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translation: Add Python and Java code for EN version (#1345)
* Add the intial translation of code of all the languages * test * revert * Remove * Add Python and Java code for EN version
This commit is contained in:
Yudong Jin
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/**
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* File: climbing_stairs_backtrack.java
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* Created Time: 2023-06-30
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* Author: krahets (krahets@163.com)
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*/
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package chapter_dynamic_programming;
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import java.util.*;
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public class climbing_stairs_backtrack {
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/* Backtracking */
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public static void backtrack(List<Integer> choices, int state, int n, List<Integer> res) {
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// When climbing to the nth step, add 1 to the number of solutions
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if (state == n)
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res.set(0, res.get(0) + 1);
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// Traverse all choices
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for (Integer choice : choices) {
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// Pruning: do not allow climbing beyond the nth step
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if (state + choice > n)
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continue;
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// Attempt: make a choice, update the state
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backtrack(choices, state + choice, n, res);
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// Retract
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}
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}
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/* Climbing stairs: Backtracking */
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public static int climbingStairsBacktrack(int n) {
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List<Integer> choices = Arrays.asList(1, 2); // Can choose to climb up 1 step or 2 steps
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int state = 0; // Start climbing from the 0th step
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List<Integer> res = new ArrayList<>();
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res.add(0); // Use res[0] to record the number of solutions
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backtrack(choices, state, n, res);
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return res.get(0);
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}
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public static void main(String[] args) {
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int n = 9;
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int res = climbingStairsBacktrack(n);
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System.out.println(String.format("There are %d solutions to climb %d stairs", n, res));
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}
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}
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@@ -0,0 +1,36 @@
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/**
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* File: climbing_stairs_constraint_dp.java
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* Created Time: 2023-07-01
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* Author: krahets (krahets@163.com)
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*/
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package chapter_dynamic_programming;
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public class climbing_stairs_constraint_dp {
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/* Constrained climbing stairs: Dynamic programming */
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static int climbingStairsConstraintDP(int n) {
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if (n == 1 || n == 2) {
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return 1;
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}
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// Initialize dp table, used to store subproblem solutions
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int[][] dp = new int[n + 1][3];
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// Initial state: preset the smallest subproblem solution
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dp[1][1] = 1;
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dp[1][2] = 0;
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dp[2][1] = 0;
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dp[2][2] = 1;
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// State transition: gradually solve larger subproblems from smaller ones
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for (int i = 3; i <= n; i++) {
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dp[i][1] = dp[i - 1][2];
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dp[i][2] = dp[i - 2][1] + dp[i - 2][2];
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}
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return dp[n][1] + dp[n][2];
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}
