Add solution #688

Author: JoshCrozier

README.md

@@ -519,6 +519,7 @@
 685|[Redundant Connection II](./0685-redundant-connection-ii.js)|Hard|
 686|[Repeated String Match](./0686-repeated-string-match.js)|Easy|
 687|[Longest Univalue Path](./0687-longest-univalue-path.js)|Medium|
+688|[Knight Probability in Chessboard](./0688-knight-probability-in-chessboard.js)|Medium|
 693|[Binary Number with Alternating Bits](./0693-binary-number-with-alternating-bits.js)|Easy|
 695|[Max Area of Island](./0695-max-area-of-island.js)|Medium|
 696|[Count Binary Substrings](./0696-count-binary-substrings.js)|Easy|

solutions/0688-knight-probability-in-chessboard.js

@@ -0,0 +1,49 @@
+/**
+ * 688. Knight Probability in Chessboard
+ * https://leetcode.com/problems/knight-probability-in-chessboard/
+ * Difficulty: Medium
+ *
+ * On an n x n chessboard, a knight starts at the cell (row, column) and attempts to make exactly
+ * k moves. The rows and columns are 0-indexed, so the top-left cell is (0, 0), and the bottom-right
+ * cell is (n - 1, n - 1).
+ *
+ * A chess knight has eight possible moves it can make, as illustrated below. Each move is two cells
+ * in a cardinal direction, then one cell in an orthogonal direction.
+ *
+ * Each time the knight is to move, it chooses one of eight possible moves uniformly at random
+ * (even if the piece would go off the chessboard) and moves there.
+ *
+ * The knight continues moving until it has made exactly k moves or has moved off the chessboard.
+ *
+ * Return the probability that the knight remains on the board after it has stopped moving.
+ */
+
+/**
+ * @param {number} n
+ * @param {number} k
+ * @param {number} row
+ * @param {number} column
+ * @return {number}
+ */
+var knightProbability = function(n, k, row, column) {
+  const moves = [[-2, -1], [-2, 1], [-1, -2], [-1, 2], [1, -2], [1, 2], [2, -1], [2, 1]];
+  const dp = new Map();
+
+  return calc(k, row, column);
+
+  function calc(movesLeft, r, c) {
+    if (r < 0 || r >= n || c < 0 || c >= n) return 0;
+    if (movesLeft === 0) return 1;
+
+    const key = `${movesLeft},${r},${c}`;
+    if (dp.has(key)) return dp.get(key);
+
+    let prob = 0;
+    for (const [dr, dc] of moves) {
+      prob += calc(movesLeft - 1, r + dr, c + dc) / 8;
+    }
+
+    dp.set(key, prob);
+    return prob;
+  }
+};