import java.util.*;
import java.lang.*;
import java.io.*;

// Problem Description: 
// Given a rope with length l, cut the rope into n sections
// with length l[0], l[1], ..., l[n-1]. Please get the maximal
// product of l[0] * l[1] * ... * l[n-1].
// Please note that you have to cut once at least.

class Ideone
{
	public static int maxProductAfterCutting_solution1(int length) {
		if(length < 2) {
			return 0;
		}
		if(length == 2) {
			return 1;
		}
		if(length == 3) {
			return 2;
		}
		
		int[] products = new int[length + 1];
		products[0] = 0;
		products[1] = 1;
		products[2] = 2;
		products[3] = 3;

		for(int i = 4; i <= length; ++i) {
			int max = 0;
			for(int j = 1; j <= i / 2; ++j) {
				int product = products[j] * products[i - j];
				if(max < product) {
					max = product;
				}

				products[i] = max;
			}
		}
		
		return products[length];
	}

	public static int maxProductAfterCutting_solution2(int length) {
		if(length < 2) {
			return 0;
		}
		if(length == 2) {
			return 1;
		}
		if(length == 3) {
			return 2;
		}
		
		int timesOf3 = length / 3;
		if((length - timesOf3 * 3) % 2 == 1) {
			timesOf3 -= 1;
		}
		
		int timesOf2 = (length - timesOf3 * 3) / 2;
		
		return (int)(Math.pow(3, timesOf3)) * (int)(Math.pow(2, timesOf2));
	}

	//////////////////////////////////////////////////////////////
	// Test Code Begins
	//////////////////////////////////////////////////////////////
	private static void test(String testName, int length, int expected) {
		int result1 = maxProductAfterCutting_solution1(length);
		if(result1 == expected) {
			System.out.println("Solution1 for " + testName + " passed.");
		}
		else {
			System.out.println("Solution1 for " + testName + " FAILED.");
		}
		
		int result2 = maxProductAfterCutting_solution2(length);
		if(result2 == expected) {
			System.out.println("Solution2 for " + testName + " passed.");
		}
		else {
			System.out.println("Solution2 for " + testName + " FAILED.");
		}
	}
	
	private static void test1() {
		int length = 1;
		int expected = 0;
		test("test1", length, expected);
	}
	
	private static void test2() {
		int length = 2;
		int expected = 1;
		test("test2", length, expected);
	}
	
	private static void test3() {
		int length = 3;
		int expected = 2;
		test("test3", length, expected);
	}
	
	private static void test4() {
		int length = 4;
		int expected = 4;
		test("test4", length, expected);
	}
	
	private static void test5() {
		int length = 5;
		int expected = 6;
		test("test5", length, expected);
	}
	
	private static void test6() {
		int length = 6;
		int expected = 9;
		test("test6", length, expected);
	}
	
	private static void test7() {
		int length = 7;
		int expected = 12;
		test("test7", length, expected);
	}
	
	private static void test8() {
		int length = 8;
		int expected = 18;
		test("test8", length, expected);
	}
	
	private static void test9() {
		int length = 9;
		int expected = 27;
		test("test9", length, expected);
	}
	
	private static void test10() {
		int length = 10;
		int expected = 36;
		test("test10", length, expected);
	}

	public static void main (String[] args) {
		test1();
		test2();
		test3();
		test4();
		test5();
		test6();
		test7();
		test8();
		test9();
		test10();
	}
}

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