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Solve shipping capacity and expression insertion

Q: Solve shipping capacity and expression insertion

This combined prompt evaluates algorithmic problem-solving skills: the first problem tests array partitioning and capacity planning under ordering and resource constraints, and the second tests combinatorial expression generation, tokenization, and numeric edge-case handling in digit strings.

Problem A: Minimum shipping capacity

You are given an array weights where weights[i] is the weight of the i-th package. Packages must be shipped in order (you cannot reorder). You have D days to ship all packages.

Each day, you load a contiguous prefix of the remaining packages onto the ship, up to the ship's capacity C. The total weight loaded that day cannot exceed C.

Task: Return the minimum integer capacity C that allows shipping all packages within D days.

Input:

weights : array of positive integers
D : positive integer

Output:

Minimum feasible ship capacity C

Example:

weights = [1,2,3,4,5,6,7,8,9,10] , D = 5 → output 15

Constraints (typical):

1 <= len(weights) <= 1e5
1 <= weights[i] <= 1e5
1 <= D <= len(weights)

Problem B: Insert `+`, `-`, or concatenate to hit target

You are given a string s consisting only of digits (e.g., "123") and an integer target.

You may insert between any two adjacent digits one of:

'+'
'-'
nothing (concatenate digits into a multi-digit number)

This forms an arithmetic expression evaluated left-to-right with normal integer addition/subtraction.

Task: Return all distinct expressions (as strings) that evaluate to target.

Rules / edge cases:

A number token cannot have leading zeros (e.g., "05" is invalid), except the token "0" itself.
You must use the digits in s in order; you cannot reorder or skip digits.

Input:

s : digit string
target : integer

Output:

List of expression strings that evaluate to target (order not important)

Example:

s = "123" , target = 6 → ["1+2+3"]
s = "105" , target = 5 → ["10-5"] (but not "1+0+5" if it doesn't match)

Constraints (typical):

1 <= len(s) <= 10~12 (small enough to allow backtracking)
Result count may be large; return all that exist

Problem A: Minimum shipping capacity

You are given an array weights where weights[i] is the weight of the i-th package. Packages must be shipped in order (you cannot reorder). You have D days to ship all packages.

Each day, you load a contiguous prefix of the remaining packages onto the ship, up to the ship's capacity C. The total weight loaded that day cannot exceed C.

Task: Return the minimum integer capacity C that allows shipping all packages within D days.

Input:

weights : array of positive integers
D : positive integer

Output:

Minimum feasible ship capacity C

Example:

weights = [1,2,3,4,5,6,7,8,9,10] , D = 5 → output 15

Constraints (typical):

1 <= len(weights) <= 1e5
1 <= weights[i] <= 1e5
1 <= D <= len(weights)

Problem B: Insert `+`, `-`, or concatenate to hit target

You are given a string s consisting only of digits (e.g., "123") and an integer target.

You may insert between any two adjacent digits one of:

'+'
'-'
nothing (concatenate digits into a multi-digit number)

This forms an arithmetic expression evaluated left-to-right with normal integer addition/subtraction.

Task: Return all distinct expressions (as strings) that evaluate to target.

Rules / edge cases:

A number token cannot have leading zeros (e.g., "05" is invalid), except the token "0" itself.
You must use the digits in s in order; you cannot reorder or skip digits.

Input:

s : digit string
target : integer

Output:

List of expression strings that evaluate to target (order not important)

Example:

s = "123" , target = 6 → ["1+2+3"]
s = "105" , target = 5 → ["10-5"] (but not "1+0+5" if it doesn't match)

Constraints (typical):

1 <= len(s) <= 10~12 (small enough to allow backtracking)
Result count may be large; return all that exist

Solve shipping capacity and expression insertion

Quick Overview

Problem A: Minimum shipping capacity

Problem B: Insert `+`, `-`, or concatenate to hit target

Comments (0)

Solve shipping capacity and expression insertion

Quick Overview

Problem A: Minimum shipping capacity

Problem B: Insert `+`, `-`, or concatenate to hit target

Comments (0)

Solve shipping capacity and expression insertion

Quick Overview