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Translate all code to English (#1836)
* Review the EN heading format. * Fix pythontutor headings. * Fix pythontutor headings. * bug fixes * Fix headings in **/summary.md * Revisit the CN-to-EN translation for Python code using Claude-4.5 * Revisit the CN-to-EN translation for Java code using Claude-4.5 * Revisit the CN-to-EN translation for Cpp code using Claude-4.5. * Fix the dictionary. * Fix cpp code translation for the multipart strings. * Translate Go code to English. * Update workflows to test EN code. * Add EN translation for C. * Add EN translation for CSharp. * Add EN translation for Swift. * Trigger the CI check. * Revert. * Update en/hash_map.md * Add the EN version of Dart code. * Add the EN version of Kotlin code. * Add missing code files. * Add the EN version of JavaScript code. * Add the EN version of TypeScript code. * Fix the workflows. * Add the EN version of Ruby code. * Add the EN version of Rust code. * Update the CI check for the English version code. * Update Python CI check. * Fix cmakelists for en/C code. * Fix Ruby comments
This commit is contained in:
Yudong Jin
@@ -0,0 +1,39 @@
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/**
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* File: climbing_stairs_backtrack.dart
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* Created Time: 2023-08-11
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* Author: liuyuxin (gvenusleo@gmail.com)
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*/
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/* Backtracking */
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void backtrack(List<int> choices, int state, int n, List<int> res) {
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// When climbing to the n-th stair, add 1 to the solution count
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if (state == n) {
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res[0]++;
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}
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// Traverse all choices
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for (int choice in choices) {
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// Pruning: not allowed to go beyond the n-th stair
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if (state + choice > n) continue;
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// Attempt: make choice, update state
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backtrack(choices, state + choice, n, res);
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// Backtrack
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}
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}
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/* Climbing stairs: Backtracking */
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int climbingStairsBacktrack(int n) {
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List<int> choices = [1, 2]; // Can choose to climb up 1 or 2 stairs
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int state = 0; // Start climbing from the 0-th stair
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List<int> res = [];
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res.add(0); // Use res[0] to record the solution count
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backtrack(choices, state, n, res);
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return res[0];
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}
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/* Driver Code */
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void main() {
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int n = 9;
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int res = climbingStairsBacktrack(n);
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print("Climbing $n stairs has $res solutions");
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}
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@@ -0,0 +1,33 @@
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/**
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* File: climbing_stairs_constraint_dp.dart
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* Created Time: 2023-08-11
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* Author: liuyuxin (gvenusleo@gmail.com)
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*/
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/* Climbing stairs with constraint: Dynamic programming */
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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 solutions to subproblems
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List<List<int>> dp = List.generate(n + 1, (index) => List.filled(3, 0));
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// Initial state: preset the solution to the smallest subproblem
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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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/* Driver Code */
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void main() {
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int n = 9;
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int res = climbingStairsConstraintDP(n);
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print("Climbing $n stairs has $res solutions");
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}
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@@ -0,0 +1,27 @@
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/**
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* File: climbing_stairs_dfs.dart
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* Created Time: 2023-08-11
