[Jeehay28] WEEK 03 solutions

combination-sum/Jeehay28.ts

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+// Approach 2: Dynamic Programming
+// ✅ Time Complexity: O(N * T * K)
+// ✅ Space Complexity: O(T * K)
+// N = Number of candidates, T = target, K = average number of combination for each dp[i]
+
+function combinationSum(candidates: number[], target: number): number[][] {
+  // candidates = [2, 3]
+  // target = 5
+  // dp = [
+  //     [[]],         // dp[0]
+  //     [],           // dp[1]
+  //     [[2]],        // dp[2]
+  //     [],           // dp[3]
+  //     [[2, 2]],     // dp[4]
+  //     []            // dp[5]
+  // ];
+
+  // dp = [
+  //     [[]],         // dp[0]
+  //     [],           // dp[1]
+  //     [[2]],        // dp[2]
+  //     [[3]],        // dp[3]
+  //     [[2, 2]],     // dp[4]
+  //     [[2, 3]]      // dp[5]
+  // ];
+
+  const dp: number[][][] = Array.from({ length: target + 1 }, () => []);
+  // each element in dp is an independent array, and modifying one will not affect others.
+  dp[0] = [[]];
+
+  for (const candidate of candidates) {
+    for (let num = candidate; num <= target; num++) {
+      for (const combination of dp[num - candidate]) {
+        dp[num].push([...combination, candidate]);
+      }
+    }
+  }
+
+  return dp[target];
+}
+
+// Approach 1: DFS + Backtracking (Recursive)
+// ✅ Time Complexity: O(N^(T / min))
+// ✅ Space Complexity: O(K + target / min)
+// If target = 7 and smallest number is 2, recursion can go up to  7 / 2 = levels deep
+// N = number of candidates, T = target value, K = total number of valid combination found
+
+// function combinationSum(candidates: number[], target: number): number[][] {
+//   // input:
+//   // 1) an array of distinct integers
+//   // 2) a target integer
+
+//   // output:
+//   // a list of all unique combinations of candinates where the chosen numbers sum to target(in any order)
+//   // duplicated numbers allowed
+
+//   let result: number[][] = [];
+//   let nums: number[] = [];
+
+//   const dfs = (start: number, total: number) => {
+//     if (total > target) {
+//       return;
+//     }
+
+//     if (total === target) {
+//       result.push([...nums]);
+//       return;
+//     }
+
+//     for (let i = start; i < candidates.length; i++) {
+//       if (total + nums[i] <= target) {
+//         nums.push(candidates[i]);
+//         dfs(i, total + candidates[i]);
+//         nums.pop(); // backtrack
+//       }
+//     }
+//   };
+
+//   dfs(0, 0);
+
+//   return result;
+// }

decode-ways/Jeehay28.ts

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+// Approach 4:
+// Time Complexity: O(n)
+// ✅ Space Complexity: O(1)
+
+function numDecodings(s: string): number {
+  // s:   2 2 6
+  // dp:    ? ? 1
+  //       cur nxt
+
+  let next = 0,
+    current = 1;
+
+  for (let start = s.length - 1; start >= 0; start--) {
+    const temp = current;
+
+    if (s[start] === "0") {
+      // dp[start] = 0
+      current = 0;
+      next = temp;
+    } else if (
+      start + 1 < s.length &&
+      parseInt(s.substring(start, start + 2)) < 27
+    ) {
+      // dp[start] = dp[start + 1] + dp[start + 2]
+      current = current + next;
+      next = temp;
+    } else {
+      // dp[start] = dp[start + 1]
+      next = temp;
+    }
+  }
+  return current;
+}
+
+
+// Approach 3: Dynamic Programming
+// Time Complexity: O(n)
+// Space Complexity: O(n)
+
+// function numDecodings(s: string): number {
+//   //    12
+//   // dp 001
+//   //    211
+
+//   //    226
+//   // dp 0001
+//   //    3211
+
+//   const dp = Array.from({ length: s.length + 1 }, (el) => 0);
+//   dp[dp.length - 1] = 1;
+
+//   for (let start = s.length - 1; start >= 0; start--) {
+//     if (s[start] === "0") {
+//       dp[start] = 0;
+//     } else if (
+//       start + 1 < s.length &&
+//       parseInt(s.substring(start, start + 2)) < 27
+//     ) {
+//       dp[start] = dp[start + 1] + dp[start + 2];
+//     } else {
+//       dp[start] = dp[start + 1];
+//     }
+//   }
+
+//   return dp[0];
+// }
+
+
+// Approach 2
+// ✅ Time Complexity: O(2^n) -> O(n)
+// Space Complexity: O(n)
+
+// function numDecodings(s: string): number {
+//   const memo = new Map<number, number>();
+//   memo.set(s.length, 1);
+
+//   const dfs = (start: number) => {
+//     if (memo.has(start)) return memo.get(start);
+//     if (s[start] === "0") {
+//       memo.set(start, 0);
+//     } else if (
+//       start + 1 < s.length &&
+//       parseInt(s.substring(start, start + 2)) < 27
+//     ) {
+//       memo.set(start, dfs(start + 1)! + dfs(start + 2)!);
+//     } else {
+//       memo.set(start, dfs(start + 1)!);
+//     }
+//     return memo.get(start);
+//   };
+//   return dfs(0)!;
+// }
+
+
+// Approach 1
+// ❌ Time Limit Exceeded!
+// Time Complexity: O(2^n), where n = s.length
+// Space Compexity: O(n), due to recursive call stack
+// function numDecodings(s: string): number {
+//   const dfs = (start: number) => {
+//     if (start === s.length) {
+//       return 1;
+//     }
+
+//     if (s[start] === "0") {
+//       return 0;
+//     }
+
+//     if (start + 1 < s.length && parseInt(s.substring(start, start + 2)) < 27) {
+//       return dfs(start + 1) + dfs(start + 2);
+//     } else {
+//       return dfs(start + 1);
+//     }
+//   };
+
+//   return dfs(0);
+// }

