From 7544a92354c63acf40b362a2e902fc49efe4bc50 Mon Sep 17 00:00:00 2001 From: junnengsoo Date: Sun, 27 Aug 2023 00:26:13 +0800 Subject: [PATCH 1/2] Add readme and both binarySearch and binarySearchTemplated implementations --- assets/BinarySearch.png | Bin 0 -> 179900 bytes .../sorting/insertionSort/README.md | 3 - .../searches/binarySearch/BinarySearch.java | 49 +++++++++++ .../binarySearch/BinarySearchTemplated.java | 66 +++++++++++++++ .../searches/binarySearch/README.md | 78 ++++++++++++++++++ .../binarySearchTest/BinarySearchTest.java | 4 + 6 files changed, 197 insertions(+), 3 deletions(-) create mode 100644 assets/BinarySearch.png delete mode 100644 out/production/src/src/algorithms/sorting/insertionSort/README.md create mode 100644 src/algorithms/searches/binarySearch/BinarySearch.java create mode 100644 src/algorithms/searches/binarySearch/BinarySearchTemplated.java create mode 100644 src/algorithms/searches/binarySearch/README.md create mode 100644 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zvWEA3+(vU+Z7iRosfb~oSyd$0d|LY0scB3{5B$*9Z+&J@8Xt7TdxE03>A0?oggqE5ld2FpCl5VmvfLIAU_5!HuuaK9uOz z4(Jl_E3O!&ddvOjN@kV2y5ZgDt-_S zVE{oCjSSQ=@MtOl2PIzbnuw0+R%$#$LG!>P8ZUh2k8bqVTH$SrGnSnWC(GWB=HFOTl zaG4>+8Z%XM?#IL1DEbxy0>{bE6z_$(sWaJ?7{ zs$dY4Lz;S|GoE+)GalNvWz)|4uitvpgZmzysn71M?`vq9YKnth zx*xL_nwbQNoVni9C?NLOz?hBNRAOyBz(iumK# target) { + high = mid - 1; // -1 since current mid is not == target and should not be in the search range anymore + } else if (arr[mid] < target) { + low = mid + 1; // +1 since current mid is not == target and should not be in the search range anymore + } else { + return mid; + } + } + + return -1; + } +} \ No newline at end of file diff --git a/src/algorithms/searches/binarySearch/BinarySearchTemplated.java b/src/algorithms/searches/binarySearch/BinarySearchTemplated.java new file mode 100644 index 00000000..99ef02d4 --- /dev/null +++ b/src/algorithms/searches/binarySearch/BinarySearchTemplated.java @@ -0,0 +1,66 @@ +package src.algorithms.searches.binarySearch; + +/** Here, we are implementing BinarySearchTemplated where we search an array for a target value at O(log n) time + * complexity. + * + * Assumptions: + * The array is sorted in ascending order. + * All elements in the array are unique. (to allow for easy testing) + * + * Brief Description and Implementation Invariant: + * With the assumption that the array is sorted in ascending order, BinarySearchTemplated reduces the search range by + * half or half + 1 (due to floor division) after every loop. This is done by reassigning the max (high) or min (low) of + * the search range to the middle of the search range when the target value is smaller than or larger than the current + * middle value respectively, and continuing the search thereafter. + * + * In this version, there is no condition to check if the current mid is equal to the target to prematurely end the + * search. Hence, the only way for the loop to complete is when low exceeds high. + * + * At the end of every loop, we know that the target value is either within the search range or does not exist in the + * array, thereby ensuring the correctness of the algorithm. + * + * Since after each iteration, the search range is halved, it will only take a maximum of O(log n) times before the + * target is either found or determined to not exist in the array. + */ +public class BinarySearchTemplated { + /** + * A utility method to compare two integers. + * @param value The current value from the array. + * @param target The value being searched for. + * @return true if the current value is less than the target, otherwise false. + */ + // The condition should be changed accordingly + public static boolean condition(int value, int target) { + return value < target; + } + + /** + * Conducts a binary search to find the target within the sorted array. + * + * @param arr The sorted input array. + * @param target The value to be searched within the array. + * @return The index of the target value if found, otherwise -1. + */ + public static int search(int[] arr, int target) { + // The search space i.e. high and low should be changed accordingly. + int high = arr.length - 1; // max index is 3 if array length is 4 + int low = 0; + while (low < high) { + int mid = low + (high - low) / 2; // equivalent to high + low / 2 but reduces cases of integer overflow + if (condition(arr[mid], target)) { // if value < target + high = mid; + } else { // if value >= target + low = mid + 1; + } + } + + // Checks if low value is indeed the target + // Note that the following checks may not