4. Unique Paths

Author: Sunjae95

unique-paths/sunjae95.js

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+/**
+ * @description
+ * brainstorming:
+ * 1. dfs -> time limited
+ * 2. dynamic programming
+ *
+ * time complexity: O(m * n)
+ * space complexity: O(m * n)
+ */
+
+var uniquePaths = function (m, n) {
+  // initialize
+  const dp = Array.from({ length: m }, (_, i) =>
+    Array.from({ length: n }, (_, j) => (i === 0 || j === 0 ? 1 : 0))
+  );
+
+  for (let i = 1; i < m; i++) {
+    for (let j = 1; j < n; j++) {
+      // recurrence relation
+      dp[i][j] = dp[i - 1][j] + dp[i][j - 1];
+    }
+  }
+
+  return dp[m - 1][n - 1];
+};