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* Author: liuyuxin (gvenusleo@gmail.com)
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*/
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/* Search */
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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) 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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int climbingStairsDFS(int n) {
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return dfs(n);
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}
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/* Driver Code */
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void main() {
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int n = 9;
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int res = climbingStairsDFS(n);
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print("Climbing $n stairs has $res solutions");
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}
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@@ -0,0 +1,33 @@
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/**
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* File: climbing_stairs_dfs_mem.dart
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* Created Time: 2023-08-11
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* Author: liuyuxin (gvenusleo@gmail.com)
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*/
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/* Memoization search */
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int dfs(int i, List<int> mem) {
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// Known dp[1] and dp[2], return them
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if (i == 1 || i == 2) return i;
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// If record dp[i] exists, return it directly
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if (mem[i] != -1) 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: Memoization search */
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int climbingStairsDFSMem(int n) {
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// mem[i] records the total number of solutions to climb to the i-th stair, -1 means no record
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List<int> mem = List.filled(n + 1, -1);
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return dfs(n, mem);
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}
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/* Driver Code */
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void main() {
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int n = 9;
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int res = climbingStairsDFSMem(n);
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print("Climbing $n stairs has $res solutions");
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}
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@@ -0,0 +1,43 @@
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/**
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* File: climbing_stairs_dp.dart
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* Created Time: 2023-08-11
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* Author: liuyuxin (gvenusleo@gmail.com)
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*/
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/* Climbing stairs: Dynamic programming */
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int climbingStairsDP(int n) {
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if (n == 1 || n == 2) return n;
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// Initialize dp table, used to store solutions to subproblems
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List<int> dp = List.filled(n + 1, 0);
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// Initial state: preset the solution to the smallest subproblem
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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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int climbingStairsDPComp(int n) {
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if (n == 1 || n == 2) 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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/* Driver Code */
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void main() {
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int n = 9;
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int res = climbingStairsDP(n);
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print("Climbing $n stairs has $res solutions");
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res = climbingStairsDPComp(n);
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print("Climbing $n stairs has $res solutions");
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}
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@@ -0,0 +1,68 @@
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/**
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* File: coin_change.dart
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* Created Time: 2023-08-11
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* Author: liuyuxin (gvenusleo@gmail.com)
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*/
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import 'dart:math';
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/* Coin change: Dynamic programming */
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int coinChangeDP(List<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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List<List<int>> dp = List.generate(n + 1, (index) => List.filled(amt + 1, 0));