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public static void main(String[] args) {
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int n = 9;
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int res = climbingStairsConstraintDP(n);
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System.out.println(String.format("There are %d solutions to climb %d stairs", n, res));
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}
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}
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@@ -0,0 +1,31 @@
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/**
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* File: climbing_stairs_dfs.java
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* Created Time: 2023-06-30
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* Author: krahets (krahets@163.com)
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*/
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package chapter_dynamic_programming;
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public class climbing_stairs_dfs {
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/* Search */
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public static int dfs(int i) {
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// Known dp[1] and dp[2], return them
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if (i == 1 || i == 2)
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return i;
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// dp[i] = dp[i-1] + dp[i-2]
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int count = dfs(i - 1) + dfs(i - 2);
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return count;
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}
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/* Climbing stairs: Search */
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public static int climbingStairsDFS(int n) {
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return dfs(n);
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}
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public static void main(String[] args) {
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int n = 9;
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int res = climbingStairsDFS(n);
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System.out.println(String.format("There are %d solutions to climb %d stairs", n, res));
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}
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}
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@@ -0,0 +1,41 @@
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/**
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* File: climbing_stairs_dfs_mem.java
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* Created Time: 2023-06-30
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* Author: krahets (krahets@163.com)
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*/
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package chapter_dynamic_programming;
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import java.util.Arrays;
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public class climbing_stairs_dfs_mem {
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/* Memoized search */
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public static int dfs(int i, int[] mem) {
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// Known dp[1] and dp[2], return them
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if (i == 1 || i == 2)
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return i;
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// If there is a record for dp[i], return it
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if (mem[i] != -1)
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return mem[i];
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// dp[i] = dp[i-1] + dp[i-2]
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int count = dfs(i - 1, mem) + dfs(i - 2, mem);
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// Record dp[i]
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mem[i] = count;
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return count;
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}
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/* Climbing stairs: Memoized search */
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public static int climbingStairsDFSMem(int n) {
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// mem[i] records the total number of solutions for climbing to the ith step, -1 means no record
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int[] mem = new int[n + 1];
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Arrays.fill(mem, -1);
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return dfs(n, mem);
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}
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public static void main(String[] args) {
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int n = 9;
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int res = climbingStairsDFSMem(n);
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System.out.println(String.format("There are %d solutions to climb %d stairs", n, res));
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}
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}
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@@ -0,0 +1,48 @@
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/**
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* File: climbing_stairs_dp.java
