Retranslate the complete English edition from Simplified Chinese (#2010)

* Retranslate the complete English edition from Simplified Chinese

* Polish three English explanations after reader-focused review

en/codes/java/chapter_dynamic_programming/climbing_stairs_backtrack.java

@@ -11,26 +11,26 @@ import java.util.*;
 public class climbing_stairs_backtrack {
     /* Backtracking */
     public static void backtrack(List<Integer> choices, int state, int n, List<Integer> res) {
-        // When climbing to the n-th stair, add 1 to the solution count
+        // When step n is reached, increase the number of ways by 1
         if (state == n)
             res.set(0, res.get(0) + 1);
-        // Traverse all choices
+        // Iterate over all choices
         for (Integer choice : choices) {
-            // Pruning: not allowed to go beyond the n-th stair
+            // Prune: do not go beyond step n
             if (state + choice > n)
                 continue;
-            // Attempt: make choice, update state
+            // Try: make a choice and update the state
             backtrack(choices, state + choice, n, res);
             // Backtrack
         }
     }
 
-    /* Climbing stairs: Backtracking */
+    /* Climbing stairs: backtracking */
     public static int climbingStairsBacktrack(int n) {
-        List<Integer> choices = Arrays.asList(1, 2); // Can choose to climb up 1 or 2 stairs
-        int state = 0; // Start climbing from the 0-th stair
+        List<Integer> choices = Arrays.asList(1, 2); // Choose to climb 1 or 2 steps
+        int state = 0; // Start climbing from step 0
         List<Integer> res = new ArrayList<>();
-        res.add(0); // Use res[0] to record the solution count
+        res.add(0); // Use res[0] to record the number of ways
         backtrack(choices, state, n, res);
         return res.get(0);
     }
@@ -39,6 +39,6 @@ public class climbing_stairs_backtrack {
         int n = 9;
 
         int res = climbingStairsBacktrack(n);
-        System.out.println(String.format("Climbing %d stairs has %d solutions", n, res));
+        System.out.println(String.format("Number of ways to climb %d stairs: %d", n, res));
     }
 }

en/codes/java/chapter_dynamic_programming/climbing_stairs_constraint_dp.java

@@ -7,19 +7,19 @@
 package chapter_dynamic_programming;
 
 public class climbing_stairs_constraint_dp {
-    /* Climbing stairs with constraint: Dynamic programming */
+    /* Climbing stairs with constraints: dynamic programming */
     static int climbingStairsConstraintDP(int n) {
         if (n == 1 || n == 2) {
             return 1;
         }
-        // Initialize dp table, used to store solutions to subproblems
+        // Initialize the dp table to store subproblem solutions
         int[][] dp = new int[n + 1][3];
-        // Initial state: preset the solution to the smallest subproblem
+        // Initial states: set the solutions to the smallest subproblems
         dp[1][1] = 1;
         dp[1][2] = 0;
         dp[2][1] = 0;
         dp[2][2] = 1;
-        // State transition: gradually solve larger subproblems from smaller ones
+        // State transitions: solve progressively larger subproblems using smaller ones
         for (int i = 3; i <= n; i++) {
             dp[i][1] = dp[i - 1][2];
             dp[i][2] = dp[i - 2][1] + dp[i - 2][2];
@@ -31,6 +31,6 @@ public class climbing_stairs_constraint_dp {
         int n = 9;
 
         int res = climbingStairsConstraintDP(n);
-        System.out.println(String.format("Climbing %d stairs has %d solutions", n, res));
+        System.out.println(String.format("Number of ways to climb %d stairs: %d", n, res));
     }
 }

en/codes/java/chapter_dynamic_programming/climbing_stairs_dfs.java

@@ -9,7 +9,7 @@ package chapter_dynamic_programming;
 public class climbing_stairs_dfs {
     /* Search */
     public static int dfs(int i) {
-        // Known dp[1] and dp[2], return them
+        // The values of dp[1] and dp[2] are known; return them
         if (i == 1 || i == 2)
             return i;
         // dp[i] = dp[i-1] + dp[i-2]
@@ -17,7 +17,7 @@ public class climbing_stairs_dfs {
         return count;
     }
 
