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

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* Retranslate the complete English edition from Simplified Chinese

* Polish three English explanations after reader-focused review
This commit is contained in:
Yudong Jin
2026-10-31 03:35:51 +08:00
committed by GitHub
parent ef46e2ed95
commit 14c314c08c
1502 changed files with 29459 additions and 23517 deletions
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20
en/codes/javascript/chapter_dynamic_programming/climbing_stairs_backtrack.js
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@@ -6,29 +6,29 @@
/* Backtracking */
function backtrack(choices, state, n, 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 (const choice of 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 */
function climbingStairsBacktrack(n) {
const choices = [1, 2]; // Can choose to climb up 1 or 2 stairs
const state = 0; // Start climbing from the 0-th stair
const choices = [1, 2]; // Choose to climb 1 or 2 steps
const state = 0; // Start climbing from step 0
const res = new Map();
res.set(0, 0); // Use res[0] to record the solution count
res.set(0, 0); // Store the number of ways at key 0 in res
backtrack(choices, state, n, res);
return res.get(0);
}
/* Driver Code */
/* Driver code */
const n = 9;
const res = climbingStairsBacktrack(n);
console.log(`Climbing ${n} stairs has ${res} solutions`);
console.log(`Number of ways to climb ${n} stairs: ${res}`);

12
en/codes/javascript/chapter_dynamic_programming/climbing_stairs_constraint_dp.js
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@@ -4,19 +4,19 @@
* Author: Gaofer Chou (gaofer-chou@qq.com)
*/
/* Climbing stairs with constraint: Dynamic programming */
/* Climbing stairs with constraints: dynamic programming */
function climbingStairsConstraintDP(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
const dp = Array.from(new Array(n + 1), () => new Array(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 (let i = 3; i <= n; i++) {
dp[i][1] = dp[i - 1][2];
dp[i][2] = dp[i - 2][1] + dp[i - 2][2];
@@ -24,7 +24,7 @@ function climbingStairsConstraintDP(n) {
return dp[n][1] + dp[n][2];
}
/* Driver Code */
/* Driver code */
const n = 9;
const res = climbingStairsConstraintDP(n);
console.log(`Climbing ${n} stairs has ${res} solutions`);
console.log(`Number of ways to climb ${n} stairs: ${res}`);

8
en/codes/javascript/chapter_dynamic_programming/climbing_stairs_dfs.js
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@@ -6,19 +6,19 @@
/* Search */
function dfs(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]
const count = dfs(i - 1) + dfs(i - 2);
return count;
}
/* Climbing stairs: Search */
/* Climbing stairs: search */
function climbingStairsDFS(n) {
return dfs(n);
}
/* Driver Code */
/* Driver code */
const n = 9;
const res = climbingStairsDFS(n);
console.log(`Climbing ${n} stairs has ${res} solutions`);
console.log(`Number of ways to climb ${n} stairs: ${res}`);

14
en/codes/javascript/chapter_dynamic_programming/climbing_stairs_dfs_mem.js
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@@ -4,11 +4,11 @@
* Author: yuan0221 (yl1452491917@gmail.com)
*/
/* Memoization search */
/* Memoized search */
function dfs(i, 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]
const count = dfs(i - 1, mem) + dfs(i - 2, mem);
@@ -17,14 +17,14 @@ function dfs(i, mem) {
return count;
}
/* Climbing stairs: Memoization search */
/* Climbing stairs: memoized search */
function climbingStairsDFSMem(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
const mem = new Array(n + 1).fill(-1);
return dfs(n, mem);
}
/* Driver Code */
/* Driver code */
const n = 9;
const res = climbingStairsDFSMem(n);
console.log(`Climbing ${n} stairs has ${res} solutions`);
console.log(`Number of ways to climb ${n} stairs: ${res}`);

16
en/codes/javascript/chapter_dynamic_programming/climbing_stairs_dp.js
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@@ -4,22 +4,22 @@
* Author: yuan0221 (yl1452491917@gmail.com)
*/
/* Climbing stairs: Dynamic programming */
/* Climbing stairs: dynamic programming */
function climbingStairsDP(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
const dp = new Array(n + 1).fill(-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 (let 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 */
function climbingStairsDPComp(n) {
if (n === 1 || n === 2) return n;
let a = 1,
@@ -32,9 +32,9 @@ function climbingStairsDPComp(n) {
return b;
}
/* Driver Code */
/* Driver code */
const n = 9;
let res = climbingStairsDP(n);
console.log(`Climbing ${n} stairs has ${res} solutions`);
console.log(`Number of ways to climb ${n} stairs: ${res}`);
res = climbingStairsDPComp(n);
console.log(`Climbing ${n} stairs has ${res} solutions`);
console.log(`Number of ways to climb ${n} stairs: ${res}`);