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* Created Time: 2023-06-30
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* Author: krahets (krahets@163.com)
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*/
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package chapter_dynamic_programming;
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public class climbing_stairs_dp {
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/* Climbing stairs: Dynamic programming */
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public static int climbingStairsDP(int n) {
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if (n == 1 || n == 2)
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return n;
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// Initialize dp table, used to store subproblem solutions
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int[] dp = new int[n + 1];
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// Initial state: preset the smallest subproblem solution
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dp[1] = 1;
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dp[2] = 2;
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// State transition: gradually solve larger subproblems from smaller ones
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for (int i = 3; i <= n; i++) {
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dp[i] = dp[i - 1] + dp[i - 2];
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}
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return dp[n];
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}
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/* Climbing stairs: Space-optimized dynamic programming */
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public static int climbingStairsDPComp(int n) {
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if (n == 1 || n == 2)
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return n;
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int a = 1, b = 2;
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for (int i = 3; i <= n; i++) {
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int tmp = b;
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b = a + b;
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a = tmp;
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}
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return b;
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}
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public static void main(String[] args) {
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int n = 9;
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int res = climbingStairsDP(n);
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System.out.println(String.format("There are %d solutions to climb %d stairs", n, res));
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res = climbingStairsDPComp(n);
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System.out.println(String.format("There are %d solutions to climb %d stairs", n, res));
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}
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}
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72
en/codes/java/chapter_dynamic_programming/coin_change.java
Normal file
72
en/codes/java/chapter_dynamic_programming/coin_change.java
Normal file
@@ -0,0 +1,72 @@
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/**
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* File: coin_change.java
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* Created Time: 2023-07-11
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* Author: krahets (krahets@163.com)
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*/
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package chapter_dynamic_programming;
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import java.util.Arrays;
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public class coin_change {
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/* Coin change: Dynamic programming */
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static int coinChangeDP(int[] coins, int amt) {
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int n = coins.length;
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int MAX = amt + 1;
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// Initialize dp table
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int[][] dp = new int[n + 1][amt + 1];
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// State transition: first row and first column
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for (int a = 1; a <= amt; a++) {
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dp[0][a] = MAX;
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}
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// State transition: the rest of the rows and columns
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for (int i = 1; i <= n; i++) {
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for (int a = 1; a <= amt; a++) {
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if (coins[i - 1] > a) {
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// If exceeding the target amount, do not choose coin i
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dp[i][a] = dp[i - 1][a];
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} else {
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// The smaller value between not choosing and choosing coin i
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dp[i][a] = Math.min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1);
