Capacity To Ship Packages Within D Days

class Solution {
public:
    bool canShip(vector<int>& weights, int capacity, int maxDays) {
        int requiredDays = 1, totalWeight = 0;
        for (int w : weights) {
            totalWeight += w;
            if (totalWeight > capacity) {
                requiredDays++;
                totalWeight = w;
            }
        }
        return requiredDays <= maxDays;
    }

    int shipWithinDays(vector<int>& weights, int days) {
        int minimumLoad = 0, maximumWeight = 0;
        for (int weight : weights) {
            minimumLoad += weight;
            if(weight > maximumWeight) maximumWeight = weight;
        }

        int low = maximumWeight, high = minimumLoad;
        while (low < high) {
            int mid = low + (high - low) / 2;
            if (canShip(weights, mid, days)) {
                high = mid;
            } else {
                low = mid + 1;
            }
        }
        return low;
    }
};

The provided C++ solution deals with determining the minimum capacity required to ship packages within a specified number of days. Here's an explanation of how the solution implements this functionality:

• The solution uses the binary search technique on the range of possible ship capacities, which efficiently narrows down the minimum possible capacity required.

• The function canShip checks whether a given capacity can be used to ship all packages within the allowed days. It iterates over package weights, grouping them together until their total exceeds the current capacity, in which case a new shipment day is started.

• In the shipWithinDays function:

  1. Calculate the minimal possible load that must be able to be shipped in a day, which is the weight of the heaviest package among weights, and accumulate the total of all weights as the maximal boundary (minimumLoad).

  2. Perform a binary search between maximumWeight and minimumLoad. For each middle value (mid), use canShip to test if it's feasible to ship with this capacity in the specified number of days. Adjust the low or high boundary based on the feasibility.

  3. The loop continues adjusting low and high limits until an optimal minimum capacity (low) is identified that satisfies the conditions.

This efficient approach optimizes the handling of large data inputs and ensures that the minimum shipping capacity is found with precision, adhering to the constraints of the given days.

class Solution {
    Boolean canShip(int[] packages, int capacity, int maxDays) {
        int requiredDays = 1, load = 0;
        for (int packageWeight : packages) {
            load += packageWeight;
            if (load > capacity) {
                requiredDays++;
                load = packageWeight;
            }
        }
        return requiredDays <= maxDays;
    }

    public int shipWithinDays(int[] weights, int days) {
        int sumWeights = 0, maxWeight = 0;
        for (int weight : weights) {
            sumWeights += weight;
            maxWeight = Math.max(maxWeight, weight);
        }

        int left = maxWeight, right = sumWeights;
        while (left < right) {
            int mid = (left + right) / 2;
            if (canShip(weights, mid, days)) {
                right = mid;
            } else {
                left = mid + 1;
            }
        }
        return left;
    }
}

The problem "Capacity To Ship Packages Within D Days" involves determining the minimum capacity of a ship so that all packages can be shipped within a given number of days. A binary search approach is applied to solve the problem efficiently in Java.

The solution class contains two methods:

• canShip: Checks if it's possible to ship all packages within the given days and capacity.
• shipWithinDays: Determines the minimum capacity using a binary search strategy.

Here's a breakdown of the implementation:

• canShip method:

  • Initialize requiredDays to 1 and load to 0 to track the total weight loaded on the ship for the current day.
  • Iterate over the package weights, adding them to the current load.
  • When the accumulated load exceeds the capacity, increment the required days and reset the load to the current package's weight.
  • The method returns true if the total required days are within the given limit.

• shipWithinDays method:

  • Calculate the sum of all weights and determine the maximum single weight.
  • Set the binary search range between this maximum weight and the sum of all weights.
  • Use a binary search loop to find the minimum possible shipping capacity:
    • Calculate the midpoint of the range as a potential shipping capacity.
    • If canShip returns true for this midpoint, narrow the search to the lower half by adjusting the right end of the range.
    • Otherwise, adjust the left end of the range to the higher half.
  • Return the left boundary of the range as this represents the minimum capacity needed.

This setup ensures that each check for feasibility (canShip) is optimized and minimizes the capacity required to meet the specified days constraint. The utilization of binary search provides a significant efficiency boost, especially useful when dealing with large data sets or tight performance requirements.