28
en/codes/javascript/chapter_dynamic_programming/coin_change.js
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@@ -4,26 +4,26 @@
* Author: Gaofer Chou (gaofer-chou@qq.com)
*/
/* Coin change: Dynamic programming */
/* Coin change: dynamic programming */
function coinChangeDP(coins, amt) {
const n = coins.length;
const MAX = amt + 1;
// Initialize dp table
// Initialize the dp table
const dp = Array.from({ length: n + 1 }, () =>
Array.from({ length: amt + 1 }, () => 0)
);
// State transition: first row and first column
// State transitions: first row and first column
for (let a = 1; a <= amt; a++) {
dp[0][a] = MAX;
}
// State transition: rest of the rows and columns
// State transitions: remaining rows and columns
for (let i = 1; i <= n; i++) {
for (let 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);
}
}
@@ -31,21 +31,21 @@ function coinChangeDP(coins, amt) {
return dp[n][amt] !== MAX ? dp[n][amt] : -1;
}
/* Coin change: Space-optimized dynamic programming */
/* Coin change: space-optimized dynamic programming */
function coinChangeDPComp(coins, amt) {
const n = coins.length;
const MAX = amt + 1;
// Initialize dp table
// Initialize the dp table
const dp = Array.from({ length: amt + 1 }, () => MAX);
dp[0] = 0;
// State transition
// State transitions
for (let i = 1; i <= n; i++) {
for (let 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);
}
}
@@ -53,14 +53,14 @@ function coinChangeDPComp(coins, amt) {
return dp[amt] !== MAX ? dp[amt] : -1;
}
/* Driver Code */
/* Driver code */
const coins = [1, 2, 5];
const amt = 4;
// Dynamic programming
let res = coinChangeDP(coins, amt);
console.log(`Minimum coins needed to make target amount is ${res}`);
console.log(`Minimum number of coins needed to make the target amount: ${res}`);
// Space-optimized dynamic programming
res = coinChangeDPComp(coins, amt);
console.log(`Minimum coins needed to make target amount is ${res}`);
console.log(`Minimum number of coins needed to make the target amount: ${res}`);

28
en/codes/javascript/chapter_dynamic_programming/coin_change_ii.js
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@@ -4,25 +4,25 @@
* Author: Gaofer Chou (gaofer-chou@qq.com)
*/
/* Coin change II: Dynamic programming */
/* Coin change II: dynamic programming */
function coinChangeIIDP(coins, amt) {
const n = coins.length;
// Initialize dp table
// Initialize the dp table
const dp = Array.from({ length: n + 1 }, () =>
Array.from({ length: amt + 1 }, () => 0)
);
// Initialize first column
// Initialize the first column
for (let i = 0; i <= n; i++) {
dp[i][0] = 1;
}
// State transition
// State transitions
for (let i = 1; i <= n; i++) {
for (let 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]];
}
}
@@ -30,20 +30,20 @@ function coinChangeIIDP(coins, amt) {
return dp[n][amt];
}
/* Coin change II: Space-optimized dynamic programming */
/* Coin change II: space-optimized dynamic programming */
function coinChangeIIDPComp(coins, amt) {
const n = coins.length;
// Initialize dp table
// Initialize the dp table
const dp = Array.from({ length: amt + 1 }, () => 0);
dp[0] = 1;
// State transition
// State transitions
for (let i = 1; i <= n; i++) {
for (let 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]];
}
}
@@ -51,14 +51,14 @@ function coinChangeIIDPComp(coins, amt) {
return dp[amt];
}
/* Driver Code */
/* Driver code */
const coins = [1, 2, 5];
const amt = 5;
// Dynamic programming
let res = coinChangeIIDP(coins, amt);
console.log(`Number of coin combinations to make target amount is ${res}`);
console.log(`Number of coin combinations that make the target amount: ${res}`);
// Space-optimized dynamic programming
res = coinChangeIIDPComp(coins, amt);
console.log(`Number of coin combinations to make target amount is ${res}`);
console.log(`Number of coin combinations that make the target amount: ${res}`);