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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: 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 exceeds target amount, don't select 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 selecting and selecting coin i
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dp[i][a] = 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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int coinChangeDPComp(List<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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List<int> dp = List.filled(amt + 1, 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 exceeds target amount, don't select coin i
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dp[a] = dp[a];
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} else {
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// The smaller value between not selecting and selecting coin i
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dp[a] = 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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/* Driver Code */
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void main() {
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List<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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print("Minimum coins needed to make target amount is $res");
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// Space-optimized dynamic programming
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res = coinChangeDPComp(coins, amt);
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print("Minimum coins needed to make target amount is $res");
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}
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@@ -0,0 +1,64 @@
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/**
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* File: coin_change_ii.dart
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* Created Time: 2023-08-11
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* Author: liuyuxin (gvenusleo@gmail.com)
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*/
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/* Coin change II: Dynamic programming */
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int coinChangeIIDP(List<int> coins, int amt) {
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int n = coins.length;
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// Initialize dp table
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List<List<int>> dp = List.generate(n + 1, (index) => List.filled(amt + 1, 0));
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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 exceeds target amount, don't select coin i
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dp[i][a] = dp[i - 1][a];
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} else {
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// Sum of the two options: not selecting and selecting 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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int coinChangeIIDPComp(List<int> coins, int amt) {
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int n = coins.length;
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// Initialize dp table
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List<int> dp = List.filled(amt + 1, 0);
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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 exceeds target amount, don't select coin i
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dp[a] = dp[a];
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} else {
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// Sum of the two options: not selecting and selecting 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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/* Driver Code */
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void main() {
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List<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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print("Number of coin combinations to make target amount is $res");
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// Space-optimized dynamic programming
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res = coinChangeIIDPComp(coins, amt);
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print("Number of coin combinations to make target amount is $res");
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}
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@@ -0,0 +1,125 @@
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/**
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* File: edit_distance.dart
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* Created Time: 2023-08-11
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* Author: liuyuxin (gvenusleo@gmail.com)
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*/
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import 'dart:math';
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/* Edit distance: Brute-force search */
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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) return 0;
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// If s is empty, return length of t
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if (i == 0) return j;
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// If t is empty, return length of s
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if (j == 0) return i;
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// If two characters are equal, skip both characters