maximum-subarray/Jeehay28.ts

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+// Approach 1:
+// Time Complexity: O(n)
+// Space Complexity: O(1)
+
+function maxSubArray(nums: number[]): number {
+  let currentSum = nums[0];
+  let maxSum = nums[0];
+
+  for (let i = 1; i < nums.length; i++) {
+    currentSum = Math.max(nums[i], currentSum + nums[i]);
+    maxSum = Math.max(currentSum, maxSum);
+  }
+
+  return maxSum;
+}
+

number-of-1-bits/Jeehay28.ts

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+// Approach 2
+// 🗓️ 2025-04-15
+// ⏳ Time Complexity: O(log n)
+// 💾 Space Complexity: O(1)
+
+function hammingWeight(n: number): number {
+  // n(이진수) & 1 -> 1: 이진수 n의 마지막 비트가 1인 경우에만 1 반환
+  // n(이진수) >> 1: 마지막 비트 제거
+  // 🔍 In binary numbers:
+  // Decimal: 11
+  // Binary:  1   0   1   1
+  //          ↑           ↑
+  //         MSB         LSB
+  //     (Most Sig.)   (Least Sig.)
+  // n & 1: only checks the least significant bit (LSB), if the LSB is 1, the result is 1.
+  // n >>= 1: Each bit is moved one place to the right.
+
+  let count = 0;
+
+  while (n) {
+    count += n & 1; // add 1 if the least significant bit of n is 1
+    n >>= 1; // The LSB is removed (dropped).
+  }
+
+  return count;
+}
+
+
+// Approach 1
+// 🗓️ 2025-04-15
+// ⏳ Time Complexity: O(log n)
+// 💾 Space Complexity: O(1)
+
+// function hammingWeight(n: number): number {
+//   // input: a positive number n
+//   // output: the number of set bits in binary representation
+//   // set bits: a bit in the binary representaton of a number that has a value of 1
+//   // 11 -> 1011 -> 3
+
+//   let cnt = 0;
+//   while (n > 0) {
+//     if (n % 2 === 1) {
+//       cnt += 1;
+//     }
+//     n = Math.floor(n / 2);
+//   }
+
+//   return cnt;
+// }
+

valid-palindrome/Jeehay28.ts

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+// Approach 2
+// 🗓️ 2025-04-14
+// ⏳ Time Complexity: O(n)
+// 💾 Space Complexity: O(1)
+
+function isPalindrome(s: string): boolean {
+  let low = 0, high = s.length - 1;
+  const reg = /[0-9a-zA-Z]/;
+
+  while (low < high) {
+    while (low < high && !reg.test(s[low])) {
+      low += 1;
+    }
+
+    while (low < high && !reg.test(s[high])) {
+      high -= 1;
+    }
+
+    if (s[low].toLowerCase() !== s[high].toLowerCase()) {
+      return false;
+    }
+    low += 1;
+    high -= 1;
+  }
+
+  return true;
+}
+
+
+// Approach 1
+// 🗓️ 2025-04-14
+// ⏳ Time Complexity: O(n)
+// 💾 Space Complexity: O(n)
+
+// function isPalindrome(s: string): boolean {
+//   // cover all uppercase letters into lowercasse letters
+//   // remove all non-alphanumeric characters (letters and numbers)
+//   // it reads the same forward and backward
+
+//   const cleaned = s.toLowerCase().match(/[0-9a-z]/g);
+
+//   // Converting to lowercase (toLowerCase()): O(n), where n is the length of the string
+//   // Matching with regex (match(/[0-9a-z]/g)): O(n), where n is the length of the string, as the regex engine needs to check each character in the string
+//   // join("") operation: O(m), where m is the length of the cleaned array.
+//   // reverse() operation: O(m), where m is the length of the cleaned array.
+//   // Comparison (s_forward === s_backward): O(n) because it checks each character one by one
+
+//   if (cleaned !== null) {
+//     const s_forward = cleaned.join("");
+//     const s_backward = cleaned.reverse().join("");
+//     return s_forward === s_backward;
+//   } else {
+//     return true;
+//   }
+// }