66
en/codes/javascript/chapter_dynamic_programming/edit_distance.js
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@@ -4,76 +4,76 @@
* Author: Gaofer Chou (gaofer-chou@qq.com)
*/
/* Edit distance: Brute-force search */
/* Edit distance: brute-force search */
function editDistanceDFS(s, t, i, j) {
// If both s and t are empty, return 0
// If the current prefixes of both s and t are 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 the current prefix length j of t
if (i === 0) return j;
// If t is empty, return length of s
// If the current prefix of t is empty, return the current prefix length i 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
const insert = editDistanceDFS(s, t, i, j - 1);
const del = editDistanceDFS(s, t, i - 1, j);
const replace = editDistanceDFS(s, t, i - 1, j - 1);
// Return minimum edit steps
// Return the minimum number of edits
return Math.min(insert, del, replace) + 1;
}
/* Edit distance: Memoization search */
/* Edit distance: memoized search */
function editDistanceDFSMem(s, t, mem, i, j) {
// If both s and t are empty, return 0
// If the current prefixes of both s and t are 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 the current prefix length j of t
if (i === 0) return j;
// If t is empty, return length of s
// If the current prefix of t is empty, return the current prefix length i 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
const insert = editDistanceDFSMem(s, t, mem, i, j - 1);
const del = editDistanceDFSMem(s, t, mem, i - 1, j);
const 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(insert, del, replace) + 1;
return mem[i][j];
}
/* Edit distance: Dynamic programming */
/* Edit distance: dynamic programming */
function editDistanceDP(s, t) {
const n = s.length,
m = t.length;
const dp = Array.from({ length: n + 1 }, () => new Array(m + 1).fill(0));
// State transition: first row and first column
// State transitions: first row and first column
for (let i = 1; i <= n; i++) {
dp[i][0] = i;
}
for (let j = 1; j <= m; j++) {
dp[0][j] = j;
}
// State transition: rest of the rows and columns
// State transitions: remaining rows and columns
for (let i = 1; i <= n; i++) {
for (let 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(dp[i][j - 1], dp[i - 1][j], dp[i - 1][j - 1]) + 1;
}
@@ -82,31 +82,31 @@ function editDistanceDP(s, t) {
return dp[n][m];
}
/* Edit distance: Space-optimized dynamic programming */
/* Edit distance: space-optimized dynamic programming */
function editDistanceDPComp(s, t) {
const n = s.length,
m = t.length;
const dp = new Array(m + 1).fill(0);
// State transition: first row
// State transitions: first row
for (let j = 1; j <= m; j++) {
dp[j] = j;
}
// State transition: rest of the rows
// State transitions: remaining rows
for (let i = 1; i <= n; i++) {
// State transition: first column
// State transitions: first column
let leftup = dp[0]; // Temporarily store dp[i-1, j-1]
dp[0] = i;
// State transition: rest of the columns
// State transitions: remaining columns
for (let j = 1; j <= m; j++) {
const 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(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];
@@ -119,17 +119,17 @@ const n = s.length,
// Brute-force search
let res = editDistanceDFS(s, t, n, m);
console.log(`Changing ${s} to ${t} requires minimum ${res} edits`);
console.log(`Minimum number of edits to transform ${s} into ${t}: ${res}`);
// Memoization search
// Memoized search
const mem = Array.from(new Array(n + 1), () => new Array(m + 1).fill(-1));
res = editDistanceDFSMem(s, t, mem, n, m);
console.log(`Changing ${s} to ${t} requires minimum ${res} edits`);
console.log(`Minimum number of edits to transform ${s} into ${t}: ${res}`);
// Dynamic programming
res = editDistanceDP(s, t);
console.log(`Changing ${s} to ${t} requires minimum ${res} edits`);
console.log(`Minimum number of edits to transform ${s} into ${t}: ${res}`);
// Space-optimized dynamic programming
res = editDistanceDPComp(s, t);
console.log(`Changing ${s} to ${t} requires minimum ${res} edits`);
console.log(`Minimum number of edits to transform ${s} into ${t}: ${res}`);