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}
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}
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}
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return dp[n][amt] != MAX ? dp[n][amt] : -1;
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}
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/* Coin change: Space-optimized dynamic programming */
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static int coinChangeDPComp(int[] coins, int amt) {
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int n = coins.length;
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int MAX = amt + 1;
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// Initialize dp table
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int[] dp = new int[amt + 1];
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Arrays.fill(dp, MAX);
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dp[0] = 0;
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// State transition
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for (int i = 1; i <= n; i++) {
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for (int a = 1; a <= amt; a++) {
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if (coins[i - 1] > a) {
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// If exceeding the target amount, do not choose coin i
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dp[a] = dp[a];
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} else {
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// The smaller value between not choosing and choosing coin i
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dp[a] = Math.min(dp[a], dp[a - coins[i - 1]] + 1);
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}
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}
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}
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return dp[amt] != MAX ? dp[amt] : -1;
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}
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public static void main(String[] args) {
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int[] coins = { 1, 2, 5 };
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int amt = 4;
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// Dynamic programming
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int res = coinChangeDP(coins, amt);
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System.out.println("The minimum number of coins required to make up the target amount is " + res);
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// Space-optimized dynamic programming
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res = coinChangeDPComp(coins, amt);
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System.out.println("The minimum number of coins required to make up the target amount is " + res);
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}
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}
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@@ -0,0 +1,67 @@
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/**
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* File: coin_change_ii.java
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* Created Time: 2023-07-11
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* Author: krahets (krahets@163.com)
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*/
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package chapter_dynamic_programming;
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public class coin_change_ii {
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/* Coin change II: Dynamic programming */
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static int coinChangeIIDP(int[] coins, int amt) {
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int n = coins.length;
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// Initialize dp table
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int[][] dp = new int[n + 1][amt + 1];
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// Initialize first column
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for (int i = 0; i <= n; i++) {
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dp[i][0] = 1;
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}
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// State transition
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for (int i = 1; i <= n; i++) {
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for (int a = 1; a <= amt; a++) {
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if (coins[i - 1] > a) {
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// If exceeding the target amount, do not choose coin i
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dp[i][a] = dp[i - 1][a];
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} else {
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// The sum of the two options of not choosing and choosing coin i
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dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]];
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}
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}
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}
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return dp[n][amt];
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}
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/* Coin change II: Space-optimized dynamic programming */
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static int coinChangeIIDPComp(int[] coins, int amt) {
