Introduction

If the goal is to print a polynomial with the minimum number of output calls, the right strategy is usually not to print term by term. Instead, build the entire polynomial as a string and emit it once. That approach is cleaner, easier to format correctly, and usually more efficient than making repeated print calls while handling signs, coefficients, and exponents on the fly.

Represent the Polynomial Cleanly

A polynomial is often stored as coefficients from highest degree to lowest degree. For example:

[4, -3, 0, 1, -7]

can represent:

4x^4 - 3x^3 + x - 7

The formatting job involves a few rules:

• skip zero coefficients
• omit 1 before non-constant terms when appropriate
• show x instead of x^1
• show the constant term without a variable
• place + and - signs correctly

That logic is easier to manage when you assemble terms first and print later.

Build the Polynomial and Print Once

Here is a Python example that formats the whole polynomial and uses a single print call.

1def format_polynomial(coeffs):
2    degree = len(coeffs) - 1
3    terms = []
4
5    for i, coef in enumerate(coeffs):
6        power = degree - i
7
8        if coef == 0:
9            continue
10
11        sign = "-" if coef < 0 else "+"
12        abs_coef = abs(coef)
13
14        if power == 0:
15            body = str(abs_coef)
16        elif power == 1:
17            if abs_coef == 1:
18                body = "x"
19            else:
20                body = f"{abs_coef}x"
21        else:
22            if abs_coef == 1:
23                body = f"x^{power}"
24            else:
25                body = f"{abs_coef}x^{power}"
26
27        terms.append((sign, body))
28
29    if not terms:
30        return "0"
31
32    first_sign, first_body = terms[0]
33    result = first_body if first_sign == "+" else f"-{first_body}"
34
35    for sign, body in terms[1:]:
36        result += f" {sign} {body}"
37
38    return result
39
40
41coeffs = [4, -3, 0, 1, -7]
42print(format_polynomial(coeffs))

This produces:

4x^4 - 3x^3 + x - 7

The important part is that formatting happens internally, and output happens once.

Why This Minimizes Calls

Suppose you tried to print as you loop:

for term in terms:
    print(term, end="")

That performs many output calls and forces formatting logic to stay tangled with I/O behavior. By contrast, the format_polynomial function separates responsibilities:

1. compute the correct textual form
2. print exactly once

That is usually the right meaning of "minimum number of calls" in this kind of problem.

Alternative: Join Preformatted Terms

Another clean pattern is to construct a list of already formatted pieces and join them at the end.

1def format_polynomial_join(coeffs):
2    degree = len(coeffs) - 1
3    pieces = []
4
5    for i, coef in enumerate(coeffs):
6        power = degree - i
7        if coef == 0:
8            continue
9
10        if power == 0:
11            core = str(abs(coef))
12        elif power == 1:
13            core = "x" if abs(coef) == 1 else f"{abs(coef)}x"
14        else:
15            core = f"x^{power}" if abs(coef) == 1 else f"{abs(coef)}x^{power}"
16
17        if not pieces:
18            pieces.append(core if coef > 0 else f"-{core}")
19        else:
20            pieces.append(f"+ {core}" if coef > 0 else f"- {core}")
21
22    return " ".join(pieces) if pieces else "0"

This gives the same benefit: one final output call.

Common Pitfalls

The first common mistake is printing each term separately and then trying to clean up spacing or trailing signs afterward. That makes the code harder to reason about and increases output calls.

Another issue is mishandling coefficients of 1 and -1. For example, 1x^2 is usually printed as x^2, and -1x as -x.

Zero coefficients also need care. If you do not skip them, you end up printing noisy terms such as + 0x^3.

Finally, always handle the zero polynomial explicitly. If every coefficient is zero, the correct result is usually just 0.

Summary

• To minimize output calls, format the full polynomial first and print it once.
• Build terms separately so sign handling and exponent formatting stay manageable.
• Skip zero coefficients and format 1 and -1 carefully.
• Joining preformatted term strings is a clean alternative to incremental printing.
• A single final output call is usually both simpler and more efficient than term-by-term printing.