241st Commit

README.md

@@ -474,13 +474,14 @@ Must-do List for Interview Prep
 | 17. Letter Combinations of a Phone Number | [Solution][17] | Medium |
 | 77. Combinations                          | Solution       | Medium |
 | 46. Permutations                          | [Solution][46] | Medium |
-| 39. Combination Sum                       | Solution       | Medium |
+| 39. Combination Sum                       | [Solution][39] | Medium |
 | 52. N-Queens II                           | Solution       | Hard   |
 | 22. Generate Parentheses                  | Solution       | Medium |
 | 79. Word Search                           | Solution       | Medium |
 
 [17]: ./src/page-1/17.%20Letter%20Combinations%20of%20a%20Phone%20Number/letterCombinations.ts
 [46]: ./src/page-1/46.%20Permutations/permute.ts
+[39]: ./src/page-1/39.%20Combination%20Sum/combinationSum.ts
 
 | Divide & Conquer                                |                 |        |
 | ----------------------------------------------- | --------------- | ------ |
@@ -587,14 +588,15 @@ Must-do List for Interview Prep
 | ----------------------------------------- | -------------- | ------ |
 | 17. Letter Combinations of a Phone Number | [Solution][17] | Medium |
 | 22. Generate Parentheses                  | Solution       | Medium |
-| 39. Combination Sum                       | Solution       | Medium |
+| 39. Combination Sum                       | [Solution][39] | Medium |
 | 46. Permutations                          | [Solution][46] | Medium |
 | 51. N-Queens                              | Solution       | Hard   |
 | 78. Subsets                               | Solution       | Medium |
 | 79. Word Search                           | Solution       | Medium |
 | 131. Palindrome Partitioning              | Solution       | Medium |
 
 [17]: ./src/page-1/17.%20Letter%20Combinations%20of%20a%20Phone%20Number/letterCombinations.ts
+[39]: ./src/page-1/39.%20Combination%20Sum/combinationSum.ts
 [46]: ./src/page-1/46.%20Permutations/permute.ts
 
 | Binary Search                                               |                |        |

algorithms/13.backtracking/README.md

@@ -9,10 +9,10 @@
 ```ts
 const result = [];
 
-function backtrack(state) {
+function backtrack() {
   // 紀錄解
   if (x) {
-    push([...state]);
+    result.push();
     return;
   }
 
@@ -23,8 +23,8 @@ function backtrack(state) {
     // 嘗試
     push();
 
-    // 下一個
-    backtrack(state);
+    // 繼續探索下一個
+    backtrack();
 
     // 回退
     pop();

src/page-1/17. Letter Combinations of a Phone Number/letterCombinations.ts

@@ -24,6 +24,7 @@ export const letterCombinations: LetterCombinations = (digits) => {
       result.push(combination);
     } else {
       const digit = nextDigits[0];
+
       for (const letter of phone[digit]) {
         backtrack(combination + letter, nextDigits.slice(1));
       }

src/page-1/39. Combination Sum/combinationSum.test.ts

@@ -0,0 +1,15 @@
+import { combinationSum } from './combinationSum';
+
+describe('39. Combination Sum', () => {
+  test('combinationSum', () => {
+    expect(combinationSum([2, 3, 6, 7], 7)).toStrictEqual([[2, 2, 3], [7]]);
+
+    expect(combinationSum([2, 3, 5], 8)).toStrictEqual([
+      [2, 2, 2, 2],
+      [2, 3, 3],
+      [3, 5],
+    ]);
+
+    expect(combinationSum([2], 1)).toStrictEqual([]);
+  });
+});

src/page-1/39. Combination Sum/combinationSum.ts

@@ -0,0 +1,44 @@
+type CombinationSum = (candidates: number[], target: number) => number[][];
+
+/**
+ * Accepted
+ */
+export const combinationSum: CombinationSum = (candidates, target) => {
+  // Result array to store all unique combinations
+  const result: number[][] = [];
+
+  // Helper function to perform the backtracking
+  // remaining: the remaining target to achieve
+  // combination: current combination being built
+  // index: current candidate index to explore
+  function backtrack(remaining: number, combination: number[], index: number): void {
+    // Base case: if remaining is 0, we found a valid combination
+    if (remaining === 0) {
+      // Push a copy of the current combination to the result array
+      result.push([...combination]);
+      return;
+    }
+
+    // Loop through the candidates starting from the current index
+    for (let i = index; i < candidates.length; i++) {
+      // If the candidate is greater than the remaining target, skip it
+      if (candidates[i] > remaining) continue;
+
+      // Add the current candidate to the combination
+      combination.push(candidates[i]);
+
+      // Recurse by reducing the remaining target by the current candidate's value
+      // and keeping the same index since we can use the same number multiple times
+      backtrack(remaining - candidates[i], combination, i);
+
+      // Backtrack by removing the last candidate added
+      combination.pop();
+    }
+  }
+
+  // Start the backtracking process with the initial target and an empty combination
+  backtrack(target, [], 0);
+
+  // Return the list of all valid combinations
+  return result;
+};