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int n = coins.length;
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// Initialize dp table
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int[] dp = new int[amt + 1];
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dp[0] = 1;
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// State transition
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for (int i = 1; i <= n; i++) {
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for (int a = 1; a <= amt; a++) {
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if (coins[i - 1] > a) {
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// If exceeding the target amount, do not choose coin i
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dp[a] = dp[a];
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} else {
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// The sum of the two options of not choosing and choosing coin i
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dp[a] = dp[a] + dp[a - coins[i - 1]];
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}
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}
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}
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return dp[amt];
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}
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public static void main(String[] args) {
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int[] coins = { 1, 2, 5 };
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int amt = 5;
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// Dynamic programming
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int res = coinChangeIIDP(coins, amt);
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System.out.println("The number of coin combinations to make up the target amount is " + res);
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// Space-optimized dynamic programming
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res = coinChangeIIDPComp(coins, amt);
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System.out.println("The number of coin combinations to make up the target amount is " + res);
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}
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}
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139
en/codes/java/chapter_dynamic_programming/edit_distance.java
Normal file
139
en/codes/java/chapter_dynamic_programming/edit_distance.java
Normal file
@@ -0,0 +1,139 @@
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/**
|
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* File: edit_distance.java
|
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* Created Time: 2023-07-13
|
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* Author: krahets (krahets@163.com)
|
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*/
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package chapter_dynamic_programming;
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import java.util.Arrays;
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public class edit_distance {
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/* Edit distance: Brute force search */
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static int editDistanceDFS(String s, String t, int i, int j) {
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// If both s and t are empty, return 0
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if (i == 0 && j == 0)
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return 0;
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// If s is empty, return the length of t
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if (i == 0)
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return j;
|
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// If t is empty, return the length of s
|
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if (j == 0)
|
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return i;
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// If the two characters are equal, skip these two characters
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if (s.charAt(i - 1) == t.charAt(j - 1))
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return editDistanceDFS(s, t, i - 1, j - 1);
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// The minimum number of edits = the minimum number of edits from three operations (insert, remove, replace) + 1
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int insert = editDistanceDFS(s, t, i, j - 1);
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int delete = editDistanceDFS(s, t, i - 1, j);
|
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int replace = editDistanceDFS(s, t, i - 1, j - 1);
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// Return the minimum number of edits
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return Math.min(Math.min(insert, delete), replace) + 1;
|
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}
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/* Edit distance: Memoized search */
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static int editDistanceDFSMem(String s, String t, int[][] mem, int i, int j) {
|
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// If both s and t are empty, return 0
|
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if (i == 0 && j == 0)
|
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return 0;
|
||||
// If s is empty, return the length of t
|
||||
if (i == 0)
|
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return j;
|
||||
// If t is empty, return the length of s
