Added problem for BitManipulation and DynamicProgramming

Author: Prashant Jain

src/in/knowledgegate/dsa/bitmanipulation/MissingNumber.java

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+package in.knowledgegate.dsa.bitmanipulation;
+
+/**
+ * Given an array nums containing n distinct numbers
+ * in the range [0, n], return the only number
+ * in the range that is missing from the array.
+ *
+ *
+ * Example 1:
+ * Input: nums = [3,0,1]
+ * Output: 2
+ * Explanation: n = 3 since there are 3 numbers,
+ * so all numbers are in the range [0,3]. 2 is the
+ * missing number in the range since it does not
+ * appear in nums.
+ *
+ * Example 2:
+ * Input: nums = [0,1]
+ * Output: 2
+ * Explanation: n = 2 since there are 2 numbers,
+ * so all numbers are in the range [0,2]. 2 is the
+ * missing number in the range since it does not
+ * appear in nums.
+ *
+ * Example 3:
+ * Input: nums = [9,6,4,2,3,5,7,0,1]
+ * Output: 8
+ * Explanation: n = 9 since there are 9 numbers,
+ * so all numbers are in the range [0,9]. 8 is the
+ * missing number in the range since it does not
+ * appear in nums.
+ *
+ *
+ * Constraints:
+ * n == nums.length
+ * 1 <= n <= 104
+ * 0 <= nums[i] <= n
+ * All the numbers of nums are unique.
+ */
+public class MissingNumber {
+  public int missingNumber(int[] nums) {
+    int num1 = 0, num2 = nums.length;
+    for (int i = 0; i < nums.length; i++) {
+      num1 = num1^nums[i];
+      num2 = num2^i;
+    }
+    return num1^num2;
+  }
+}

src/in/knowledgegate/dsa/dynamicprogramming/ClimbingStairs.java

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+package in.knowledgegate.dsa.dynamicprogramming;
+
+/**
+ * You are climbing a staircase. It takes n steps
+ * to reach the top.
+ *
+ * Each time you can either climb 1 or 2 steps.
+ * In how many distinct ways can you climb to
+ * the top?
+ *
+ * Example 1:
+ * Input: n = 2
+ * Output: 2
+ * Explanation: There are two ways to climb to the top.
+ * 1. 1 step + 1 step
+ * 2. 2 steps
+ *
+ * Example 2:
+ * Input: n = 3
+ * Output: 3
+ * Explanation: There are three ways to climb to the top.
+ * 1. 1 step + 1 step + 1 step
+ * 2. 1 step + 2 steps
+ * 3. 2 steps + 1 step
+ *
+ *
+ * Constraints:
+ * 1 <= n <= 45
+ */
+public class ClimbingStairs {
+  /**
+   * f(n) = f(n-1) + f(n-2)
+   */
+  public int climbStairs(int n) {
+    if (n == 1) return 1;
+    if (n == 2) return 2;
+
+    int first = 1, second = 2, current = 0;
+    for (int i = 2; i < n; i++) {
+      current = first + second;
+      first = second;
+      second = current;
+    }
+    return current;
+  }
+}