-    /* Climbing stairs: Search */
+    /* Climbing stairs: search */
     public static int climbingStairsDFS(int n) {
         return dfs(n);
     }
@@ -26,6 +26,6 @@ public class climbing_stairs_dfs {
         int n = 9;
 
         int res = climbingStairsDFS(n);
-        System.out.println(String.format("Climbing %d stairs has %d solutions", n, res));
+        System.out.println(String.format("Number of ways to climb %d stairs: %d", n, res));
     }
 }

en/codes/java/chapter_dynamic_programming/climbing_stairs_dfs_mem.java

@@ -9,12 +9,12 @@ package chapter_dynamic_programming;
 import java.util.Arrays;
 
 public class climbing_stairs_dfs_mem {
-    /* Memoization search */
+    /* Memoized search */
     public static int dfs(int i, int[] mem) {
-        // Known dp[1] and dp[2], return them
+        // The values of dp[1] and dp[2] are known; return them
         if (i == 1 || i == 2)
             return i;
-        // If record dp[i] exists, return it directly
+        // If dp[i] has been recorded, return it directly
         if (mem[i] != -1)
             return mem[i];
         // dp[i] = dp[i-1] + dp[i-2]
@@ -24,9 +24,9 @@ public class climbing_stairs_dfs_mem {
         return count;
     }
 
-    /* Climbing stairs: Memoization search */
+    /* Climbing stairs: memoized search */
     public static int climbingStairsDFSMem(int n) {
-        // mem[i] records the total number of solutions to climb to the i-th stair, -1 means no record
+        // mem[i] stores the number of ways to reach step i; -1 means no result has been recorded
         int[] mem = new int[n + 1];
         Arrays.fill(mem, -1);
         return dfs(n, mem);
@@ -36,6 +36,6 @@ public class climbing_stairs_dfs_mem {
         int n = 9;
 
         int res = climbingStairsDFSMem(n);
-        System.out.println(String.format("Climbing %d stairs has %d solutions", n, res));
+        System.out.println(String.format("Number of ways to climb %d stairs: %d", n, res));
     }
 }

en/codes/java/chapter_dynamic_programming/climbing_stairs_dp.java

@@ -7,23 +7,23 @@
 package chapter_dynamic_programming;
 
 public class climbing_stairs_dp {
-    /* Climbing stairs: Dynamic programming */
+    /* Climbing stairs: dynamic programming */
     public static int climbingStairsDP(int n) {
         if (n == 1 || n == 2)
             return n;
-        // Initialize dp table, used to store solutions to subproblems
+        // Initialize the dp table to store subproblem solutions
         int[] dp = new int[n + 1];
-        // Initial state: preset the solution to the smallest subproblem
+        // Initial states: set the solutions to the smallest subproblems
         dp[1] = 1;
         dp[2] = 2;
-        // State transition: gradually solve larger subproblems from smaller ones
+        // State transitions: solve progressively larger subproblems using smaller ones
         for (int i = 3; i <= n; i++) {
             dp[i] = dp[i - 1] + dp[i - 2];
         }
         return dp[n];
     }
 
-    /* Climbing stairs: Space-optimized dynamic programming */
+    /* Climbing stairs: space-optimized dynamic programming */
     public static int climbingStairsDPComp(int n) {
         if (n == 1 || n == 2)
             return n;
@@ -40,9 +40,9 @@ public class climbing_stairs_dp {
         int n = 9;
 
         int res = climbingStairsDP(n);
-        System.out.println(String.format("Climbing %d stairs has %d solutions", n, res));
+        System.out.println(String.format("Number of ways to climb %d stairs: %d", n, res));
 
         res = climbingStairsDPComp(n);
-        System.out.println(String.format("Climbing %d stairs has %d solutions", n, res));
+        System.out.println(String.format("Number of ways to climb %d stairs: %d", n, res));
     }
 }