|
||||
if (j == 0)
|
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return i;
|
||||
// If there is a record, return it
|
||||
if (mem[i][j] != -1)
|
||||
return mem[i][j];
|
||||
// If the two characters are equal, skip these two characters
|
||||
if (s.charAt(i - 1) == t.charAt(j - 1))
|
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return editDistanceDFSMem(s, t, mem, i - 1, j - 1);
|
||||
// The minimum number of edits = the minimum number of edits from three operations (insert, remove, replace) + 1
|
||||
int insert = editDistanceDFSMem(s, t, mem, i, j - 1);
|
||||
int delete = editDistanceDFSMem(s, t, mem, i - 1, j);
|
||||
int replace = editDistanceDFSMem(s, t, mem, i - 1, j - 1);
|
||||
// Record and return the minimum number of edits
|
||||
mem[i][j] = Math.min(Math.min(insert, delete), replace) + 1;
|
||||
return mem[i][j];
|
||||
}
|
||||
|
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/* Edit distance: Dynamic programming */
|
||||
static int editDistanceDP(String s, String t) {
|
||||
int n = s.length(), m = t.length();
|
||||
int[][] dp = new int[n + 1][m + 1];
|
||||
// State transition: first row and first column
|
||||
for (int i = 1; i <= n; i++) {
|
||||
dp[i][0] = i;
|
||||
}
|
||||
for (int j = 1; j <= m; j++) {
|
||||
dp[0][j] = j;
|
||||
}
|
||||
// State transition: the rest of the rows and columns
|
||||
for (int i = 1; i <= n; i++) {
|
||||
for (int j = 1; j <= m; j++) {
|
||||
if (s.charAt(i - 1) == t.charAt(j - 1)) {
|
||||
// If the two characters are equal, skip these two characters
|
||||
dp[i][j] = dp[i - 1][j - 1];
|
||||
} else {
|
||||
// The minimum number of edits = the minimum number of edits from three operations (insert, remove, replace) + 1
|
||||
dp[i][j] = Math.min(Math.min(dp[i][j - 1], dp[i - 1][j]), dp[i - 1][j - 1]) + 1;
|
||||
}
|
||||
}
|
||||
}
|
||||
return dp[n][m];
|
||||
}
|
||||
|
||||
/* Edit distance: Space-optimized dynamic programming */
|
||||
static int editDistanceDPComp(String s, String t) {
|
||||
int n = s.length(), m = t.length();
|
||||
int[] dp = new int[m + 1];
|
||||
// State transition: first row
|
||||
for (int j = 1; j <= m; j++) {
|
||||
dp[j] = j;
|
||||
}
|
||||
// State transition: the rest of the rows
|
||||
for (int i = 1; i <= n; i++) {
|
||||
// State transition: first column
|
||||
int leftup = dp[0]; // Temporarily store dp[i-1, j-1]
|
||||
dp[0] = i;
|
||||
// State transition: the rest of the columns
|
||||
for (int j = 1; j <= m; j++) {
|
||||
int temp = dp[j];
|
||||
if (s.charAt(i - 1) == t.charAt(j - 1)) {
|
||||
// If the two characters are equal, skip these two characters
|
||||
dp[j] = leftup;
|
||||
} else {
|
||||
// The minimum number of edits = the minimum number of edits from three operations (insert, remove, replace) + 1
|
||||
dp[j] = Math.min(Math.min(dp[j - 1], dp[j]), leftup) + 1;
|
||||
}
|
||||
leftup = temp; // Update for the next round of dp[i-1, j-1]
|
||||
}
|
||||
}
|
||||
return dp[m];
|
||||
}
|
||||
|
||||
public static void main(String[] args) {
|
||||
String s = "bag";
|
||||
String t = "pack";
|
||||
int n = s.length(), m = t.length();
|
||||
|
||||
// Brute force search
|
||||
int res = editDistanceDFS(s, t, n, m);
|
||||
System.out.println("Changing " + s + " to " + t + " requires a minimum of " + res + " edits");
|
||||
|
||||
// Memoized search
|
||||
int[][] mem = new int[n + 1][m + 1];
|
||||
for (int[] row : mem)
|
||||
Arrays.fill(row, -1);
|
||||
res = editDistanceDFSMem(s, t, mem, n, m);
|
||||
System.out.println("Changing " + s + " to " + t + " requires a minimum of " + res + " edits");
|
||||
|
||||
// Dynamic programming
|
||||
res = editDistanceDP(s, t);
|
||||
System.out.println("Changing " + s + " to " + t + " requires a minimum of " + res + " edits");
|
||||
|
||||
// Space-optimized dynamic programming
|
||||
res = editDistanceDPComp(s, t);
|
||||
System.out.println("Changing " + s + " to " + t + " requires a minimum of " + res + " edits");
|
||||
}
|
||||
}
|
||||
116
en/codes/java/chapter_dynamic_programming/knapsack.java
Normal file
116
en/codes/java/chapter_dynamic_programming/knapsack.java
Normal file
@@ -0,0 +1,116 @@
|
||||
/**
|
||||
* File: knapsack.java
|
||||
* Created Time: 2023-07-10
|
||||
* Author: krahets (krahets@163.com)
|
||||
*/
|
||||
|
||||
package chapter_dynamic_programming;
|
||||
|
||||
import java.util.Arrays;
|
||||
|
||||
public class knapsack {
|
||||
|
||||
/* 0-1 Knapsack: Brute force search */
|
||||
static int knapsackDFS(int[] wgt, int[] val, int i, int c) {
|
||||
// If all items have been chosen or the knapsack has no remaining capacity, return value 0
|
||||
if (i == 0 || c == 0) {
|
||||
return 0;
|
||||
}
|
||||
// If exceeding the knapsack capacity, can only choose not to put it in the knapsack
|
||||
if (wgt[i - 1] > c) {
|
||||
return knapsackDFS(wgt, val, i - 1, c);
|
||||
}
|
||||
// Calculate the maximum value of not putting in and putting in item i
|
||||
int no = knapsackDFS(wgt, val, i - 1, c);
|
||||
int yes = knapsackDFS(wgt, val, i - 1, c - wgt[i - 1]) + val[i - 1];
|
||||
// Return the greater value of the two options
|
||||
return Math.max(no, yes);
|
||||
}
|
||||
|
||||
/* 0-1 Knapsack: Memoized search */
|
||||
static int knapsackDFSMem(int[] wgt, int[] val, int[][] mem, int i, int c) {
|
||||
// If all items have been chosen or the knapsack has no remaining capacity, return value 0
|
||||
if (i == 0 || c == 0) {
|
||||
return 0;
|
||||
}
|
||||
// If there is a record, return it
|
||||
if (mem[i][c] != -1) {
|
||||
return mem[i][c];
|
||||
}
|
||||
// If exceeding the knapsack capacity, can only choose not to put it in the knapsack
|
||||
if (wgt[i - 1] > c) {
|
||||