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if (s[i - 1] == t[j - 1]) return editDistanceDFS(s, t, i - 1, j - 1);
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// Minimum edit steps = minimum edit steps of insert, delete, 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 minimum edit steps
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return min(min(insert, delete), replace) + 1;
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}
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/* Edit distance: Memoization search */
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int editDistanceDFSMem(String s, String t, List<List<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) return 0;
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// If s is empty, return length of t
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if (i == 0) return j;
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// If t is empty, return length of s
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if (j == 0) return i;
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// If there's a record, return it directly
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if (mem[i][j] != -1) return mem[i][j];
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// If two characters are equal, skip both characters
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if (s[i - 1] == t[j - 1]) return editDistanceDFSMem(s, t, mem, i - 1, j - 1);
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// Minimum edit steps = minimum edit steps of insert, delete, replace + 1
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int insert = editDistanceDFSMem(s, t, mem, i, j - 1);
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int delete = editDistanceDFSMem(s, t, mem, i - 1, j);
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int replace = editDistanceDFSMem(s, t, mem, i - 1, j - 1);
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// Record and return minimum edit steps
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mem[i][j] = min(min(insert, delete), replace) + 1;
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return mem[i][j];
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}
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/* Edit distance: Dynamic programming */
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int editDistanceDP(String s, String t) {
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int n = s.length, m = t.length;
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List<List<int>> dp = List.generate(n + 1, (_) => List.filled(m + 1, 0));
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// State transition: first row and first column
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for (int i = 1; i <= n; i++) {
|
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dp[i][0] = i;
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}
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for (int j = 1; j <= m; j++) {
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dp[0][j] = j;
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}
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// State transition: rest of the rows and columns
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for (int i = 1; i <= n; i++) {
|
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for (int j = 1; j <= m; j++) {
|
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if (s[i - 1] == t[j - 1]) {
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// If two characters are equal, skip both characters
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dp[i][j] = dp[i - 1][j - 1];
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} else {
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// Minimum edit steps = minimum edit steps of insert, delete, replace + 1
|
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dp[i][j] = min(min(dp[i][j - 1], dp[i - 1][j]), dp[i - 1][j - 1]) + 1;
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}
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}
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}
|
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return dp[n][m];
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}
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/* Edit distance: Space-optimized dynamic programming */
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int editDistanceDPComp(String s, String t) {
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int n = s.length, m = t.length;
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List<int> dp = List.filled(m + 1, 0);
|
||||
// State transition: first row
|
||||
for (int j = 1; j <= m; j++) {
|
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dp[j] = j;
|
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}
|
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// State transition: rest of the rows
|
||||
for (int i = 1; i <= n; i++) {
|
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// State transition: first column
|
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int leftup = dp[0]; // Temporarily store dp[i-1, j-1]
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dp[0] = i;
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// State transition: rest of the columns
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for (int j = 1; j <= m; j++) {
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int temp = dp[j];
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if (s[i - 1] == t[j - 1]) {
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// If two characters are equal, skip both characters
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dp[j] = leftup;
|
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} else {
