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ZeroOneKnapsack.java
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ZeroOneKnapsack.java
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/**
*
*/
public class ZeroOneKnapsack {
/*
Q1. V 的起始点为 Ci 还是 0? Ci 起始是否有效? 为什么?
Q2. V 起始 bound 为 bound = max(V - sum(Ci ... Cn), Ci)。 为什么?
Q3. 初始化值,恰好装满背包 vs 没有要求必须把背包装满?
*/
/**
* dp[i][v] = max{dp[i-1][v], dp[i-1][v-c[i]] + w[i]}
*/
public int maxValue(int[] costs, int[] weights, int V) {
if (costs == null || weights == null) return 0;
int N = costs.length;
int[][] dp = new int[N + 1][V + 1];
for (int i=1; i<=N; i++) {
for (int v=1; v<=V; v++) {
if (v < costs[i-1]) {
dp[i][v] = dp[i-1][v];
} else {
dp[i][v] = Math.max(dp[i-1][v], dp[i-1][v - costs[i-1]] + weights[i-1]);
}
}
}
return dp[N][V];
}
/**
* dp[v] = max{dp[v], dp[v-c[i]] + w[i]}
*/
public int maxValue2(int[] costs, int[] weights, int V) {
if (costs == null || weights == null) return 0;
int N = costs.length;
int[] dp = new int[V + 1];
for (int i=0; i<N; i++) {
for (int v=V; v>=costs[i]; v--) {
dp[v] = Math.max(dp[v], dp[v - costs[i]] + weights[i]);
}
}
return dp[V];
}
public static void main(String[] args) {
ZeroOneKnapsack slt = new ZeroOneKnapsack();
int[] costs = new int[]{10, 20, 30};
int[] weights = new int[]{60, 100, 120};
System.out.println(slt.maxValue(costs, weights, 50));
System.out.println(slt.maxValue2(costs, weights, 50));
costs = new int[]{10, 20, 30};
weights = new int[]{60, 100, 10};
System.out.println(slt.maxValue(costs, weights, 50));
System.out.println(slt.maxValue2(costs, weights, 50));
costs = new int[]{2, 2, 6, 5, 4};
weights = new int[]{6, 3, 5, 4, 6};
System.out.println(slt.maxValue(costs, weights, 10));
System.out.println(slt.maxValue2(costs, weights, 10));
costs = new int[]{2, 2, 6, 5, 4};
weights = new int[]{6, 3, 10, 4, 6};
System.out.println(slt.maxValue(costs, weights, 10));
System.out.println(slt.maxValue2(costs, weights, 10));
costs = new int[]{5, 5, 5, 5, 4};
weights = new int[]{6, 3, 5, 4, 6};
System.out.println(slt.maxValue(costs, weights, 10));
System.out.println(slt.maxValue2(costs, weights, 10));
costs = new int[]{2, 2, 6, 5, 4};
weights = new int[]{6, 3, 5, 4, 6};
System.out.println(slt.maxValue(costs, weights, 10));
System.out.println(slt.maxValue2(costs, weights, 10));
costs = new int[]{};
weights = new int[]{};
System.out.println(slt.maxValue(costs, weights, 10));
System.out.println(slt.maxValue2(costs, weights, 10));
costs = new int[]{2};
weights = new int[]{2};
System.out.println(slt.maxValue(costs, weights, 2));
System.out.println(slt.maxValue2(costs, weights, 2));
costs = new int[]{2};
weights = new int[]{2};
System.out.println(slt.maxValue(costs, weights, 3));
System.out.println(slt.maxValue2(costs, weights, 3));
costs = new int[]{2};
weights = new int[]{2};
System.out.println(slt.maxValue(costs, weights, 1));
System.out.println(slt.maxValue2(costs, weights, 1));
}
// for i=1..N
// ZeroOnePack(c[i],w[i]);
// procedure ZeroOnePack(cost,weight)
// for v=V..cost
// f[v]=max{f[v],f[v-cost]+weight}
}