return knapsackDFSMem(wgt, val, mem, i - 1, c);
|
||||
}
|
||||
// Calculate the maximum value of not putting in and putting in item i
|
||||
int no = knapsackDFSMem(wgt, val, mem, i - 1, c);
|
||||
int yes = knapsackDFSMem(wgt, val, mem, i - 1, c - wgt[i - 1]) + val[i - 1];
|
||||
// Record and return the greater value of the two options
|
||||
mem[i][c] = Math.max(no, yes);
|
||||
return mem[i][c];
|
||||
}
|
||||
|
||||
/* 0-1 Knapsack: Dynamic programming */
|
||||
static int knapsackDP(int[] wgt, int[] val, int cap) {
|
||||
int n = wgt.length;
|
||||
// Initialize dp table
|
||||
int[][] dp = new int[n + 1][cap + 1];
|
||||
// State transition
|
||||
for (int i = 1; i <= n; i++) {
|
||||
for (int c = 1; c <= cap; c++) {
|
||||
if (wgt[i - 1] > c) {
|
||||
// If exceeding the knapsack capacity, do not choose item i
|
||||
dp[i][c] = dp[i - 1][c];
|
||||
} else {
|
||||
// The greater value between not choosing and choosing item i
|
||||
dp[i][c] = Math.max(dp[i - 1][c], dp[i - 1][c - wgt[i - 1]] + val[i - 1]);
|
||||
}
|
||||
}
|
||||
}
|
||||
return dp[n][cap];
|
||||
}
|
||||
|
||||
/* 0-1 Knapsack: Space-optimized dynamic programming */
|
||||
static int knapsackDPComp(int[] wgt, int[] val, int cap) {
|
||||
int n = wgt.length;
|
||||
// Initialize dp table
|
||||
int[] dp = new int[cap + 1];
|
||||
// State transition
|
||||
for (int i = 1; i <= n; i++) {
|
||||
// Traverse in reverse order
|
||||
for (int c = cap; c >= 1; c--) {
|
||||
if (wgt[i - 1] <= c) {
|
||||
// The greater value between not choosing and choosing item i
|
||||
dp[c] = Math.max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);
|
||||
}
|
||||
}
|
||||
}
|
||||
return dp[cap];
|
||||
}
|
||||
|
||||
public static void main(String[] args) {
|
||||
int[] wgt = { 10, 20, 30, 40, 50 };
|
||||
int[] val = { 50, 120, 150, 210, 240 };
|
||||
int cap = 50;
|
||||
int n = wgt.length;
|
||||
|
||||
// Brute force search
|
||||
int res = knapsackDFS(wgt, val, n, cap);
|
||||
System.out.println("The maximum value within the bag capacity is " + res);
|
||||
|
||||
// Memoized search
|
||||
int[][] mem = new int[n + 1][cap + 1];
|
||||
for (int[] row : mem) {
|
||||
Arrays.fill(row, -1);
|
||||
}
|
||||
res = knapsackDFSMem(wgt, val, mem, n, cap);
|
||||
System.out.println("The maximum value within the bag capacity is " + res);
|
||||
|
||||
// Dynamic programming
|
||||
res = knapsackDP(wgt, val, cap);
|
||||
System.out.println("The maximum value within the bag capacity is " + res);
|
||||
|
||||
// Space-optimized dynamic programming
|
||||
res = knapsackDPComp(wgt, val, cap);
|
||||
System.out.println("The maximum value within the bag capacity is " + res);
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,53 @@
|
||||
/**
|
||||
* File: min_cost_climbing_stairs_dp.java
|
||||
* Created Time: 2023-06-30
|
||||
* Author: krahets (krahets@163.com)
|
||||
*/
|
||||
|
||||
package chapter_dynamic_programming;
|
||||
|
||||
import java.util.Arrays;
|
||||
|
||||
public class min_cost_climbing_stairs_dp {
|
||||
/* Climbing stairs with minimum cost: Dynamic programming */
|
||||
public static int minCostClimbingStairsDP(int[] cost) {
|
||||
int n = cost.length - 1;
|
||||
if (n == 1 || n == 2)
|
||||
return cost[n];
|
||||
// Initialize dp table, used to store subproblem solutions
|
||||
int[] dp = new int[n + 1];
|
||||
// Initial state: preset the smallest subproblem solution
|
||||
dp[1] = cost[1];
|
||||
dp[2] = cost[2];
|
||||
// State transition: gradually solve larger subproblems from smaller ones
|
||||
for (int i = 3; i <= n; i++) {
|
||||
dp[i] = Math.min(dp[i - 1], dp[i - 2]) + cost[i];
|
||||
}
|
||||
return dp[n];
|
||||
}
|
||||
|
||||
/* Climbing stairs with minimum cost: Space-optimized dynamic programming */
|
||||
public static int minCostClimbingStairsDPComp(int[] cost) {
|
||||
int n = cost.length - 1;
|
||||
if (n == 1 || n == 2)
|
||||
return cost[n];
|
||||
int a = cost[1], b = cost[2];
|
||||
for (int i = 3; i <= n; i++) {
|
||||
int tmp = b;
|
||||
b = Math.min(a, tmp) + cost[i];
|
||||
a = tmp;
|
||||
}
|
||||
return b;
|
||||
}
|
||||
|
||||
public static void main(String[] args) {
|
||||
int[] cost = { 0, 1, 10, 1, 1, 1, 10, 1, 1, 10, 1 };
|
||||
System.out.println(String.format("Input the cost list for stairs as %s", Arrays.toString(cost)));
|
||||
|
||||
int res = minCostClimbingStairsDP(cost);
|
||||
System.out.println(String.format("Minimum cost to climb the stairs %d", res));
|
||||
|
||||
res = minCostClimbingStairsDPComp(cost);
|
||||
System.out.println(String.format("Minimum cost to climb the stairs %d", res));
|
||||
}
|
||||
}
|
||||
125
en/codes/java/chapter_dynamic_programming/min_path_sum.java
Normal file
125
en/codes/java/chapter_dynamic_programming/min_path_sum.java
Normal file
@@ -0,0 +1,125 @@
|
||||
/**
|
||||
* File: min_path_sum.java
|
||||
* Created Time: 2023-07-10
|
||||
* Author: krahets (krahets@163.com)
|
||||
*/
|
||||
|
||||
package chapter_dynamic_programming;
|
||||
|
||||
import java.util.Arrays;
|
||||
|
||||
public class min_path_sum {
|
||||
/* Minimum path sum: Brute force search */
|
||||
static int minPathSumDFS(int[][] grid, int i, int j) {
|
||||
// If it's the top-left cell, terminate the search
|
||||
if (i == 0 && j == 0) {
|
||||
return grid[0][0];
|
||||
}
|
||||
// If the row or column index is out of bounds, return a +∞ cost
|
||||
if (i < 0 || j < 0) {
|
||||
return Integer.MAX_VALUE;
|
||||
}
|
||||
// Calculate the minimum path cost from the top-left to (i-1, j) and (i, j-1)
|
||||
int up = minPathSumDFS(grid, i - 1, j);
|
||||
int left = minPathSumDFS(grid, i, j - 1);
|
||||
// Return the minimum path cost from the top-left to (i, j)
|
||||
return Math.min(left, up) + grid[i][j];
|
||||