en/codes/java/chapter_dynamic_programming/coin_change.java

@@ -9,24 +9,24 @@ package chapter_dynamic_programming;
 import java.util.Arrays;
 
 public class coin_change {
-    /* Coin change: Dynamic programming */
+    /* Coin change: dynamic programming */
     static int coinChangeDP(int[] coins, int amt) {
         int n = coins.length;
         int MAX = amt + 1;
-        // Initialize dp table
+        // Initialize the dp table
         int[][] dp = new int[n + 1][amt + 1];
-        // State transition: first row and first column
+        // State transitions: first row and first column
         for (int a = 1; a <= amt; a++) {
             dp[0][a] = MAX;
         }
-        // State transition: rest of the rows and columns
+        // State transitions: remaining rows and columns
         for (int i = 1; i <= n; i++) {
             for (int a = 1; a <= amt; a++) {
                 if (coins[i - 1] > a) {
-                    // If exceeds target amount, don't select coin i
+                    // If the coin exceeds the target amount, do not choose coin i
                     dp[i][a] = dp[i - 1][a];
                 } else {
-                    // The smaller value between not selecting and selecting coin i
+                    // Take the smaller result of not choosing and choosing coin i
                     dp[i][a] = Math.min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1);
                 }
             }
@@ -34,22 +34,22 @@ public class coin_change {
         return dp[n][amt] != MAX ? dp[n][amt] : -1;
     }
 
-    /* Coin change: Space-optimized dynamic programming */
+    /* Coin change: space-optimized dynamic programming */
     static int coinChangeDPComp(int[] coins, int amt) {
         int n = coins.length;
         int MAX = amt + 1;
-        // Initialize dp table
+        // Initialize the dp table
         int[] dp = new int[amt + 1];
         Arrays.fill(dp, MAX);
         dp[0] = 0;
-        // State transition
+        // State transitions
         for (int i = 1; i <= n; i++) {
             for (int a = 1; a <= amt; a++) {
                 if (coins[i - 1] > a) {
-                    // If exceeds target amount, don't select coin i
+                    // If the coin exceeds the target amount, do not choose coin i
                     dp[a] = dp[a];
                 } else {
-                    // The smaller value between not selecting and selecting coin i
+                    // Take the smaller result of not choosing and choosing coin i
                     dp[a] = Math.min(dp[a], dp[a - coins[i - 1]] + 1);
                 }
             }
@@ -63,10 +63,10 @@ public class coin_change {
 
         // Dynamic programming
         int res = coinChangeDP(coins, amt);
-        System.out.println("Minimum number of coins needed to make target amount is " + res);
+        System.out.println("Minimum number of coins needed to make the target amount: " + res);
 
         // Space-optimized dynamic programming
         res = coinChangeDPComp(coins, amt);
-        System.out.println("Minimum number of coins needed to make target amount is " + res);
+        System.out.println("Minimum number of coins needed to make the target amount: " + res);
     }
 }

en/codes/java/chapter_dynamic_programming/coin_change_ii.java

@@ -7,23 +7,23 @@
 package chapter_dynamic_programming;
 
 public class coin_change_ii {
-    /* Coin change II: Dynamic programming */
+    /* Coin change II: dynamic programming */
     static int coinChangeIIDP(int[] coins, int amt) {
         int n = coins.length;
-        // Initialize dp table
+        // Initialize the dp table
         int[][] dp = new int[n + 1][amt + 1];
-        // Initialize first column
+        // Initialize the first column
         for (int i = 0; i <= n; i++) {
             dp[i][0] = 1;
         }
-        // State transition
+        // State transitions
         for (int i = 1; i <= n; i++) {
             for (int a = 1; a <= amt; a++) {
                 if (coins[i - 1] > a) {
-                    // If exceeds target amount, don't select coin i
+                    // If the coin exceeds the target amount, do not choose coin i
                     dp[i][a] = dp[i - 1][a];
                 } else {
-                    // Sum of the two options: not selecting and selecting coin i
+                    // Add the numbers of ways without and with coin i
                     dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]];
                 }
             }
@@ -31,20 +31,20 @@ public class coin_change_ii {
         return dp[n][amt];
     }
 