54
en/codes/javascript/chapter_dynamic_programming/knapsack.js
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@@ -4,61 +4,61 @@
* Author: Gaofer Chou (gaofer-chou@qq.com)
*/
/* 0-1 knapsack: Brute-force search */
/* 0-1 knapsack: brute-force search */
function knapsackDFS(wgt, val, i, 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
const no = knapsackDFS(wgt, val, i - 1, c);
const 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 */
function knapsackDFSMem(wgt, val, mem, i, 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
const no = knapsackDFSMem(wgt, val, mem, i - 1, c);
const 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 */
function knapsackDP(wgt, val, cap) {
const n = wgt.length;
// Initialize dp table
// Initialize the dp table
const dp = Array(n + 1)
.fill(0)
.map(() => Array(cap + 1).fill(0));
// State transition
// State transitions
for (let i = 1; i <= n; i++) {
for (let 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 @@ function knapsackDP(wgt, val, cap) {
return dp[n][cap];
}
/* 0-1 knapsack: Space-optimized dynamic programming */
/* 0-1 knapsack: space-optimized dynamic programming */
function knapsackDPComp(wgt, val, cap) {
const n = wgt.length;
// Initialize dp table
// Initialize the dp table
const dp = Array(cap + 1).fill(0);
// State transition
// State transitions
for (let i = 1; i <= n; i++) {
// Traverse in reverse order
// Traverse in decreasing order
for (let 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]);
}
}
@@ -87,7 +87,7 @@ function knapsackDPComp(wgt, val, cap) {
return dp[cap];
}
/* Driver Code */
/* Driver code */
const wgt = [10, 20, 30, 40, 50];
const val = [50, 120, 150, 210, 240];
const cap = 50;
@@ -95,19 +95,19 @@ const n = wgt.length;
// Brute-force search
let res = knapsackDFS(wgt, val, n, cap);
console.log(`Maximum item value not exceeding knapsack capacity is ${res}`);
console.log(`Maximum item value within the knapsack capacity: ${res}`);
// Memoization search
// Memoized search
const mem = Array.from({ length: n + 1 }, () =>
Array.from({ length: cap + 1 }, () => -1)
);
res = knapsackDFSMem(wgt, val, mem, n, cap);
console.log(`Maximum item value not exceeding knapsack capacity is ${res}`);
console.log(`Maximum item value within the knapsack capacity: ${res}`);
// Dynamic programming
res = knapsackDP(wgt, val, cap);
console.log(`Maximum item value not exceeding knapsack capacity is ${res}`);
console.log(`Maximum item value within the knapsack capacity: ${res}`);
// Space-optimized dynamic programming
res = knapsackDPComp(wgt, val, cap);
console.log(`Maximum item value not exceeding knapsack capacity is ${res}`);
console.log(`Maximum item value within the knapsack capacity: ${res}`);

18
en/codes/javascript/chapter_dynamic_programming/min_cost_climbing_stairs_dp.js
View File

@@ -4,25 +4,25 @@
* Author: Gaofer Chou (gaofer-chou@qq.com)
*/
/* Minimum cost climbing stairs: Dynamic programming */
/* Minimum cost to climb stairs: dynamic programming */
function minCostClimbingStairsDP(cost) {
const 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
const dp = new Array(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 (let 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 */
function minCostClimbingStairsDPComp(cost) {
const n = cost.length - 1;
if (n === 1 || n === 2) {
@@ -38,12 +38,12 @@ function minCostClimbingStairsDPComp(cost) {
return b;
}
/* Driver Code */
/* Driver code */
const cost = [0, 1, 10, 1, 1, 1, 10, 1, 1, 10, 1];
console.log('Input stair cost list is:', cost);
console.log('Input list of stair costs:', cost);
let res = minCostClimbingStairsDP(cost);
console.log(`Minimum cost to climb stairs is: ${res}`);
console.log(`Minimum cost to climb the stairs: ${res}`);
res = minCostClimbingStairsDPComp(cost);
console.log(`Minimum cost to climb stairs is: ${res}`);
console.log(`Minimum cost to climb the stairs: ${res}`);

