01背包模型及维度优化

java/priv/pront/code/national/acwing/dp/bags/A2_01背包问题.java

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+package priv.pront.code.national.acwing.dp.bags;
+
+import java.util.Scanner;
+/*fixme 为何采用倒序遍历*/
+public class A2_01背包问题 {
+
+    static int n, V;
+    static int[] w , v ;
+    static int[] dp;
+    public static void main(String[] args){
+        Scanner scanner = new Scanner(System.in);
+        n = scanner.nextInt();
+        V = scanner.nextInt();
+        w = new int[n + 1];
+        v = new int[n + 1];
+        dp = new int[V + 1];
+
+        for(int i = 1; i <= n; i++){
+            v[i] = scanner.nextInt();
+            w[i] = scanner.nextInt();
+        }
+        for(int i = 1; i <= n; i++){
+            for(int j = V; j >= v[i]; j--){
+                dp[j] = Math.max(dp[j], dp[j - v[i]] + w[i]);
+            }
+        }
+        System.out.println(dp[V]);
+    }
+}

java/priv/pront/code/national/acwing/dp/bags/Acwing1022_收服宠物小精灵.java

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+package priv.pront.code.national.acwing.dp.bags;
+
+import java.util.Scanner;
+
+public class Acwing1022_收服宠物小精灵 {
+
+    static int n, m, k, hit = 0;
+    static int[] hurt, num;
+    static int[][] dp;
+
+    public static void main(String[] args) {
+        Scanner scanner = new Scanner(System.in);
+        n = scanner.nextInt(); //精灵球数量
+        m = scanner.nextInt();  //皮卡丘初始的体力值
+        k = scanner.nextInt();  //野生小精灵的数量
+        hurt = new int[k + 1];
+        num = new int[k + 1];
+        dp = new int[1005][505];
+        for (int i = 1; i <= k; i++) {
+            num[i] = scanner.nextInt();
+            hurt[i] = scanner.nextInt();
+        }
+        for (int i = 1; i <= k; i++) {
+            for (int j = n; j >= 1; j--) {  // 剩余的精灵球数量
+                for (int t = m; t >= 1; k--) {  // 剩余体力值
+                    // 捕捉
+                    if (j - num[i] >= 0 && t - hurt[i] >= 0) {
+                        if (dp[j][t] == dp[j - num[i]][t - hurt[i]]) {
+                            dp[j][t] = t > t - hurt[i] ? dp[j][t] : dp[j - num[i]][t - hurt[i]];
+                        } else {
+                            dp[j][t] = Math.max(dp[j][t], dp[j - num[i]][t - hurt[i]]);
+                        }
+                    }
+
+                }
+            }
+        }
+        System.out.println(dp[n][m]);
+    }
+}

java/priv/pront/code/national/acwing/dp/bags/Acwing278_数字组合.java

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+package priv.pront.code.national.acwing.dp.bags;
+
+import java.util.Scanner;
+
+public class Acwing278_数字组合 {
+
+    static int[] dp;
+    static int[] a;
+    public static void main(String[] args){
+        Scanner scanner = new Scanner(System.in);
+        int n = scanner.nextInt();
+        int m = scanner.nextInt();
+        a = new int[n + 1];
+        dp = new int[m + 1];
+        dp[0] = 1;
+        for(int i = 1; i <= n; i++) {a[i] = scanner.nextInt();}
+        for(int i = 1; i <= n; i++){
+            for(int j = m; j >= a[i]; j--){
+                dp[j] += dp[j - a[i]];
+            }
+        }
+        System.out.println(dp[m]);
+    }
+}

java/priv/pront/code/national/acwing/dp/bags/Acwing423_采药.java

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+package priv.pront.code.national.acwing.dp.bags;
+
+import java.util.Scanner;
+
+public class Acwing423_采药 {
+
+    static int T, M;
+    static int[] t, w;
+    static int[] dp;
+    public static void main(String[] args){
+        Scanner scanner = new Scanner(System.in);
+        T = scanner.nextInt(); M = scanner.nextInt();
+        t = new int[M + 1];
+        w = new int[M + 1];
+        for(int i = 1; i <= M; i++){
+            t[i] = scanner.nextInt();
+            w[i] = scanner.nextInt();
+        }
+        dp = new int[T + 1];
+        for(int i = 1; i <= M; i++){
+            for(int j = T; j >= 1; j--){
+                dp[j] = dp[j];
+                if(j - t[i] >= 0){
+                    dp[j] = Math.max(dp[j], dp[j - t[i]] + w[i]);
+                }
+            }
+        }
+        System.out.println(dp[T]);
+    }
+}