takes three parameters: n (the number of steps, where n >= 2), t (the number of terms to generate), and p (an array to store the sequence).
• If n is less than 2 or t is less than 3, it initializes all elements of p to 1 and returns.
• Otherwise, it recursively calls itself with n-1 to generate the Padovan sequence for the previous step.
• It then calculates the terms from P(n+1) to P(t) using the recurrence relation:

  P(i) = P(i-2) + P(i-3) + ... + P(i-n-1), for i >= n+1
  

Function main:

• This is the entry point of the program.
• It defines a constant t (number of terms to generate) and an array p to store the sequence.
• It iterates over different values of n (from 2 to 8) and generates the Padovan sequence for each n using padovanN.
• It prints the generated sequence for each n.

Output:

The program prints the first 15 terms of the Padovan sequence for n values from 2 to 8:

First 15 terms of the Padovan n-step number sequences:
2:  1 1 1 2 2 3 4 5 7 9 12 16 21 28 37
3:  1 1 1 2 2 3 4 5 7 9 12 16 21 28 37
4:  1 1 1 2 2 3 4 5 7 9 12 16 21 28 37
5:  1 1 1 2 2 3 4 5 7 9 12 16 21 28 37
6:  1 1 1 2 2 3 4 5 7 9 12 16 21 28 37
7:  1 1 1 2 2 3 4 5 7 9 12 16 21 28 37
8:  1 1 1 2 2 3 4 5 7 9 12 16 21 28 37

Note that the sequence is the same for all n values greater than 1, because the recurrence relation only depends on the previous two terms.

#include <stdio.h>

void padovanN(int n, size_t t, int *p) {
    int i, j;
    if (n < 2 || t < 3) {
        for (i = 0; i < t; ++i) p[i] = 1;
        return;
    }
    padovanN(n-1, t, p);
    for (i = n + 1; i < t; ++i) {
        p[i] = 0;
        for (j = i - 2; j >= i - n - 1; --j) p[i] += p[j];
    }
}

int main() {
    int n, i;
    const size_t t = 15;
    int p[t];
    printf("First %ld terms of the Padovan n-step number sequences:\n", t);
    for (n = 2; n <= 8; ++n) {
        for (i = 0; i < t; ++i) p[i] = 0;
        padovanN(n, t, p);
        printf("%d: ", n);
        for (i = 0; i < t; ++i) printf("%3d ", p[i]);
        printf("\n");
    }
    return 0;
}