We use cookies (including Google cookies) to personalize ads and analyze traffic. By continuing to use our site, you accept our Privacy Policy.

SimplyLeet
TagsDisclaimersPrivacyTermsContactAbout Us

Minimum Cost to Cut a Stick

Difficulty: Hard

Problem Description

Given a wooden stick of length n units, and an integer array cuts where cuts[i] denotes a position to perform a cut, you should perform the cuts in any order to minimize the total cost. The cost of one cut is the length of the stick being cut, and the total cost is the sum of all cuts.

Key Insights

  • The order of cuts can significantly affect the total cost.
  • Each cut reduces the effective length of the stick for subsequent cuts.
  • A dynamic programming approach can be used to systematically find the minimum cost by considering different subproblems.

Space and Time Complexity

Time Complexity: O(c^2), where c is the number of cuts (maximum 100). Space Complexity: O(c^2), for the dynamic programming table.

Solution

To solve this problem, we can employ a dynamic programming approach. We define a 2D DP table where dp[i][j] represents the minimum cost to cut the stick from position i to position j. We will iterate over all possible lengths of stick sections, and for each section, we will try every possible cut position to find the optimal order of cuts.

  1. Initialize the DP table.
  2. Sort the cuts array.
  3. Loop through all possible lengths of stick sections.
  4. For each section, compute the minimum cost for every possible cut.
  5. Return the result found in dp[0][c+1] where c is the number of cuts.

Code Solutions

def minCost(n, cuts):
    cuts.sort()
    cuts = [0] + cuts + [n]
    c = len(cuts)
    dp = [[0] * c for _ in range(c)]

    for length in range(2, c):
        for i in range(c - length):
            j = i + length
            dp[i][j] = float('inf')
            for k in range(i + 1, j):
                dp[i][j] = min(dp[i][j], dp[i][k] + dp[k][j] + cuts[j] - cuts[i])

    return dp[0][c - 1]
← Back to All Questions