TheAlgorithms · StepfenShawn · Aug 15, 2020 · Aug 10, 2020 · Aug 10, 2020
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+/**
+ * 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)
+}
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+/**
+ * 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))