be required in other use cases of this template + if (low < arr.length && arr[low] == target) { + // returned value should be changed accordingly (low or low - 1) + return low; + } + // Returns -1 if loop was exited without finding the target + return -1; + } +} \ No newline at end of file diff --git a/src/algorithms/searches/binarySearch/README.md b/src/algorithms/searches/binarySearch/README.md new file mode 100644 index 00000000..73f1b195 --- /dev/null +++ b/src/algorithms/searches/binarySearch/README.md @@ -0,0 +1,78 @@ +# Binary Search +Binary search is a search algorithm that finds the position of a target value within a sorted array or list. It compares +the target value to the middle element of the search range, then, based on the comparison, narrows the search to the +upper or lower half of the current search range. + +Two versions of binary search has been implemented in this repository - BinarySearch and BinarySearchTemplated. + +## BinarySearch +![binary search img](../../../../assets/BinarySearch.png) +Image Source: GeeksforGeeks + +BinarySearch is a more straightforward and intuitive version of the binary search algorithm. In this approach, after the +mid-value is calculated, the high and low pointers are adjusted by just one unit. From the above example, after mid +points to index 4 in the first search, the low pointer moves to index 5 (+1) when narrowing the search. Similarly, when +mid points to index 7 in the second search, the high pointer shifts to index 6 (-1) when narrowing the search. This +prevents any possibility of infinite loops. + +## BinarySearchTemplated + +BinarySearchTemplated removes the condition that checks if the current mid-value is equal to the target (which helps to +end the search the moment the target is found). The template adds a "condition" method which will be modified based on +the requirements of the implementation. + +The narrowing of the search space differs from BinarySearch - only one of the high or low pointers will be adjusted by +one unit. + +This template will work for most binary search problems and will only require the following changes: +- Search space (high and low) +- Condition method +- Returned value (low or low - 1) + +### Search Space (Requires change) +Simply modify the initialisation of the high and low pointer according to the search space. + +### Condition (Requires change) +We assume that when the condition returns true, the current value "fails" and when the condition returns false, the +current value "passes". + +In this template, we want to find the first "pass" in the array. + +INSERT IMAGE OF FIRST PASS + +### Returned Value (Requires change) +In the implementation of BinarySearchTemplated, return low was used to find the first "pass". + +EXPLANATION TBC, STILL THINKING HOW TO PHRASE IT. + +### Search Space Adjustment +What should be the search space adjustment? (Why only low = mid + 1) + +Due to the nature of floor division in Java's \ operator, the searched mid-index will always be smaller than the high +pointer of the previous search range. On the other hand, low = mid + 1, ensures that the searched mid-index is always +larger than the low pointer of the previous search range. This ensures that the search range is narrowed in every loop +and prevents the possibility of infinite loops. + +INSERT IMAGE HERE TO EXPLAIN + +As we close in towards the target value, the final low = mid + 1 narrows the search range from low. TBC ON EXPLANATION + +Credits: [Powerful Ultimate Binary Search Template](https://leetcode.com/discuss/general-discussion/786126/python-powerful-ultimate-binary-search-template-solved-many-problems) + +## Complexity Analysis +**Time**: +- Worst case: O(log n) +- Average case: O(log n) +- Best case: + - BinarySearch O(1) + - BinarySearchTemplated O(log n) + +BinarySearch: +In the worst case, the target is either in the first index or does not exist in the array at all. +In the best case, the target is the middle (odd number of element) or the first middle element (even number of elements) +if floor division is used to determine the middle. + +BinaryTemplated: +In all cases, O(log n) iterations will be required as there is no condition to exit the loop prematurely. + +**Space**: O(1) since no new data structures are used and searching is only done within the array given diff --git a/test/algorithms/binarySearchTest/BinarySearchTest.java b/test/algorithms/binarySearchTest/BinarySearchTest.java new file mode 100644 index 00000000..97dae628 --- /dev/null +++ b/test/algorithms/binarySearchTest/BinarySearchTest.java @@ -0,0 +1,4 @@ +package test.algorithms.binarySearchTest; + +public class BinarySearchTest { +} From dc37ab5498966b9cbaff1477ed80a773b5f618ea Mon Sep 17 00:00:00 2001 From: junnengsoo Date: Sun, 27 Aug 2023 00:54:39 +0800 Subject: [PATCH 2/2] Add BinarySearchTest for both implementations --- .../disjointSet/quickFind/quick_find.iml | 7 --- .../binarySearch/BinarySearchTemplated.java | 6 +-- .../searches/binarySearch/README.md | 4 +- .../binarySearchTest/BinarySearchTest.java | 47 +++++++++++++++++++ 4 files changed, 52 insertions(+), 12 deletions(-) delete mode 100644 out/production/src/src/dataStructures/disjointSet/quickFind/quick_find.iml diff --git a/out/production/src/src/dataStructures/disjointSet/quickFind/quick_find.iml b/out/production/src/src/dataStructures/disjointSet/quickFind/quick_find.iml deleted file mode 100644 index f4cd67e5..00000000 --- a/out/production/src/src/dataStructures/disjointSet/quickFind/quick_find.iml +++ /dev/null @@ -1,7 +0,0 @@ - - - - - - - \ No newline at end of file diff --git a/src/algorithms/searches/binarySearch/BinarySearchTemplated.java b/src/algorithms/searches/binarySearch/BinarySearchTemplated.java index 99ef02d4..f89c5acf 100644 --- a/src/algorithms/searches/binarySearch/BinarySearchTemplated.java +++ b/src/algorithms/searches/binarySearch/BinarySearchTemplated.java @@ -31,7 +31,7 @@ public class BinarySearchTemplated { */ // The condition should be changed accordingly public static boolean condition(int value, int target) { - return value < target; + return value >= target; } /** @@ -47,9 +47,9 @@ public static int search(int[] arr, int target) { int low = 0; while (low < high) { int mid = low + (high - low) / 2; // equivalent to high + low / 2 but reduces cases of integer overflow - if (condition(arr[mid], target)) { // if value < target + if (condition(arr[mid], target)) { // if value >= target high = mid; - } else { // if value >= target + } else { // if value < target low = mid + 1; } } diff --git a/src/algorithms/searches/binarySearch/README.md b/src/algorithms/searches/binarySearch/README.md index 73f1b195..5323412b 100644 --- a/src/algorithms/searches/binarySearch/README.md +++ b/src/algorithms/searches/binarySearch/README.md @@ -33,8 +33,8 @@ This template will work for most binary search problems and will only require th Simply modify the initialisation of the high and low pointer according to the search space. ### Condition (Requires change) -We assume that when the condition returns true, the current value "fails" and when the condition returns false, the -current value "passes". +We assume that when the condition returns true, the current value "passes" and when the condition returns false, the +current value "fails". In this template, we want to find the first "pass" in the array. diff --git a/test/algorithms/binarySearchTest/BinarySearchTest.java b/test/algorithms/binarySearchTest/BinarySearchTest.java index 97dae628..76c821cc 100644 --- a/test/algorithms/binarySearchTest/BinarySearchTest.java +++ b/test/algorithms/binarySearchTest/BinarySearchTest.java @@ -1,4 +1,51 @@ package test.algorithms.binarySearchTest; +import org.junit.Test; + +import src.algorithms.searches.binarySearch.BinarySearchTemplated; +import src.algorithms.searches.binarySearch.BinarySearch; + +import java.util.Arrays; + +import static org.junit.Assert.assertArrayEquals; +import static org.junit.Assert.assertEquals; + public class BinarySearchTest { + @Test + public void test_binarySearch() { + // Test 1: even number of elements + int[] firstArray = {1, 5, 10, 12}; + int firstResult = BinarySearch.search(firstArray, 1); + + // Test 2: odd number of elements + int[] secondArray = {1, 5, 10, 11, 12}; + int secondResult = BinarySearch.search(secondArray, 11); + + // Test 3: target not in array + int[] thirdArray = {1, 5, 10, 11, 12}; + int thirdResult = BinarySearch.search(thirdArray, 3); + + assertEquals(0, firstResult); + assertEquals(3, secondResult); + assertEquals(-1, thirdResult); + } + + @Test + public void test_binarySearchTemplated() { + // Test 1: even number of elements + int[] firstArray = {1, 5, 10, 12}; + int firstResult = BinarySearchTemplated.search(firstArray, 1); + + // Test 2: odd number of elements + int[] secondArray = {1, 5, 10, 11, 12}; + int secondResult = BinarySearchTemplated.search(secondArray, 11); + + // Test 3: target not in array + int[] thirdArray = {1, 5, 10, 11, 12}; + int thirdResult = BinarySearchTemplated.search(thirdArray, 3); + + assertEquals(0, firstResult); + assertEquals(3, secondResult); + assertEquals(-1, thirdResult); + } }