Add solution for 935 (#60)

Author: havanagrawal

README.md

@@ -60,6 +60,7 @@ Your ideas/fixes/algorithms are more than welcome!
 |941|[Valid Mountain Array](https://leetcode.com/problems/valid-mountain-array/)|[Solution](../master/src/main/java/com/fishercoder/solutions/_941.java) | O(n) | O(1) | |Easy|
 |938|[Range Sum of BST](https://leetcode.com/problems/range-sum-of-bst/)|[Solution](../master/src/main/java/com/fishercoder/solutions/_938.java) | O(n) | O(n) | |Medium| BST, recursion, DFS
 |937|[Reorder Log Files](https://leetcode.com/problems/reorder-log-files/)|[Solution](../master/src/main/java/com/fishercoder/solutions/_937.java) | O(n) | O(n) | |Easy|
+|935|[Knight Dialer](https://leetcode.com/problems/knight-dialer/)|[Solution](../master/src/main/java/com/fishercoder/solutions/_935.java) | O(n) | O(1) | |Medium|
 |933|[Number of Recent Calls](https://leetcode.com/problems/number-of-recent-calls/)|[Solution](../master/src/main/java/com/fishercoder/solutions/_933.java) | O(n) | O(n) | |Easy|
 |929|[Unique Email Addresses](https://leetcode.com/problems/unique-email-addresses/)|[Solution](../master/src/main/java/com/fishercoder/solutions/_929.java) | O(n) | O(n) | |Easy|
 |925|[Long Pressed Name](https://leetcode.com/problems/long-pressed-name/)|[Solution](../master/src/main/java/com/fishercoder/solutions/_925.java) | O(n) | O(1) | |Easy|

src/main/java/com/fishercoder/solutions/_935.java

@@ -0,0 +1,89 @@
+package com.fishercoder.solutions;
+
+/**
+ * A chess knight can move as indicated in the chess diagram below:
+ *
+ * https://assets.leetcode.com/uploads/2018/10/12/knight.png
+ *
+ * |---|---|---|
+ * | 1 | 2 | 3 |
+ * |---|---|---|
+ * | 4 | 5 | 6 |
+ * |---|---|---|
+ * | 7 | 8 | 9 |
+ * |---|---|---|
+ * | x | 0 | x |
+ * |---|---|---|
+ *
+ * This time, we place our chess knight on any numbered key of a phone pad (indicated above), and the knight makes N-1 hops.
+ * Each hop must be from one key to another numbered key.
+ *
+ * Each time it lands on a key (including the initial placement of the knight), it presses the number of that key, pressing N digits total.
+ *
+ * How many distinct numbers can you dial in this manner?
+ *
+ * Since the answer may be large, output the answer modulo 10^9 + 7.
+ *
+ * Note:
+ *  * 1 <= N <= 5000
+ */
+
+public class _935 {
+    /*
+     * The intuition is to calculate the number of ways
+     * we can reach a key k after i hops, based on the number of ways we can reach keys x after i-1 hops
+     * s.t. the knight can move from x to k in one move
+     * For example,
+     * We can reach 6 in 3 ways after 1 hop (1 -> 6, 7 -> 6 or 0 -> 6)
+     * We can reach 8 in 2 ways after 1 hop (1 -> 8 or 3 -> 8)
+     * Thus, we can reach 1 in 5 ways after 2 hops:
+     * . 1. 1 -> 6 -> 1
+     * . 2. 7 -> 6 -> 1
+     * . 3. 0 -> 6 -> 1
+     *   4. 1 -> 8 -> 1
+     *   5. 3 -> 8 -> 1
+     */
+    public static class Solution1 {
+        private static final int MOD = 1000_000_007;
+
+        // whereFromHere[i] is an array of keys that can be reached from the ith digit
+        private static final int[][] whereFromHere = {
+            {4, 6},    {6, 8},  {7, 9},    {4, 8},  // 0, 1, 2, 3
+            {3, 9, 0}, {},      {1, 7, 0},          // 4, 5, 6
+            {2, 6},    {1, 3},  {2, 4}              // 7, 8, 9
+        };
+
+        public int knightDialer(int N) {
+            // a[i] is the number of ways we can end up on the ith digit
+            // The initial array is for N = 1, i.e. for 0 hops.
+            long[] a = new long[]{1, 1, 1, 1, 1, 1, 1, 1, 1, 1};
+
+            // Simulate N - 1 hops
+            for (int i = 0; i < N - 1; ++i) {
+                long[] tmp = new long[10];
+
+                // For each digit
+                for (int j = 0; j < 10; j++) {
+                    // Which other digits can we reach?
+                    for (int k : whereFromHere[j]) {
+                        tmp[j] = (tmp[j] + a[k]) % MOD;
+                    }
+                }
+
+                // Sanity checks based on symmetry of the keypad
+                assert tmp[1] == tmp[3];
+                assert tmp[4] == tmp[6];
+                assert tmp[7] == tmp[9];
+
+                a = tmp;
+            }
+
+            long ans = 0;
+            for (long k : a) {
+                ans = (ans + k) % MOD;
+            }
+
+            return (int) ans;
+        }
+    }
+}

src/test/java/com/fishercoder/_935Test.java

@@ -0,0 +1,29 @@
+package com.fishercoder;
+
+import com.fishercoder.solutions._935;
+import org.junit.BeforeClass;
+import org.junit.Test;
+
+import static org.junit.Assert.assertEquals;
+
+public class _935Test {
+    private static _935.Solution1 solution1;
+
+    @BeforeClass
+    public static void setup() { solution1 = new _935.Solution1(); }
+
+    @Test
+    public void test1() {
+        assertEquals(solution1.knightDialer(1), 10);
+    }
+
+    @Test
+    public void test2() {
+        assertEquals(solution1.knightDialer(2), 20);
+    }
+
+    @Test
+    public void test3() {
+        assertEquals(solution1.knightDialer(3), 46);
+    }
+}