Day-71 Two divide and conquer problems

Author: mandliya

README.md

@@ -6,9 +6,9 @@
 
 | Current Status|     Stats     |
 | :------------: | :----------: |
-| Total Problems | 101 |
-| Current Streak | 70 days |
-| Longest Streak | 70 ( August 17, 2015 - October 25, 2015 ) |
+| Total Problems | 103 |
+| Current Streak | 71 days |
+| Longest Streak | 71 ( August 17, 2015 - October 26, 2015 ) |
 
 </center>
 
@@ -150,6 +150,8 @@ Include contains single header implementation of data structures and some algori
 | :------------ | :----------: |
 | Given a sorted vector, return first index of the occurrence of a value in vector, if number does not exist, return -1 | [first_occurrence_binary_search.cpp](sort_search_problems/first_occurrence_binary_search.cpp) |
 | Given a list of unsorted integers, A={a<sub>1</sub>,a<sub>2</sub>,…,a<sub>N</sub>}, Find the pair of elements that have the smallest absolute difference between them? If there are multiple pairs, find them all.| [closest_numbers.cpp](sort_search_problems/closest_numbers.cpp)|
+| Given a sorted array, determine index of fixed point in this array. If array does not have a fixed point return -1. An array has a fixed point when index of the element is same as index i.e. i == arr[i], Expected time complexity O(logn)| [fixedPoint.cpp](sort_search_problems/fixedPoint.cpp)|
+| Find the maximum element in an array which is first increasing and then decreasing. Input: arr[] = {8, 10, 20, 80, 100, 200, 400, 500, 3, 2, 1}, output : 500. Array may be strictly increasing or decreasing as well. ExpectedTime complexity is O(logn).| [findMaximum.cpp](sort_search_problems/findMaximum.cpp)|
 
 ### Graph Problems
 | Problem | Solution |

sort_search_problems/findMaximum.cpp

@@ -0,0 +1,65 @@
+/**
+ * Find the maximum element in an array which is first increasing and then decreasing.
+ * Input: arr[] = {8, 10, 20, 80, 100, 200, 400, 500, 3, 2, 1}
+ * Output: 500
+ *
+ * Also consider cases like
+ * Input: arr[] = {10, 20, 30, 40, 50}
+ * Output: 50
+ *
+ * Input: arr[] = {120, 100, 80, 20, 0}
+ * Output: 120
+ */
+
+#include <iostream>
+#include <vector>
+
+int findMaximum(std::vector<int> & arr, int low, int high) {
+	// subset has only one element
+	if ( high == low ) {
+		return arr[low];
+	}
+
+	//subset has 2 elements
+	if ( high - low == 1 ) {
+		return arr[high] > arr[low] ? arr[high] : arr[low];
+	}
+
+	int mid = ( high + low )/2;
+	if ( arr[mid-1] > arr[mid] ) {
+		return findMaximum(arr, low, mid-1);
+	} else {
+		return findMaximum(arr, mid+1, high);
+	}
+
+}
+
+void printVec( std::vector<int> & arr ) {
+	std::cout << "Arr:";
+	for ( auto & a : arr ) {
+		std::cout << a << " ";
+	}
+	std::cout << std::endl;
+}
+
+
+int main() {
+	std::vector<int> arr1{ 8, 10, 20, 80, 100, 200, 400, 500, 3, 2, 1 };
+	printVec(arr1);
+	std::cout << "Max in above arr:" << findMaximum( arr1, 0, arr1.size()-1 ) << std::endl;
+
+	std::vector<int> arr2{1, 3, 50, 10, 9, 7, 6};
+	printVec(arr2);
+	std::cout << "Max in above arr:" << findMaximum( arr2, 0, arr2.size()-1 ) << std::endl;
+
+
+	std::vector<int> arr3{10, 20, 30, 40, 50};
+	printVec(arr3);
+	std::cout << "Max in above arr:" << findMaximum( arr3, 0, arr3.size()-1 ) << std::endl;
+
+	std::vector<int> arr4{120, 100, 80, 20, 0};
+	printVec(arr4);
+	std::cout << "Max in above arr:" << findMaximum( arr4, 0, arr4.size()-1 ) << std::endl;
+
+	return 0;
+}

sort_search_problems/fixedPoint.cpp

@@ -0,0 +1,42 @@
+/**
+ * Given a sorted array of numbers, determine if there exists a fixed point, if so return index, or return -1. Fixed point in array is when i = arr[i].
+ */
+
+#include<iostream>
+#include<vector>
+
+int binarySearchFixedPoint( const std::vector<int> & arr) {
+	int high = arr.size() -1;
+	int low = 0;
+	while ( low <= high ) {
+		int mid = (low + high)/2;
+		if ( arr[mid] == mid ) {
+			return mid;
+		} else if ( mid > arr[mid] ) {
+			low = mid + 1;
+		} else {
+			high = mid - 1;
+		}
+	}
+	return -1;
+}
+
+void printVec( std::vector<int> & vec ) {
+	std::cout << "VEC:";
+	for ( auto & v : vec ) {
+		std::cout << v << " ";
+	}
+	std::cout << std::endl;
+}
+
+int main() {
+	std::vector<int> vec { -10, -1, 0, 3, 10, 11, 30, 50, 100 };
+	printVec(vec);
+	int fixedPoint = binarySearchFixedPoint(vec);
+	if (fixedPoint != -1) {
+		std::cout << "Above vector has a fixed point at index(0 indexed): " << fixedPoint << std::endl;
+	} else {
+		std::cout << "Above vector has no fixed point\n";
+	}
+	return 0;
+}