Recognize that the minimum capacity lies between the maximum package weight and the sum of all weights. Use binary search on the capacity and for each candidate, simulate the shipping process greedily to check if all packages can be delivered within D days. Return the smallest feasible capacity.
Pro tip: Clarify that packages must be shipped in the given order, so a greedy simulation is valid. Mention that binary search reduces the time complexity to O(n log(sum(weights))), which is efficient for large inputs.
Set the lower bound to the maximum package weight (since capacity cannot be less than the heaviest package) and the upper bound to the sum of all weights (a single day shipment).
While lower bound < upper bound, compute mid capacity and check if it's feasible to ship within D days using a greedy simulation.
Simulate shipping: iterate through packages, accumulate weights until adding the next would exceed capacity, then increment day count and start a new day. If days exceed D, capacity is too small.
If feasible, set upper bound to mid; otherwise set lower bound to mid+1. Continue until bounds converge.
The converged lower bound is the minimum ship capacity needed.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Backtracking, but the leading zeros edge case and the concatenation tracking both bit me.
Use backtracking to explore all possible ways to split the digit string into numbers and insert operators, maintaining the current expression and its evaluated value. Handle multiplication by tracking the last operand to correctly adjust the value when a '*' is inserted, since multiplication has higher precedence than addition and subtraction.
Pro tip: Clarify with the interviewer whether the expression should be built left-to-right with standard operator precedence (which requires the last-operand trick) or if they expect a simpler approach without precedence. Also, discuss how to handle leading zeros in multi-digit numbers, as this is a common edge case.
Ask about operator precedence, handling of leading zeros, and whether the output should include duplicate expressions. Confirm that the digit string can be split into multi-digit numbers.
Define a recursive function that processes the digit string from left to right, building the current expression and tracking the current evaluated value and the last operand (for multiplication).
At each step, try inserting '+', '-', or nothing (concatenation) between the current number and the next digit(s). For multiplication, adjust the value by subtracting the last operand and adding the product.
Discuss potential pruning: if the remaining digits cannot possibly reach the target due to magnitude, or if using memoization to avoid recomputing subproblems (though state includes expression, so memoization is tricky).
Explain that the time complexity is exponential (O(4^n) in the worst case) due to branching, and space complexity is O(n) for recursion depth. Mention iterative approaches or dynamic programming as alternatives but note backtracking is standard.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.