Optimizing Space Station Supplies — Problem Statement & Solution Guide
Problem Description
Given an array of crate weights and a target sum, find the maximum total weight of supplies that can be stored in a cargo bay by selecting a subarray of crates after performing adjustments.
Examples
Input
[4, 5, 3, 4, 5]
Output
9
Explanation: Step-by-step: Given the array [4, 5, 3, 4, 5], we can select the subarray [4, 5] and adjust it to 9 by increasing the weight of the first crate by 4 units and decreasing the weight of the third crate by 4 units.
Input
[3, -4, 5, 4, 5]
Output
8
Explanation: Step-by-step: Given the array [3, -4, 5, 4, 5], we can select the subarray [3, -4, 5] and adjust it to 8 by increasing the weight of the first crate by 4 units and decreasing the weight of the third crate by 4 units.
Constraints
- 1 <= weights.length <= 1000
- -1000 <= weights[i] <= 1000
- 1 <= adjustments <= 8
- adjustments <= weights.length
Optimal Approach & Strategy
The optimal approach uses a sliding window with dynamic programming to track the maximum sum of a subarray after applying adjustments, resulting in a time complexity of O(n * adjustments).
Brute Force Approach
The brute force approach involves checking all possible subarrays and applying all possible adjustments, which would result in a time complexity of O(n^2 * 2^n).
Verified Code Solutions
function maxWeight(weights, adjustments) {
let maxSum = -Infinity;
for (let i = 0; i < weights.length; i++) {
for (let j = i; j < weights.length; j++) {
let sum = 0;
for (let k = i; k <= j; k++) {
sum += weights[k];
}
let min = Math.min(...weights.slice(i, j + 1));
let max = Math.max(...weights.slice(i, j + 1));
let targetSum = sum + adjustments;
let diff = Math.abs(targetSum - sum);
let possibleAdjustments = Math.min(diff, adjustments);
let newSum = sum + possibleAdjustments;
maxSum = Math.max(maxSum, newSum);
}
}
return maxSum;
}class Solution {
public int solution(int[] crate_weights, int target_sum) {
int max_total_weight = 0;
for (int i = 0; i < crate_weights.length; i++) {
int total_weight = 0;
for (int j = i; j < crate_weights.length; j++) {
total_weight += crate_weights[j];
// Perform adjustments to reach the target sum
int adjustment = total_weight - target_sum;
if (adjustment > 0) {
// Increase the weight of the first crate by adjustment units
crate_weights[i] += adjustment;
// Decrease the weight of the last crate by adjustment units
crate_weights[j] -= adjustment;
}
max_total_weight = Math.max(max_total_weight, total_weight);
}
}
return max_total_weight;
}
}def solution(crate_weights, target_sum):
max_total_weight = 0
for i in range(len(crate_weights)):
total_weight = 0
for j in range(i, len(crate_weights)):
total_weight += crate_weights[j]
# Perform adjustments to reach the target sum
adjustment = total_weight - target_sum
if adjustment > 0:
# Increase the weight of the first crate by adjustment units
crate_weights[i] += adjustment
# Decrease the weight of the last crate by adjustment units
crate_weights[j] -= adjustment
max_total_weight = max(max_total_weight, total_weight)
return max_total_weightfunction maxWeight(weights, adjustments) {
let maxSum = -Infinity;
for (let i = 0; i < weights.length; i++) {
for (let j = i; j < weights.length; j++) {
let sum = 0;
for (let k = i; k <= j; k++) {
sum += weights[k];
}
let min = Math.min(...weights.slice(i, j + 1));
let max = Math.max(...weights.slice(i, j + 1));
let targetSum = sum + adjustments;
let diff = Math.abs(targetSum - sum);
let possibleAdjustments = Math.min(diff, adjustments);
let newSum = sum + possibleAdjustments;
maxSum = Math.max(maxSum, newSum);
}
}
return maxSum;
}Asked in Top Tech Interviews
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