[Algo] 87. Max Product Of Cutting Rope

Given a rope with positive integer-length n, how to cut the rope into m integer-length parts with length p[0], p[1], ...,p[m-1], in order to get the maximal product of p[0]*p[1]* ... *p[m-1]? m is determined by you and must be greater than 0 (at least one cut must be made). Return the max product you can have.

Assumptions

• n >= 2

Examples

• n = 12, the max product is 3 * 3 * 3 * 3 = 81(cut the rope into 4 pieces with length of each is 3).

public class Solution {
  public int maxProduct(int length) {
    // Write your solution here
    if (length == 0 || length == 1) {
      return 0;
    }
    int[] cutArr = new int[length + 1];
    cutArr[1] = 0;
    for (int i = 2; i <= length; i++) {
      for (int j = 1; j < i; j++) {
        int curMax = Math.max((i - j) * j, cutArr[i - j] * j);
        cutArr[i] = Math.max(cutArr[i], curMax);
      }
    }
    return cutArr[length];
  }
}

DFS

public class Solution {
  public int maxProduct(int length) {
    // Write your solution here
    if (length == 0 || length == 1) {
      return 0;
    }
    int res = 0;
    for (int i = 1; i < length; i++) {
      int curMax = Math.max(i * (length - i), i * maxProduct(length - i));
      res = Math.max(res, curMax);
    }
    return res;
  }
}