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// Minimum edit steps = minimum edit steps of insert, delete, replace + 1
|
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dp[j] = min(min(dp[j - 1], dp[j]), leftup) + 1;
|
||||
}
|
||||
leftup = temp; // Update for next round's dp[i-1, j-1]
|
||||
}
|
||||
}
|
||||
return dp[m];
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||||
}
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|
||||
/* Driver Code */
|
||||
void main() {
|
||||
String s = "bag";
|
||||
String t = "pack";
|
||||
int n = s.length, m = t.length;
|
||||
|
||||
// Brute-force search
|
||||
int res = editDistanceDFS(s, t, n, m);
|
||||
print("Changing " + s + " to " + t + " requires minimum $res edits");
|
||||
|
||||
// Memoization search
|
||||
List<List<int>> mem = List.generate(n + 1, (_) => List.filled(m + 1, -1));
|
||||
res = editDistanceDFSMem(s, t, mem, n, m);
|
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print("Changing " + s + " to " + t + " requires minimum $res edits");
|
||||
|
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// Dynamic programming
|
||||
res = editDistanceDP(s, t);
|
||||
print("Changing " + s + " to " + t + " requires minimum $res edits");
|
||||
|
||||
// Space-optimized dynamic programming
|
||||
res = editDistanceDPComp(s, t);
|
||||
print("Changing " + s + " to " + t + " requires minimum $res edits");
|
||||
}
|
||||
@@ -0,0 +1,116 @@
|
||||
/**
|
||||
* File: knapsack.dart
|
||||
* Created Time: 2023-08-11
|
||||
* Author: liuyuxin (gvenusleo@gmail.com)
|
||||
*/
|
||||
|
||||
import 'dart:math';
|
||||
|
||||
/* 0-1 knapsack: Brute-force search */
|
||||
int knapsackDFS(List<int> wgt, List<int> val, int i, int c) {
|
||||
// If all items have been selected or knapsack has no remaining capacity, return value 0
|
||||
if (i == 0 || c == 0) {
|
||||
return 0;
|
||||
}
|
||||
// If exceeds knapsack capacity, can only choose not to put it in
|
||||
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 larger value of the two options
|
||||
return max(no, yes);
|
||||
}
|
||||
|
||||
/* 0-1 knapsack: Memoization search */
|
||||
int knapsackDFSMem(
|
||||
List<int> wgt,
|
||||
List<int> val,
|
||||
List<List<int>> mem,
|
||||
int i,
|
||||
int c,
|
||||
) {
|
||||
// If all items have been selected or knapsack has no remaining capacity, return value 0
|
||||
if (i == 0 || c == 0) {
|
||||
return 0;
|
||||
}
|
||||
// If there's a record, return it directly
|
||||
if (mem[i][c] != -1) {
|
||||
return mem[i][c];
|
||||
}
|
||||
// If exceeds knapsack capacity, can only choose not to put it in
|
||||
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 larger value of the two options
|
||||
mem[i][c] = max(no, yes);
|
||||
return mem[i][c];
|
||||
}
|
||||
|
||||
/* 0-1 knapsack: Dynamic programming */
|
||||
int knapsackDP(List<int> wgt, List<int> val, int cap) {
|
||||
int n = wgt.length;
|
||||
// Initialize dp table
|
||||
List<List<int>> dp = List.generate(n + 1, (index) => List.filled(cap + 1, 0));
|
||||
// State transition
|
||||
for (int i = 1; i <= n; i++) {
|
||||
for (int c = 1; c <= cap; c++) {
|
||||
if (wgt[i - 1] > c) {
|
||||
// If exceeds knapsack capacity, don't select item i
|
||||
dp[i][c] = dp[i - 1][c];
|
||||
} else {
|
||||
// The larger value between not selecting and selecting item i
|
||||
dp[i][c] = 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 */
|
||||
int knapsackDPComp(List<int> wgt, List<int> val, int cap) {
|
||||
int n = wgt.length;
|
||||
// Initialize dp table
|
||||
List<int> dp = List.filled(cap + 1, 0);
|
||||
// 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 larger value between not selecting and selecting item i
|
||||
dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);
|
||||
}
|
||||
}
|
||||
}
|
||||
return dp[cap];
|
||||
}
|
||||
|
||||
/* Driver Code */
|
||||
void main() {
|
||||
List<int> wgt = [10, 20, 30, 40, 50];
|
||||
List<int> val = [50, 120, 150, 210, 240];
|
||||
int cap = 50;
|
||||
int n = wgt.length;
|
||||
|
||||
// Brute-force search
|
||||
int res = knapsackDFS(wgt, val, n, cap);
|
||||
print("Maximum item value not exceeding knapsack capacity is $res");
|
||||
|
||||
// Memoization search
|
||||
List<List<int>> mem =
|
||||
List.generate(n + 1, (index) => List.filled(cap + 1, -1));
|
||||
res = knapsackDFSMem(wgt, val, mem, n, cap);
|
||||
print("Maximum item value not exceeding knapsack capacity is $res");
|
||||
|
||||
// Dynamic programming
|
||||
res = knapsackDP(wgt, val, cap);
|
||||
print("Maximum item value not exceeding knapsack capacity is $res");
|
||||
|
||||
// Space-optimized dynamic programming
|
||||
res = knapsackDPComp(wgt, val, cap);
|
||||
print("Maximum item value not exceeding knapsack capacity is $res");
|
||||
}
|
||||
@@ -0,0 +1,48 @@
|
||||
/**
|
||||
* File: min_cost_climbing_stairs_dp.dart
|
||||
* Created Time: 2023-08-11
|
||||
* Author: liuyuxin (gvenusleo@gmail.com)
|
||||
*/
|
||||
|
||||
import 'dart:math';
|
||||
|
||||
/* Minimum cost climbing stairs: Dynamic programming */
|
||||
int minCostClimbingStairsDP(List<int> cost) {
|
||||
int n = cost.length - 1;
|
||||
if (n == 1 || n == 2) return cost[n];
|
||||
// Initialize dp table, used to store solutions to subproblems
|
||||
List<int> dp = List.filled(n + 1, 0);
|
||||
// Initial state: preset the solution to the smallest subproblem
|
||||
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] = min(dp[i - 1], dp[i - 2]) + cost[i];
|
||||
}
|
||||
return dp[n];
|
||||
}
|
||||
|
||||
/* Minimum cost climbing stairs: Space-optimized dynamic programming */
|
||||
int minCostClimbingStairsDPComp(List<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 = min(a, tmp) + cost[i];
|
||||
a = tmp;
|
||||
}
|
||||
return b;
|
||||
}
|
||||
|
||||
/* Driver Code */
|
||||
