How should I practice Parse, Normalize, and Combine Polynomials?

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Problem · String

Parse, Normalize, and Combine Polynomials

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Squarepoint CapitalFULLTIMEPHONE SCREEN

Problem statement

You are given one or more valid single-variable polynomial strings in polynomials. Each expression contains no whitespace and is a sequence of signed terms. A term is a decimal integer constant or a decimal coefficient followed by x and an optional nonnegative exponent, such as -7, x, -3x, or 12x^4. An omitted coefficient is 1, and an omitted exponent is 1.

Add all input polynomials and return one canonical string. Collect equal exponents, omit zero terms, order terms by decreasing exponent, omit coefficient 1 and -1 on nonconstant terms, and use normalized signs without whitespace. Return 0 when every term cancels.

Every parsed signed coefficient and every intermediate combined coefficient must fit in a signed 64-bit integer. Return exactly OVERFLOW as soon as either a parsed coefficient or an addition is outside that range.

Function

combinePolynomials(polynomials: String[]) → String

Examples

Example 1

polynomials = ["3x^2-x+4","-x^2+5x-4"]return = "2x^2+4x"

Like powers are added and zero constant terms disappear.

Example 2

polynomials = ["x^3-x","-x^3+x"]return = "0"

Every coefficient cancels, so the canonical representation is zero.

Example 3

polynomials = ["9223372036854775807","1"]return = "OVERFLOW"

Adding the constants would exceed the signed 64-bit maximum.

Constraints

1 <= polynomials.length <= 200.
Every expression is valid under the grammar above and has length from 1 through 2000.
Coefficient magnitudes contain at most 20 decimal digits.
Every exponent is from 0 through 10^6.