Bitonic Sequence and Wiggle Subsequence

Author: kalpak92

Dynamic Programming/Bitonic Sequence/BitonicSequence.java

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+/**
+ * A sequence of numbers is called a bitonic sequence if the differences between successive numbers strictly alternate between positive and negative. The first difference (if one exists) may be either positive or negative. 
+ * A sequence with fewer than two elements is trivially a wiggle sequence.
+ */
+
+ public class BitonicSequence
+ {
+     public int getMaxLenBitonicSeq(int[] arr)
+     {
+        int[] lis = new int[arr.length];
+        int[] lds = new int[arr.length];
+
+        for(int i = 0; i < arr.length; i++)
+        {
+            lis[i] = 1;
+            lds[i] = 1;
+        }
+
+        for(int i = 1; i < arr.length; i++)
+        {
+            for(int j = 0; j < i; j++)
+            {
+                if(arr[j] < arr[i])
+                    lis[i] = Math.max(lis[i], lis[j] + 1);
+            }
+        }
+
+        for(int i = arr.length - 2; i >= 0; i--)
+        {
+            for(int j = arr.length - 1; j > i; j--)
+            {
+                if(arr[i] > arr[j])
+                    lds[i] = Math.max(lds[i], lds[j] + 1);
+            }
+        }
+
+        int max = 0;
+        for(int i = 0; i < arr.length; i++)
+        {
+            if(max < lis[i] + lds[i] - 1)
+                max = lis[i] + lds[i] - 1;
+        }
+
+        return max;
+     }
+
+     public static void main(String[] args)
+     {
+         BitonicSequence bs = new BitonicSequence();
+         int[] arr = {1,4,3,7,2,1,8,11,13,0};
+         int[] arr2 = {1,7,4,9,2,5};
+         System.out.println(bs.getMaxLenBitonicSeq(arr2));
+     }
+ }

Dynamic Programming/Count occurence of subsquence in a given string/Solution.java

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+/**
+ * Given two strings, find the number of times the second string occurs in the first string, whether continuous or discontinuous.
+ * 
+ * Examples:
+ * Input:  
+ * string a = "GeeksforGeeks"
+ * string b = "Gks"
+ * 
+ * Output: 4
+ * 
+ * Explanation:  
+ * The four strings are 
+ *      'G'ee'k''s'forGeeks
+ *      'G'eeksforGee'k''s'
+ *      'G'ee'k'sforGeek's'
+ *      Geeksfor'G'ee'k''s'
+ */
+
+class Solution  
+{ 
+      
+    public static int count(String a, String b) 
+    { 
+        int m = a.length(); 
+        int n = b.length(); 
+    
+        int dp[][] = new int[m + 1][n + 1]; 
+    
+        // If first string is empty 
+        for (int i = 0; i <= n; ++i) 
+            dp[0][i] = 0; 
+    
+        // If second string is empty 
+        for (int i = 0; i <= m; ++i) 
+            dp[i][0] = 1; 
+    
+        // Fill dp[][] in  
+        // bottom up manner 
+        for (int i = 1; i <= m; i++) 
+        { 
+            for (int j = 1; j <= n; j++) 
+            { 
+                // If last characters are  
+                // same, we have two options - 
+                // 1. consider last characters  
+                //    of both strings in solution 
+                // 2. ignore last character 
+                //    of first string 
+                if (a.charAt(i - 1) == b.charAt(j - 1)) 
+                    dp[i][j] = dp[i - 1][j - 1] +  
+                                dp[i - 1][j]; 
+                    
+                else
+                    // If last character are  
+                    // different, ignore last 
+                    // character of first string 
+                    dp[i][j] = dp[i - 1][j]; 
+            } 
+        } 
+    
+        return dp[m][n]; 
+    } 
+  
+    // Driver Code 
+    public static void main (String[] args) 
+    { 
+        Solution obj = new Solution();
+        String a = "GeeksforGeeks"; 
+        String b = "Gks"; 
+        
+        System.out.println(obj.count(a, b)); 
+    } 
+} 

LeetCode/376. Wiggle Subsequence/Solution.java

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+/**
+ * A sequence of numbers is called a wiggle sequence if the differences between successive numbers strictly alternate between positive and negative. 
+ * The first difference (if one exists) may be either positive or negative. 
+ * A sequence with fewer than two elements is trivially a wiggle sequence.
+ * 
+ * For example, [1,7,4,9,2,5] is a wiggle sequence because the differences (6,-3,5,-7,3) are alternately positive and negative. 
+ * In contrast, [1,4,7,2,5] and [1,7,4,5,5] are not wiggle sequences, \
+ * the first because its first two differences are positive and the second because its last difference is zero.
+ * 
+ * Given a sequence of integers, return the length of the longest subsequence that is a wiggle sequence. 
+ * A subsequence is obtained by deleting some number of elements (eventually, also zero) from the original sequence, leaving the remaining elements in their original order.
+ * Example 1:
+ * Input: [1,7,4,9,2,5]
+ * Output: 6
+ * Explanation: The entire sequence is a wiggle sequence.
+ * 
+ * Example 2:
+ * Input: [1,17,5,10,13,15,10,5,16,8]
+ * Output: 7
+ * Explanation: There are several subsequences that achieve this length. One is [1,17,10,13,10,16,8].
+ * 
+ * Example 3:
+ * Input: [1,2,3,4,5,6,7,8,9]
+ * Output: 2
+ */
+
+class Solution {
+    public int wiggleMaxLength(int[] nums) {
+        if(nums.length == 0)
+            return 0;
+        
+        /**
+         * If nums[i] > nums[i-1], that means it wiggles up. the element before it must be a down position. 
+         *   so up[i] = down[i-1] + 1; down[i] keeps the same with before.
+         *   
+         * If nums[i] < nums[i-1], that means it wiggles down. the element before it must be a up position. 
+         *    so down[i] = up[i-1] + 1; up[i] keeps the same with before.
+         *
+         * If nums[i] == nums[i-1], that means it will not change anything becasue it didn't wiggle at all. so both down[i] and up[i] keep the same.
+         */
+        
+        int up = 1, down = 1;
+        
+        for(int i = 1; i < nums.length; i++)
+        {
+            if(nums[i] > nums[i - 1])
+            {
+                up = down + 1;
+            }
+            else if (nums[i] < nums[i - 1])
+            {
+                down = up + 1;
+            }
+        }
+        
+        return Math.max(up, down);
+    }
+}

LeetCode/README.md

@@ -267,6 +267,7 @@
 - [x] [Delete Operations for Two Strings](https://github.com/kalpak92/DataStructures_Algorithms/tree/master/LeetCode/583.%20Delete%20Operations%20for%20Two%20Strings)
 - [x] [Longest Increasing Subsequence](https://github.com/kalpak92/DataStructures_Algorithms/tree/master/LeetCode/300%20Longest%20Increasing%20Subsequence)
 - [x] [Shortest Common Supersequence](https://github.com/kalpak92/DataStructures_Algorithms/tree/master/LeetCode/1092.%20Shortest%20Common%20Supersequence)
+- [x] [Wiggle Subsequence]()
 - [x] [Word Break](https://github.com/kalpak92/DataStructures_Algorithms/tree/master/LeetCode/139.%20Word%20Break)
 - [x] [Decode Ways](https://github.com/kalpak92/DataStructures_Algorithms/tree/master/LeetCode/91.%20Decode%20Ways)
 - [x] [Minimum Path Sum](https://github.com/kalpak92/DataStructures_Algorithms/tree/master/LeetCode/64.%20Minimum%20Path%20Sum)