-    /* Coin change II: Space-optimized dynamic programming */
+    /* Coin change II: space-optimized dynamic programming */
     static int coinChangeIIDPComp(int[] coins, int amt) {
         int n = coins.length;
-        // Initialize dp table
+        // Initialize the dp table
         int[] dp = new int[amt + 1];
         dp[0] = 1;
-        // State transition
+        // State transitions
         for (int i = 1; i <= n; i++) {
             for (int a = 1; a <= amt; a++) {
                 if (coins[i - 1] > a) {
-                    // If exceeds target amount, don't select coin i
+                    // If the coin exceeds the target amount, do not choose coin i
                     dp[a] = dp[a];
                 } else {
-                    // Sum of the two options: not selecting and selecting coin i
+                    // Add the numbers of ways without and with coin i
                     dp[a] = dp[a] + dp[a - coins[i - 1]];
                 }
             }
@@ -58,10 +58,10 @@ public class coin_change_ii {
 
         // Dynamic programming
         int res = coinChangeIIDP(coins, amt);
-        System.out.println("Number of coin combinations to make target amount is " + res);
+        System.out.println("Number of coin combinations that make the target amount: " + res);
 
         // Space-optimized dynamic programming
         res = coinChangeIIDPComp(coins, amt);
-        System.out.println("Number of coin combinations to make target amount is " + res);
+        System.out.println("Number of coin combinations that make the target amount: " + res);
     }
 }

en/codes/java/chapter_dynamic_programming/edit_distance.java

@@ -9,73 +9,73 @@ package chapter_dynamic_programming;
 import java.util.Arrays;
 
 public class edit_distance {
-    /* Edit distance: Brute-force search */
+    /* Edit distance: brute-force search */
     static int editDistanceDFS(String s, String t, int i, int j) {
-        // If both s and t are empty, return 0
+        // If the current prefixes of s and t are both empty, return 0
         if (i == 0 && j == 0)
             return 0;
-        // If s is empty, return length of t
+        // If the current prefix of s is empty, return j, the length of the current prefix of t
         if (i == 0)
             return j;
-        // If t is empty, return length of s
+        // If the current prefix of t is empty, return i, the length of the current prefix of s
         if (j == 0)
             return i;
-        // If two characters are equal, skip both characters
+        // If the two characters are equal, skip both of them
         if (s.charAt(i - 1) == t.charAt(j - 1))
             return editDistanceDFS(s, t, i - 1, j - 1);
-        // Minimum edit steps = minimum edit steps of insert, delete, replace + 1
+        // Minimum edits = the minimum among the insertion, deletion, and replacement subproblems + 1
         int insert = editDistanceDFS(s, t, i, j - 1);
         int delete = editDistanceDFS(s, t, i - 1, j);
         int replace = editDistanceDFS(s, t, i - 1, j - 1);
-        // Return minimum edit steps
+        // Return the minimum number of edits
         return Math.min(Math.min(insert, delete), replace) + 1;
     }
 
-    /* Edit distance: Memoization search */
+    /* Edit distance: memoized search */
     static int editDistanceDFSMem(String s, String t, int[][] mem, int i, int j) {
-        // If both s and t are empty, return 0
+        // If the current prefixes of s and t are both empty, return 0
         if (i == 0 && j == 0)
             return 0;
-        // If s is empty, return length of t
+        // If the current prefix of s is empty, return j, the length of the current prefix of t
         if (i == 0)
             return j;
-        // If t is empty, return length of s
+        // If the current prefix of t is empty, return i, the length of the current prefix of s
         if (j == 0)
             return i;
-        // If there's a record, return it directly
+        // If a result has already been recorded, return it directly
         if (mem[i][j] != -1)
             return mem[i][j];
-        // If two characters are equal, skip both characters
+        // If the two characters are equal, skip both of them
         if (s.charAt(i - 1) == t.charAt(j - 1))
             return editDistanceDFSMem(s, t, mem, i - 1, j - 1);
-        // Minimum edit steps = minimum edit steps of insert, delete, replace + 1
+        // Minimum edits = the minimum among the insertion, deletion, and replacement subproblems + 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 minimum edit steps
+        // Record and return the minimum number of edits
         mem[i][j] = Math.min(Math.min(insert, delete), replace) + 1;
         return mem[i][j];
     }
 