void main() {
|
||||
List<int> cost = [0, 1, 10, 1, 1, 1, 10, 1, 1, 10, 1];
|
||||
print("Input stair cost list is $cost");
|
||||
|
||||
int res = minCostClimbingStairsDP(cost);
|
||||
print("Minimum cost to climb stairs is $res");
|
||||
|
||||
res = minCostClimbingStairsDPComp(cost);
|
||||
print("Minimum cost to climb stairs is $res");
|
||||
}
|
||||
@@ -0,0 +1,120 @@
|
||||
/**
|
||||
* File: min_path_sum.dart
|
||||
* Created Time: 2023-08-11
|
||||
* Author: liuyuxin (gvenusleo@gmail.com)
|
||||
*/
|
||||
|
||||
import 'dart:math';
|
||||
|
||||
/* Minimum path sum: Brute-force search */
|
||||
int minPathSumDFS(List<List<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 row or column index is out of bounds, return +∞ cost
|
||||
if (i < 0 || j < 0) {
|
||||
// In Dart, int type is fixed-range integer, no value representing "infinity"
|
||||
return BigInt.from(2).pow(31).toInt();
|
||||
}
|
||||
// Calculate the minimum path cost from 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 top-left to (i, j)
|
||||
return min(left, up) + grid[i][j];
|
||||
}
|
||||
|
||||
/* Minimum path sum: Memoization search */
|
||||
int minPathSumDFSMem(List<List<int>> grid, List<List<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 row or column index is out of bounds, return +∞ cost
|
||||
if (i < 0 || j < 0) {
|
||||
// In Dart, int type is fixed-range integer, no value representing "infinity"
|
||||
return BigInt.from(2).pow(31).toInt();
|
||||
}
|
||||
// If there's a record, return it directly
|
||||
if (mem[i][j] != -1) {
|
||||
return mem[i][j];
|
||||
}
|
||||
// Minimum path cost for left and upper 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 top-left to (i, j)
|
||||
mem[i][j] = min(left, up) + grid[i][j];
|
||||
return mem[i][j];
|
||||
}
|
||||
|
||||
/* Minimum path sum: Dynamic programming */
|
||||
int minPathSumDP(List<List<int>> grid) {
|
||||
int n = grid.length, m = grid[0].length;
|
||||
// Initialize dp table
|
||||
List<List<int>> dp = List.generate(n, (i) => List.filled(m, 0));
|
||||
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: rest of the rows and columns
|
||||
for (int i = 1; i < n; i++) {
|
||||
for (int j = 1; j < m; j++) {
|
||||
dp[i][j] = 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 */
|
||||
int minPathSumDPComp(List<List<int>> grid) {
|
||||
int n = grid.length, m = grid[0].length;
|
||||
// Initialize dp table
|
||||
List<int> dp = List.filled(m, 0);
|
||||
dp[0] = grid[0][0];
|
||||
for (int j = 1; j < m; j++) {
|
||||
dp[j] = dp[j - 1] + grid[0][j];
|
||||
}
|
||||
// State transition: rest of the rows
|
||||
for (int i = 1; i < n; i++) {
|
||||
// State transition: first column
|
||||
dp[0] = dp[0] + grid[i][0];
|
||||
// State transition: rest of the columns
|
||||
for (int j = 1; j < m; j++) {
|
||||
dp[j] = min(dp[j - 1], dp[j]) + grid[i][j];
|
||||
}
|
||||
}
|
||||
return dp[m - 1];
|
||||
}
|
||||
|
||||
/* Driver Code */
|
||||
void main() {
|
||||
List<List<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);
|
||||
print("Minimum path sum from top-left to bottom-right is $res");
|
||||
|
||||
// Memoization search
|
||||
List<List<int>> mem = List.generate(n, (i) => List.filled(m, -1));
|
||||
res = minPathSumDFSMem(grid, mem, n - 1, m - 1);
|
||||
print("Minimum path sum from top-left to bottom-right is $res");
|
||||
|
||||
// Dynamic programming
|
||||
res = minPathSumDP(grid);
|
||||
print("Minimum path sum from top-left to bottom-right is $res");
|
||||
|
||||
// Space-optimized dynamic programming
|
||||
res = minPathSumDPComp(grid);
|
||||
print("Minimum path sum from top-left to bottom-right is $res");
|
||||
}
|
||||
@@ -0,0 +1,62 @@
|
||||
/**
|
||||
* File: unbounded_knapsack.dart
|
||||
* Created Time: 2023-08-11
|
||||
* Author: liuyuxin (gvenusleo@gmail.com)
|
||||
*/
|
||||
|
||||
import 'dart:math';
|
||||
|
||||
/* Unbounded knapsack: Dynamic programming */
|
||||
int unboundedKnapsackDP(List<int> wgt, List<int> val, int cap) {
|
||||
int n = wgt.length;
|
||||
// Initialize dp table
|
||||
List<List<int>> dp = List.generate(n + 1, (index) => List.filled(cap + 1, 0));
|
||||
// State transition
|
||||
for (int i = 1; i <= n; i++) {
|
||||
for (int c = 1; c <= cap; c++) {
|
||||
if (wgt[i - 1] > c) {
|
||||
// If exceeds knapsack capacity, don't select item i
|
||||
dp[i][c] = dp[i - 1][c];
|
||||
} else {
|
||||
// The larger value between not selecting and selecting item i
|
||||
dp[i][c] = max(dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1]);
|
||||
}
|
||||
}
|
||||
}
|
||||
return dp[n][cap];
|
||||
}
|
||||
|
||||
/* Unbounded knapsack: Space-optimized dynamic programming */
|
||||
int unboundedKnapsackDPComp(List<int> wgt, List<int> val, int cap) {
|
||||
int n = wgt.length;
|
||||
// Initialize dp table
|
||||
List<int> dp = List.filled(cap + 1, 0);
|
||||
// State transition
|
||||
for (int i = 1; i <= n; i++) {
|
||||
for (int c = 1; c <= cap; c++) {
|
||||
if (wgt[i - 1] > c) {
|
||||
// If exceeds knapsack capacity, don't select item i
|
||||
dp[c] = dp[c];
|
||||
} else {
|
||||
// The larger value between not selecting and selecting item i
|
||||
dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);
|
||||
}
|
||||
}
|
||||
}
|
||||
return dp[cap];
|
||||
}
|
||||
|
||||
/* Driver Code */
|
||||
void main() {
|
||||
List<int> wgt = [1, 2, 3];
|
||||
List<int> val = [5, 11, 15];
|
||||
int cap = 4;
|
||||
|
||||
// Dynamic programming
|
||||
int res = unboundedKnapsackDP(wgt, val, cap);
|
||||
print("Maximum item value not exceeding knapsack capacity is $res");
|
||||
|
||||
// Space-optimized dynamic programming
|
||||
int resComp = unboundedKnapsackDPComp(wgt, val, cap);
|
||||
print("Maximum item value not exceeding knapsack capacity is $resComp");
|
||||
}
|
||||
Reference in New Issue
Block a user