Feat: 62. Unique Paths

Author: HC-kang

unique-paths/HC-kang.ts

@@ -0,0 +1,65 @@
+/**
+ * Solution 1. recursive - failed with Stack Overflow
+ */
+function uniquePaths(m: number, n: number): number {
+  function factorialMemo() {
+    const cache = [0, 1];
+    return function factorial(n: number) {
+      if (cache[n]) return cache[n];
+      cache[n] = n * factorial(n - 1);
+      return cache[n];
+    };
+  }
+
+  const factorial = factorialMemo();
+  const total = m + n - 2;
+  const right = m - 1;
+  return Math.round(
+    factorial(total) / (factorial(right) * factorial(total - right))
+  );
+}
+
+/**
+ * Solution 2. for loop (with some 야매.. but it works)
+ * https://leetcode.com/problems/unique-paths
+ * T.C. O(m + n)
+ * S.C. O(m + n)
+ */
+function uniquePaths(m: number, n: number): number {
+  function factorialMemo() {
+    const cache = [1, 1];
+    return function factorial(n: number) {
+      if (cache[n]) return cache[n];
+      let result = cache[cache.length - 1];
+      for (let i = cache.length; i <= n; i++) {
+        result = result * i;
+        cache[i] = result;
+      }
+      return result;
+    };
+  }
+
+  const factorial = factorialMemo();
+  const total = m + n - 2;
+  const right = m - 1;
+  return Math.round(
+    factorial(total) / (factorial(right) * factorial(total - right))
+  );
+}
+
+/**
+ * Solution 3. DP
+ * T.C. O(m * n)
+ * S.C. O(m * n)
+ */
+function uniquePaths(m: number, n: number): number {
+  const dp: number[][] = Array.from({ length: m }, () => Array(n).fill(1));
+
+  for (let i = 1; i < m; i++) {
+    for (let j = 1; j < n; j++) {
+      dp[i][j] = dp[i - 1][j] + dp[i][j - 1];
+    }
+  }
+
+  return dp[m - 1][n - 1];
+}