56
en/codes/javascript/chapter_dynamic_programming/min_path_sum.js
View File

@@ -4,63 +4,63 @@
* Author: Gaofer Chou (gaofer-chou@qq.com)
*/
/* Minimum path sum: Brute-force search */
/* Minimum path sum: brute-force search */
function minPathSumDFS(grid, i, 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 Infinity;
}
// 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)
const up = minPathSumDFS(grid, i - 1, j);
const 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 */
function minPathSumDFSMem(grid, mem, i, 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 Infinity;
}
// 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
const up = minPathSumDFSMem(grid, mem, i - 1, j);
const 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 */
function minPathSumDP(grid) {
const n = grid.length,
m = grid[0].length;
// Initialize dp table
// Initialize the dp table
const dp = Array.from({ length: n }, () =>
Array.from({ length: m }, () => 0)
);
dp[0][0] = grid[0][0];
// State transition: first row
// State transitions: first row
for (let j = 1; j < m; j++) {
dp[0][j] = dp[0][j - 1] + grid[0][j];
}
// State transition: first column
// State transitions: first column
for (let 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 (let i = 1; i < n; i++) {
for (let j = 1; j < m; j++) {
dp[i][j] = Math.min(dp[i][j - 1], dp[i - 1][j]) + grid[i][j];
@@ -69,22 +69,22 @@ function minPathSumDP(grid) {
return dp[n - 1][m - 1];
}
/* Minimum path sum: Space-optimized dynamic programming */
/* Minimum path sum: space-optimized dynamic programming */
function minPathSumDPComp(grid) {
const n = grid.length,
m = grid[0].length;
// Initialize dp table
// Initialize the dp table
const dp = new Array(m);
// State transition: first row
// State transitions: first row
dp[0] = grid[0][0];
for (let j = 1; j < m; j++) {
dp[j] = dp[j - 1] + grid[0][j];
}
// State transition: rest of the rows
// State transitions: remaining rows
for (let 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 (let j = 1; j < m; j++) {
dp[j] = Math.min(dp[j - 1], dp[j]) + grid[i][j];
}
@@ -92,7 +92,7 @@ function minPathSumDPComp(grid) {
return dp[m - 1];
}
/* Driver Code */
/* Driver code */
const grid = [
[1, 3, 1, 5],
[2, 2, 4, 2],
@@ -103,19 +103,19 @@ const n = grid.length,
m = grid[0].length;
// Brute-force search
let res = minPathSumDFS(grid, n - 1, m - 1);
console.log(`Minimum path sum from top-left to bottom-right is ${res}`);
console.log(`Minimum path sum from the top-left to the bottom-right: ${res}`);
// Memoization search
// Memoized search
const mem = Array.from({ length: n }, () =>
Array.from({ length: m }, () => -1)
);
res = minPathSumDFSMem(grid, mem, n - 1, m - 1);
console.log(`Minimum path sum from top-left to bottom-right is ${res}`);
console.log(`Minimum path sum from the top-left to the bottom-right: ${res}`);
// Dynamic programming
res = minPathSumDP(grid);
console.log(`Minimum path sum from top-left to bottom-right is ${res}`);
console.log(`Minimum path sum from the top-left to the bottom-right: ${res}`);
// Space-optimized dynamic programming
res = minPathSumDPComp(grid);
console.log(`Minimum path sum from top-left to bottom-right is ${res}`);
console.log(`Minimum path sum from the top-left to the bottom-right: ${res}`);

26
en/codes/javascript/chapter_dynamic_programming/unbounded_knapsack.js
View File

@@ -4,21 +4,21 @@
* Author: Gaofer Chou (gaofer-chou@qq.com)
*/
/* Unbounded knapsack: Dynamic programming */
/* Unbounded knapsack: dynamic programming */
function unboundedKnapsackDP(wgt, val, cap) {
const n = wgt.length;
// Initialize dp table
// Initialize the dp table
const dp = Array.from({ length: n + 1 }, () =>
Array.from({ length: cap + 1 }, () => 0)
);
// State transition
// State transitions
for (let i = 1; i <= n; i++) {
for (let 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]
@@ -29,19 +29,19 @@ function unboundedKnapsackDP(wgt, val, cap) {
return dp[n][cap];
}
/* Unbounded knapsack: Space-optimized dynamic programming */
/* Unbounded knapsack: space-optimized dynamic programming */
function unboundedKnapsackDPComp(wgt, val, cap) {
const n = wgt.length;
// Initialize dp table
// Initialize the dp table
const dp = Array.from({ length: cap + 1 }, () => 0);
// State transition
// State transitions
for (let i = 1; i <= n; i++) {
for (let 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]);
}
}
@@ -49,15 +49,15 @@ function unboundedKnapsackDPComp(wgt, val, cap) {
return dp[cap];
}
/* Driver Code */
/* Driver code */
const wgt = [1, 2, 3];
const val = [5, 11, 15];
const cap = 4;
// Dynamic programming
let res = unboundedKnapsackDP(wgt, val, cap);
console.log(`Maximum item value not exceeding knapsack capacity is ${res}`);
console.log(`Maximum item value within the knapsack capacity: ${res}`);
// Space-optimized dynamic programming
res = unboundedKnapsackDPComp(wgt, val, cap);
console.log(`Maximum item value not exceeding knapsack capacity is ${res}`);
console.log(`Maximum item value within the knapsack capacity: ${res}`);