-    /* Edit distance: Dynamic programming */
+    /* 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
+        // State transitions: 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: rest of the rows and columns
+        // State transitions: remaining 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 two characters are equal, skip both characters
+                    // If the two characters are equal, skip both of them
                     dp[i][j] = dp[i - 1][j - 1];
                 } else {
-                    // Minimum edit steps = minimum edit steps of insert, delete, replace + 1
+                    // Minimum edits = the minimum among the insertion, deletion, and replacement subproblems + 1
                     dp[i][j] = Math.min(Math.min(dp[i][j - 1], dp[i - 1][j]), dp[i - 1][j - 1]) + 1;
                 }
             }
@@ -83,30 +83,30 @@ public class edit_distance {
         return dp[n][m];
     }
 
-    /* Edit distance: Space-optimized dynamic programming */
+    /* 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
+        // State transitions: first row
         for (int j = 1; j <= m; j++) {
             dp[j] = j;
         }
-        // State transition: rest of the rows
+        // State transitions: remaining rows
         for (int i = 1; i <= n; i++) {
-            // State transition: first column
+            // State transitions: first column
             int leftup = dp[0]; // Temporarily store dp[i-1, j-1]
             dp[0] = i;
-            // State transition: rest of the columns
+            // State transitions: remaining columns
             for (int j = 1; j <= m; j++) {
                 int temp = dp[j];
                 if (s.charAt(i - 1) == t.charAt(j - 1)) {
-                    // If two characters are equal, skip both characters
+                    // If the two characters are equal, skip both of them
                     dp[j] = leftup;
                 } else {
-                    // Minimum edit steps = minimum edit steps of insert, delete, replace + 1
+                    // Minimum edits = the minimum among the insertion, deletion, and replacement subproblems + 1
                     dp[j] = Math.min(Math.min(dp[j - 1], dp[j]), leftup) + 1;
                 }
-                leftup = temp; // Update for next round's dp[i-1, j-1]
+                leftup = temp; // Update to dp[i-1, j-1] for the next iteration
             }
         }
         return dp[m];
@@ -119,21 +119,21 @@ public class edit_distance {
 
         // Brute-force search
         int res = editDistanceDFS(s, t, n, m);
-        System.out.println("Changing " + s + " to " + t + " requires a minimum of " + res + " edits");
+        System.out.println("Changing " + s + " to " + t + " requires at least " + res + " edits");
 
-        // Memoization search
+        // 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");
+        System.out.println("Changing " + s + " to " + t + " requires at least " + res + " edits");
 
         // Dynamic programming
         res = editDistanceDP(s, t);
-        System.out.println("Changing " + s + " to " + t + " requires a minimum of " + res + " edits");
+        System.out.println("Changing " + s + " to " + t + " requires at least " + res + " edits");
 
         // Space-optimized dynamic programming
         res = editDistanceDPComp(s, t);
-        System.out.println("Changing " + s + " to " + t + " requires a minimum of " + res + " edits");
+        System.out.println("Changing " + s + " to " + t + " requires at least " + res + " edits");
     }
 }

en/codes/java/chapter_dynamic_programming/knapsack.java

@@ -10,58 +10,58 @@ import java.util.Arrays;
 
 public class knapsack {
 
-    /* 0-1 knapsack: Brute-force search */
+    /* 0-1 knapsack: brute-force search */
     static int knapsackDFS(int[] wgt, int[] val, int i, int c) {
-        // If all items have been selected or knapsack has no remaining capacity, return value 0
+        // If all items have been considered or no capacity remains, return value 0
         if (i == 0 || c == 0) {
             return 0;
         }
-        // If exceeds knapsack capacity, can only choose not to put it in
+        // If the item exceeds the remaining capacity, it must be excluded
         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
+        // Calculate the maximum values obtained by excluding and including 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 the larger value from the two choices
         return Math.max(no, yes);
     }
 
