diff --git a/Search/ExponentialSearch.js b/Search/ExponentialSearch.js new file mode 100644 index 000000000..e46a5ee89 --- /dev/null +++ b/Search/ExponentialSearch.js @@ -0,0 +1,58 @@ +/** + * Exponential Search + * + * The algorithm consists of two stages. The first stage determines a + * range in which the search key would reside if it were in the list. + * In the second stage, a binary search is performed on this range. + * + * + * + */ + +function binarySearch (arr, x, floor, ceiling) { + // Middle index + const mid = Math.floor((floor + ceiling) / 2) + + // If value is at the mid position return this position + if (arr[mid] === x) { + return mid + } + + if (floor > ceiling) return -1 + + // If the middle element is great than the value + // search the left part of the array + if (arr[mid] > value) { + return binarySearch(arr, value, floor, mid - 1) + // If the middle element is lower than the value + // search the right part of the array + } else { + return binarySearch(arr, value, mid + 1, ceiling) + } +} + +function exponentialSearch (arr, length, value) { + // If value is the first element of the array return this position + if (arr[0] === value) { + return 0 + } + + // Find range for binary search + let i = 1 + while (i < length && arr[i] <= value) { + i = i * 2 + } + + // Call binary search for the range found above + return binarySearch(arr, value, i / 2, Math.min(i, length)) +} + +const arr = [2, 3, 4, 10, 40, 65, 78, 100] +const value = 78 +const result = exponentialSearch(arr, arr.length, value) + +if (result < 0) { + console.log('Element not found') +} else { + console.log('Element found at position :' + result) +} diff --git a/Search/InterpolationSearch.js b/Search/InterpolationSearch.js new file mode 100644 index 000000000..c256fd8c7 --- /dev/null +++ b/Search/InterpolationSearch.js @@ -0,0 +1,46 @@ +/** + * Interpolation Search + * + * Time Complexity: + * -Best case: O(1) + * -Worst case: O(n) + * -O((log(log(n))) If the data are uniformly distributed + * + * + */ + +function interpolationSearch (arr, key) { + const length = arr.length - 1 + let low = 0 + let high = length + let position = -1 + let delta = -1 + + // Because the array is sorted the key must be between low and high + while (low <= high && key >= arr[low] && key <= arr[high]) { + delta = (key - arr[low]) / (arr[high] - arr[low]) + position = low + Math.floor((high - low) * delta) + + // Target found return its position + if (arr[position] === key) { + return position + } + + // If the key is larger then it is in the upper part of the array + if (arr[position] < key) { + low = position + 1 + // If the key is smaller then it is in the lower part of the array + } else { + high = position - 1 + } + } + + return -1 +} + +const arr = [2, 6, 8, 10, 12, 14, 16, 18, 20, 22, 26, 34, 39] + +console.log('Found at position :' + interpolationSearch(arr, 2)) +console.log('Found at position :' + interpolationSearch(arr, 12)) +console.log('Found at position :' + interpolationSearch(arr, 1000)) +console.log('Found at position :' + interpolationSearch(arr, 39))