add 668

Author: fishercoder1534

README.md

@@ -22,6 +22,7 @@ Your ideas/fixes/algorithms are more than welcome!
 
 |  #  |      Title     |   Solutions   | Time          | Space         | Difficulty  | Tag          | Notes
 |-----|----------------|---------------|---------------|---------------|-------------|--------------|-----
+|668|[Kth Smallest Number in Multiplication Table](https://leetcode.com/problems/kth-smallest-number-in-multiplication-table/)|[Solution](../master/src/main/java/com/fishercoder/solutions/_668.java) | O(logm*n) | O(1) | Hard | Binary Search
 |666|[Path Sum IV](https://leetcode.com/problems/path-sum-iv/)|[Solution](../master/src/main/java/com/fishercoder/solutions/_666.java) | O(1) | O(1) | Medium | Tree, DFS
 |665|[Non-decreasing Array](https://leetcode.com/problems/non-decreasing-array/)|[Solution](../master/src/main/java/com/fishercoder/solutions/_665.java) | O(n) | O(n) | Easy |
 |664|[Strange Printer](https://leetcode.com/problems/strange-printer/)|[Solution](../master/src/main/java/com/fishercoder/solutions/_664.java) | O(n^3) | O(n^2) | Hard | DP

src/main/java/com/fishercoder/solutions/_668.java

@@ -0,0 +1,93 @@
+package com.fishercoder.solutions;
+
+import java.util.PriorityQueue;
+
+/**
+ * 668. Kth Smallest Number in Multiplication Table
+ *
+ *  Nearly every one have used the Multiplication Table.
+ *  But could you find out the k-th smallest number quickly from the multiplication table?
+ *  Given the height m and the length n of a m * n Multiplication Table,
+ *  and a positive integer k, you need to return the k-th smallest number in this table.
+
+ Example 1:
+ Input: m = 3, n = 3, k = 5
+ Output:
+ Explanation:
+ The Multiplication Table:
+ 1	2	3
+ 2	4	6
+ 3	6	9
+
+ The 5-th smallest number is 3 (1, 2, 2, 3, 3).
+
+
+ Example 2:
+ Input: m = 2, n = 3, k = 6
+ Output:
+ Explanation:
+ The Multiplication Table:
+ 1	2	3
+ 2	4	6
+
+ The 6-th smallest number is 6 (1, 2, 2, 3, 4, 6).
+
+ Note:
+
+ The m and n will be in the range [1, 30000].
+ The k will be in the range [1, m * n]
+ */
+
+public class _668 {
+    public static class Solution1 {
+        /**
+         * This brute force approach resulted in
+         * TLE on Leetcode and
+         * OOM error by _668test.test3() when running in my localhost:
+         * java.lang.OutOfMemoryError: Java heap space
+         * at java.util.Arrays.copyOf(Arrays.java:3210)
+         * at java.util.Arrays.copyOf(Arrays.java:3181)
+         * at java.util.PriorityQueue.grow(PriorityQueue.java:300)
+         * at java.util.PriorityQueue.offer(PriorityQueue.java:339)
+         */
+        public int findKthNumber(int m, int n, int k) {
+            PriorityQueue<Integer> minHeap = new PriorityQueue<>((a, b) -> a - b);
+            for (int i = 1; i <= m; i++) {
+                for (int j = 1; j <= n; j++) {
+                    minHeap.offer(i * j);
+                }
+            }
+            while (k-- > 1) {
+                minHeap.poll();
+            }
+            return minHeap.peek();
+        }
+    }
+
+    public static class Solution2 {
+        /**reference: https://discuss.leetcode.com/topic/101132/java-solution-binary-search*/
+        public int findKthNumber(int m, int n, int k) {
+            int low = 1;
+            int high = m * n + 1;
+            while (low < high) {
+                int mid = low + (high - low) / 2;
+                int c = count(mid, m, n);
+                if (c >= k) {
+                    high = mid;
+                } else {
+                    low = mid + 1;
+                }
+            }
+            return high;
+        }
+
+        int count(int v, int m, int n) {
+            int count = 0;
+            for (int i = 1; i <= m; i++) {
+                int temp = Math.min(v / i, n);
+                count += temp;
+            }
+            return count;
+        }
+    }
+}

src/test/java/com/fishercoder/_668Test.java

@@ -0,0 +1,37 @@
+package com.fishercoder;
+
+import com.fishercoder.solutions._668;
+import org.junit.BeforeClass;
+import org.junit.Test;
+
+import static junit.framework.TestCase.assertEquals;
+
+public class _668Test {
+    private static _668.Solution1 solution1;
+    private static _668.Solution2 solution2;
+
+    @BeforeClass
+    public static void setup() {
+        solution1 = new _668.Solution1();
+        solution2 = new _668.Solution2();
+    }
+
+    @Test
+    public void test1() {
+        assertEquals(3, solution1.findKthNumber(3, 3, 5));
+        assertEquals(3, solution2.findKthNumber(3, 3, 5));
+    }
+
+    @Test
+    public void test2() {
+        assertEquals(6, solution1.findKthNumber(2, 3, 6));
+        assertEquals(6, solution2.findKthNumber(2, 3, 6));
+    }
+
+    @Test
+    public void test3() {
+//        assertEquals(31666344, solution1.findKthNumber(9895, 28405, 100787757));//this will run into OOM error, so comment out
+        assertEquals(31666344, solution2.findKthNumber(9895, 28405, 100787757));
+    }
+
+}