-    /* 0-1 knapsack: Memoization search */
+    /* 0-1 knapsack: memoized search */
     static int knapsackDFSMem(int[] wgt, int[] val, int[][] mem, int i, int c) {
-        // If all items have been selected or knapsack has no remaining capacity, return value 0
+        // If all items have been considered or no capacity remains, return value 0
         if (i == 0 || c == 0) {
             return 0;
         }
-        // If there's a record, return it directly
+        // If a result has already been recorded, 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 the item exceeds the remaining capacity, it must be excluded
         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
+        // Calculate the maximum values obtained by excluding and including 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
+        // Record and return the larger value from the two choices
         mem[i][c] = Math.max(no, yes);
         return mem[i][c];
     }
 
-    /* 0-1 knapsack: Dynamic programming */
+    /* 0-1 knapsack: dynamic programming */
     static int knapsackDP(int[] wgt, int[] val, int cap) {
         int n = wgt.length;
-        // Initialize dp table
+        // Initialize the dp table
         int[][] dp = new int[n + 1][cap + 1];
-        // State transition
+        // State transitions
         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
+                    // If item i exceeds the remaining capacity, do not choose it
                     dp[i][c] = dp[i - 1][c];
                 } else {
-                    // The larger value between not selecting and selecting item i
+                    // Take the larger value obtained by excluding and including item i
                     dp[i][c] = Math.max(dp[i - 1][c], dp[i - 1][c - wgt[i - 1]] + val[i - 1]);
                 }
             }
@@ -69,17 +69,17 @@ public class knapsack {
         return dp[n][cap];
     }
 
-    /* 0-1 knapsack: Space-optimized dynamic programming */
+    /* 0-1 knapsack: space-optimized dynamic programming */
     static int knapsackDPComp(int[] wgt, int[] val, int cap) {
         int n = wgt.length;
-        // Initialize dp table
+        // Initialize the dp table
         int[] dp = new int[cap + 1];
-        // State transition
+        // State transitions
         for (int i = 1; i <= n; i++) {
-            // Traverse in reverse order
+            // Traverse in decreasing order
             for (int c = cap; c >= 1; c--) {
                 if (wgt[i - 1] <= c) {
-                    // The larger value between not selecting and selecting item i
+                    // Take the larger value obtained by excluding and including item i
                     dp[c] = Math.max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);
                 }
             }
@@ -95,22 +95,22 @@ public class knapsack {
 
         // Brute-force search
         int res = knapsackDFS(wgt, val, n, cap);
-        System.out.println("Maximum item value not exceeding knapsack capacity is " + res);
+        System.out.println("Maximum total item value within the knapsack capacity: " + res);
 
-        // Memoization search
+        // 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("Maximum item value not exceeding knapsack capacity is " + res);
+        System.out.println("Maximum total item value within the knapsack capacity: " + res);
 
         // Dynamic programming
         res = knapsackDP(wgt, val, cap);
-        System.out.println("Maximum item value not exceeding knapsack capacity is " + res);
+        System.out.println("Maximum total item value within the knapsack capacity: " + res);
 
