我查看了http://rosettacode.org/wiki/Knapsack_problem/0-1来解决基本的背包动态编程问题，我得到了一个可行的解决方案（knapsack1（）），但是当我尝试了一个不同的解决方案（knapsack2（） ）我觉得我在某个地方不正确，因为我没有得到正确的价值。
有问题的代码是底部的方法 knapsack2。我确定问题很小，但我觉得很荒谬，因为我找不到问题。正确答案应该是 1030 而不是 880。
（我知道大小为 [n][S] 的数组应该足够了，如 knapsack1() 所示，它有效，但 knapsack2() 并不奇怪。）
提前感谢任何浏览此内容的人。
/**
* http://rosettacode.org/wiki/Knapsack_problem/0-1
*/
public class Knapsack {
public static void main(String[] args) {
int n = 22;
int S = 400;
int s[] = new int[22];
int v[] = new int[22];
int i = 0;
s[i] = 9;
v[i] = 150;
i++;
s[i] = 13;
v[i] = 35;
i++;
s[i] = 153;
v[i] = 200;
i++;
s[i] = 50;
v[i] = 160;
i++;
s[i] = 15;
v[i] = 60;
i++;
s[i] = 68;
v[i] = 45;
i++;
s[i] = 27;
v[i] = 60;
i++;
s[i] = 39;
v[i] = 40;
i++;
s[i] = 23;
v[i] = 30;
i++;
s[i] = 52;
v[i] = 10;
i++;
s[i] = 11;
v[i] = 70;
i++;
s[i] = 32;
v[i] = 30;
i++;
s[i] = 24;
v[i] = 15;
i++;
s[i] = 48;
v[i] = 10;
i++;
s[i] = 73;
v[i] = 40;
i++;
s[i] = 42;
v[i] = 70;
i++;
s[i] = 43;
v[i] = 75;
i++;
s[i] = 22;
v[i] = 80;
i++;
s[i] = 7;
v[i] = 20;
i++;
s[i] = 18;
v[i] = 12;
i++;
s[i] = 4;
v[i] = 50;
i++;
s[i] = 30;
v[i] = 10;
System.out.println("--Given items with these values--");
System.out.println("[item, weight (dag), value]");
System.out.println("map 9 150");
System.out.println("compass 13 35");
System.out.println("water 153 200");
System.out.println("sandwich 50 160");
System.out.println("glucose 15 60");
System.out.println("tin 68 45");
System.out.println("banana 27 60");
System.out.println("apple 39 40");
System.out.println("cheese 23 30");
System.out.println("beer 52 10");
System.out.println("suntan cream 11 70");
System.out.println("camera 32 30");
System.out.println("T-shirt 24 15");
System.out.println("trousers 48 10");
System.out.println("umbrella 73 40");
System.out.println("waterproof trousers 42 70");
System.out.println("waterproof overclothes 43 75");
System.out.println("note-case 22 80");
System.out.println("sunglasses 7 20");
System.out.println("towel 18 12");
System.out.println("socks 4 50");
System.out.println("book 30 10");
System.out.println("--The max value you can achieve in your knapsack--");
System.out.println(knapsack2(n, S, s, v));
// proper value should be 1030, from website
}
/**
* @param n items
* @param S bag size/capacity
* @param s array where s[i] is size/weight of item at index i
* @param v array where v[i] is value of item at index i
* @return best/max value possible
*/
@SuppressWarnings("unused")
private static int knapsack1(int n, int S, int s[], int v[]) {
int dp[][] = new int[n][S];
for (int i=n-1; i >= 0; i--) { // # items being left out + 1
for (int j=0; j < S; j++) { // size/weight + 1
if (i == n-1) {
dp[i][j] = 0;
} else {
int choices[] = {0,0};
choices[0] = dp[i+1][j];
if (j >= s[i])
choices[1] = v[i] + dp[i+1][j-s[i]];
dp[i][j] = max(choices);
}
}
}
return dp[0][S-1];
}
private static int max(int choices[]) {
if (choices[0] > choices[1])
return choices[0];
else
return choices[1];
}
/**
* @param n items
* @param S bag size/capacity
* @param s array where s[i] is size/weight of item at index i
* @param v array where v[i] is value of item at index i
* @return best/max value possible
*/
// @SuppressWarnings("unused")
private static int knapsack2(int n, int S, int s[], int v[]) {
int dp[][] = new int[n][S]; // dp[i][j] holds max value using i items and not exceeding weight j+1
for (int i=0; i < n; i++) { // # items. don't need to reach n because we assume we can fit at most n-1 items.
for (int j=0; j < S; j++) { // size/weight+1
if (i == 0) {
dp[i][j] = 0;
} else {
int choices[] = {0,0};
choices[0] = dp[i-1][j];
if (j >= s[i])
choices[1] = v[i] + dp[i-1][j-s[i]];
dp[i][j] = max(choices);
}
}
}
return dp[n-1][S-1]; // TODO: WHY IS THIS 880 AND NOT 1030?
}
}