割绳子

/*
 * Problem: LeetCode 1891 - Cutting Ropes
 * Description: You are given a rope of length `n` and you need to cut it into `m` segments
 * such that the product of their lengths is maximized. Return the maximum product you can get.
 * 
 * Approach:
 * 1. Use dynamic programming to store the maximum product for each length.
 * 2. Initialize an array `dp` where `dp[i]` will store the maximum product for length `i`.
 * 3. Use Java Streams to iterate over each length from 1 to `n` and calculate the maximum product by considering all possible cuts.
 * 4. Return the maximum product for length `n`.
 */

import java.util.stream.IntStream;

public class Solution {
    public int cuttingRope(int n) {
        if (n <= 3) return n - 1;
        int[] dp = new int[n + 1];
        dp[1] = 1;
        dp[2] = 1;
        IntStream.range(3, n + 1).forEach(i -> {
            dp[i] = IntStream.range(1, i).map(j -> Math.max(j * (i - j), j * dp[i - j])).max().getAsInt();
        });
        return dp[n];
    }
}