}
|
||||
|
||||
/* Minimum path sum: Memoized search */
|
||||
static int minPathSumDFSMem(int[][] grid, int[][] mem, int i, int j) {
|
||||
// If it's the top-left cell, terminate the search
|
||||
if (i == 0 && j == 0) {
|
||||
return grid[0][0];
|
||||
}
|
||||
// If the row or column index is out of bounds, return a +∞ cost
|
||||
if (i < 0 || j < 0) {
|
||||
return Integer.MAX_VALUE;
|
||||
}
|
||||
// If there is a record, return it
|
||||
if (mem[i][j] != -1) {
|
||||
return mem[i][j];
|
||||
}
|
||||
// The minimum path cost from the left and top cells
|
||||
int up = minPathSumDFSMem(grid, mem, i - 1, j);
|
||||
int left = minPathSumDFSMem(grid, mem, i, j - 1);
|
||||
// Record and return the minimum path cost from the top-left to (i, j)
|
||||
mem[i][j] = Math.min(left, up) + grid[i][j];
|
||||
return mem[i][j];
|
||||
}
|
||||
|
||||
/* Minimum path sum: Dynamic programming */
|
||||
static int minPathSumDP(int[][] grid) {
|
||||
int n = grid.length, m = grid[0].length;
|
||||
// Initialize dp table
|
||||
int[][] dp = new int[n][m];
|
||||
dp[0][0] = grid[0][0];
|
||||
// State transition: first row
|
||||
for (int j = 1; j < m; j++) {
|
||||
dp[0][j] = dp[0][j - 1] + grid[0][j];
|
||||
}
|
||||
// State transition: first column
|
||||
for (int i = 1; i < n; i++) {
|
||||
dp[i][0] = dp[i - 1][0] + grid[i][0];
|
||||
}
|
||||
// State transition: the rest of the rows and columns
|
||||
for (int i = 1; i < n; i++) {
|
||||
for (int j = 1; j < m; j++) {
|
||||
dp[i][j] = Math.min(dp[i][j - 1], dp[i - 1][j]) + grid[i][j];
|
||||
}
|
||||
}
|
||||
return dp[n - 1][m - 1];
|
||||
}
|
||||
|
||||
/* Minimum path sum: Space-optimized dynamic programming */
|
||||
static int minPathSumDPComp(int[][] grid) {
|
||||
int n = grid.length, m = grid[0].length;
|
||||
// Initialize dp table
|
||||
int[] dp = new int[m];
|
||||
// State transition: first row
|
||||
dp[0] = grid[0][0];
|
||||
for (int j = 1; j < m; j++) {
|
||||
dp[j] = dp[j - 1] + grid[0][j];
|
||||
}
|
||||
// State transition: the rest of the rows
|
||||
for (int i = 1; i < n; i++) {
|
||||
// State transition: first column
|
||||
dp[0] = dp[0] + grid[i][0];
|
||||
// State transition: the rest of the columns
|
||||
for (int j = 1; j < m; j++) {
|
||||
dp[j] = Math.min(dp[j - 1], dp[j]) + grid[i][j];
|
||||
}
|
||||
}
|
||||
return dp[m - 1];
|
||||
}
|
||||
|
||||
public static void main(String[] args) {
|
||||
int[][] grid = {
|
||||
{ 1, 3, 1, 5 },
|
||||
{ 2, 2, 4, 2 },
|
||||
{ 5, 3, 2, 1 },
|
||||
{ 4, 3, 5, 2 }
|
||||
};
|
||||
int n = grid.length, m = grid[0].length;
|
||||
|
||||
// Brute force search
|
||||
int res = minPathSumDFS(grid, n - 1, m - 1);
|
||||
System.out.println("The minimum path sum from the top left corner to the bottom right corner is " + res);
|
||||
|
||||
// Memoized search
|
||||
int[][] mem = new int[n][m];
|
||||
for (int[] row : mem) {
|
||||
Arrays.fill(row, -1);
|
||||
}
|
||||
res = minPathSumDFSMem(grid, mem, n - 1, m - 1);
|
||||
System.out.println("The minimum path sum from the top left corner to the bottom right corner is " + res);
|
||||
|
||||
// Dynamic programming
|
||||
res = minPathSumDP(grid);
|
||||
System.out.println("The minimum path sum from the top left corner to the bottom right corner is " + res);
|
||||
|
||||
// Space-optimized dynamic programming
|
||||
res = minPathSumDPComp(grid);
|
||||
System.out.println("The minimum path sum from the top left corner to the bottom right corner is " + res);
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,63 @@
|
||||
/**
|
||||
* File: unbounded_knapsack.java
|
||||
* Created Time: 2023-07-11
|
||||
* Author: krahets (krahets@163.com)
|
||||
*/
|
||||
|
||||
package chapter_dynamic_programming;
|
||||
|
||||
public class unbounded_knapsack {
|
||||
/* Complete knapsack: Dynamic programming */
|
||||
static int unboundedKnapsackDP(int[] wgt, int[] val, int cap) {
|
||||
int n = wgt.length;
|
||||
// Initialize dp table
|
||||
int[][] dp = new int[n + 1][cap + 1];
|
||||
// State transition
|
||||
for (int i = 1; i <= n; i++) {
|
||||
for (int c = 1; c <= cap; c++) {
|
||||
if (wgt[i - 1] > c) {
|
||||
// If exceeding the knapsack capacity, do not choose item i
|
||||
dp[i][c] = dp[i - 1][c];
|
||||
} else {
|
||||
// The greater value between not choosing and choosing item i
|
||||
dp[i][c] = Math.max(dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1]);
|
||||
}
|
||||
}
|
||||
}
|
||||
return dp[n][cap];
|
||||
}
|
||||
|
||||
/* Complete knapsack: Space-optimized dynamic programming */
|
||||
static int unboundedKnapsackDPComp(int[] wgt, int[] val, int cap) {
|
||||
int n = wgt.length;
|
||||
// Initialize dp table
|
||||
int[] dp = new int[cap + 1];
|
||||
// State transition
|
||||
for (int i = 1; i <= n; i++) {
|
||||
for (int c = 1; c <= cap; c++) {
|
||||
if (wgt[i - 1] > c) {
|
||||
// If exceeding the knapsack capacity, do not choose item i
|
||||
dp[c] = dp[c];
|
||||
} else {
|
||||
// The greater value between not choosing and choosing item i
|
||||
dp[c] = Math.max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);
|
||||
}
|
||||
}
|
||||
}
|
||||
return dp[cap];
|
||||
}
|
||||
|
||||
public static void main(String[] args) {
|
||||
int[] wgt = { 1, 2, 3 };
|
||||
int[] val = { 5, 11, 15 };
|
||||
int cap = 4;
|
||||
|
||||
// Dynamic programming
|
||||
int res = unboundedKnapsackDP(wgt, val, cap);
|
||||
System.out.println("The maximum value within the bag capacity is " + res);
|
||||
|
||||
// Space-optimized dynamic programming
|
||||
res = unboundedKnapsackDPComp(wgt, val, cap);
|
||||
System.out.println("The maximum value within the bag capacity is " + res);
|
||||
}
|
||||
}
|
||||
Reference in New Issue
Block a user