         // Space-optimized dynamic programming
         res = knapsackDPComp(wgt, val, cap);
-        System.out.println("Maximum item value not exceeding knapsack capacity is " + res);
+        System.out.println("Maximum total item value within the knapsack capacity: " + res);
     }
 }

en/codes/java/chapter_dynamic_programming/min_cost_climbing_stairs_dp.java

@@ -9,24 +9,24 @@ package chapter_dynamic_programming;
 import java.util.Arrays;
 
 public class min_cost_climbing_stairs_dp {
-    /* Minimum cost climbing stairs: Dynamic programming */
+    /* Minimum cost to climb stairs: 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 solutions to subproblems
+        // Initialize the dp table to store subproblem solutions
         int[] dp = new int[n + 1];
-        // Initial state: preset the solution to the smallest subproblem
+        // Initial states: set the solutions to the smallest subproblems
         dp[1] = cost[1];
         dp[2] = cost[2];
-        // State transition: gradually solve larger subproblems from smaller ones
+        // State transitions: solve progressively larger subproblems using smaller ones
         for (int i = 3; i <= n; i++) {
             dp[i] = Math.min(dp[i - 1], dp[i - 2]) + cost[i];
         }
         return dp[n];
     }
 
-    /* Minimum cost climbing stairs: Space-optimized dynamic programming */
+    /* Minimum cost to climb stairs: space-optimized dynamic programming */
     public static int minCostClimbingStairsDPComp(int[] cost) {
         int n = cost.length - 1;
         if (n == 1 || n == 2)
@@ -42,12 +42,12 @@ public class min_cost_climbing_stairs_dp {
 
     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 staircase cost list is %s", Arrays.toString(cost)));
+        System.out.println(String.format("Input stair costs: %s", Arrays.toString(cost)));
 
         int res = minCostClimbingStairsDP(cost);
-        System.out.println(String.format("Minimum cost to climb staircase is %d", res));
+        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 staircase is %d", res));
+        System.out.println(String.format("Minimum cost to climb the stairs: %d", res));
     }
 }

en/codes/java/chapter_dynamic_programming/min_path_sum.java

@@ -9,60 +9,60 @@ package chapter_dynamic_programming;
 import java.util.Arrays;
 
 public class min_path_sum {
-    /* Minimum path sum: Brute-force search */
+    /* 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
+        // Stop searching at the top-left cell
         if (i == 0 && j == 0) {
             return grid[0][0];
         }
-        // If row or column index is out of bounds, return +∞ cost
+        // If a row or column index is out of bounds, return a cost of +∞
         if (i < 0 || j < 0) {
             return Integer.MAX_VALUE;
         }
-        // Calculate the minimum path cost from top-left to (i-1, j) and (i, j-1)
+        // Calculate the minimum path costs from the top-left corner 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 the minimum path cost from the top-left corner to (i, j)
         return Math.min(left, up) + grid[i][j];
     }
 
-    /* Minimum path sum: Memoization search */
+    /* 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
+        // Stop searching at the top-left cell
         if (i == 0 && j == 0) {
             return grid[0][0];
         }
-        // If row or column index is out of bounds, return +∞ cost
+        // If a row or column index is out of bounds, return a cost of +∞
         if (i < 0 || j < 0) {
             return Integer.MAX_VALUE;
         }
-        // If there's a record, return it directly
+        // If a result has already been recorded, return it directly
         if (mem[i][j] != -1) {
             return mem[i][j];
         }
-        // Minimum path cost for left and upper cells
+        // Minimum path costs to the cells on the left and above
         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)
+        // Record and return the minimum path cost from the top-left corner to (i, j)
         mem[i][j] = Math.min(left, up) + grid[i][j];
         return mem[i][j];
     }
 
-    /* Minimum path sum: Dynamic programming */
+    /* Minimum path sum: dynamic programming */
     static int minPathSumDP(int[][] grid) {
         int n = grid.length, m = grid[0].length;
-        // Initialize dp table
+        // Initialize the dp table
         int[][] dp = new int[n][m];
         dp[0][0] = grid[0][0];
-        // State transition: first row
+        // State transitions: first row
         for (int j = 1; j < m; j++) {
             dp[0][j] = dp[0][j - 1] + grid[0][j];
         }
-        // State transition: first column
+        // State transitions: 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
+        // State transitions: remaining 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];
@@ -71,21 +71,21 @@ public class min_path_sum {
         return dp[n - 1][m - 1];
     }
 
-    /* Minimum path sum: Space-optimized dynamic programming */
+    /* Minimum path sum: space-optimized dynamic programming */
     static int minPathSumDPComp(int[][] grid) {
         int n = grid.length, m = grid[0].length;
-        // Initialize dp table
+        // Initialize the dp table
         int[] dp = new int[m];
-        // State transition: first row
+        // State transitions: first row
         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
+        // State transitions: remaining rows
         for (int i = 1; i < n; i++) {
-            // State transition: first column
+            // State transitions: first column
             dp[0] = dp[0] + grid[i][0];
-            // State transition: rest of the columns
+            // State transitions: remaining columns
             for (int j = 1; j < m; j++) {
                 dp[j] = Math.min(dp[j - 1], dp[j]) + grid[i][j];
             }
@@ -104,22 +104,22 @@ public class min_path_sum {
 
         // Brute-force search
         int res = minPathSumDFS(grid, n - 1, m - 1);
-        System.out.println("Minimum path sum from top-left to bottom-right is " + res);
+        System.out.println("Minimum path sum from the top-left to the bottom-right corner: " + res);
 
-        // Memoization search
+        // 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("Minimum path sum from top-left to bottom-right is " + res);
+        System.out.println("Minimum path sum from the top-left to the bottom-right corner: " + res);
 
         // Dynamic programming
         res = minPathSumDP(grid);
-        System.out.println("Minimum path sum from top-left to bottom-right is " + res);
+        System.out.println("Minimum path sum from the top-left to the bottom-right corner: " + res);
 
         // Space-optimized dynamic programming
         res = minPathSumDPComp(grid);
-        System.out.println("Minimum path sum from top-left to bottom-right is " + res);
+        System.out.println("Minimum path sum from the top-left to the bottom-right corner: " + res);
     }
 }

en/codes/java/chapter_dynamic_programming/unbounded_knapsack.java

@@ -7,19 +7,19 @@
 package chapter_dynamic_programming;
 
 public class unbounded_knapsack {
-    /* Unbounded knapsack: Dynamic programming */
+    /* Unbounded knapsack: dynamic programming */
     static int unboundedKnapsackDP(int[] wgt, int[] val, int cap) {
         int n = wgt.length;
-        // Initialize dp table
+        // Initialize the dp table
         int[][] dp = new int[n + 1][cap + 1];
-        // State transition
+        // State transitions
         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
+                    // If item i exceeds the remaining capacity, do not choose it
                     dp[i][c] = dp[i - 1][c];
                 } else {
-                    // The larger value between not selecting and selecting item i
+                    // Take the larger value obtained by excluding and including item i
                     dp[i][c] = Math.max(dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1]);
                 }
             }
@@ -27,19 +27,19 @@ public class unbounded_knapsack {
         return dp[n][cap];
     }
 
-    /* Unbounded knapsack: Space-optimized dynamic programming */
+    /* Unbounded knapsack: space-optimized dynamic programming */
     static int unboundedKnapsackDPComp(int[] wgt, int[] val, int cap) {
         int n = wgt.length;
-        // Initialize dp table
+        // Initialize the dp table
         int[] dp = new int[cap + 1];
-        // State transition
+        // State transitions
         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
+                    // If item i exceeds the remaining capacity, do not choose it
                     dp[c] = dp[c];
                 } else {
-                    // The larger value between not selecting and selecting item i
+                    // Take the larger value obtained by excluding and including item i
                     dp[c] = Math.max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);
                 }
             }
@@ -54,10 +54,10 @@ public class unbounded_knapsack {
 
         // Dynamic programming
         int res = unboundedKnapsackDP(wgt, val, cap);
-        System.out.println("Maximum item value not exceeding knapsack capacity is " + res);
+        System.out.println("Maximum total item value within the knapsack capacity: " + res);
 
         // Space-optimized dynamic programming
         res = unboundedKnapsackDPComp(wgt, val, cap);
-        System.out.println("Maximum item value not exceeding knapsack capacity is " + res);
+        System.out.println("Maximum total item value within the knapsack capacity: " + res);
     }
 }