find smallest number in a sorted rotated array

in linear and log(n) time

Author: williscool

javascript/interview_questions/find_smallest_num.js

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+/*
+
+// https://www.interviewbit.com/problems/rotated-array/
+
+[]
+[1]
+[2,1]
+[3,4,5,6,1,2]
+
+*/
+
+function smallestNum(arr){
+  
+  if(arr.length < 1) return false;
+  
+  var smallest = arr[0];
+  
+  arr.forEach(function(num){
+    if(num < smallest){
+      smallest = num;
+    }
+  });
+  
+  return smallest;
+}
+
+
+function bSearchSmallestNum(arr){
+  
+  var len = arr.length;
+  
+  if(len < 1) return false;
+  
+  var min = 0;
+  var max = len - 1;
+  
+  // Binary search looking for element where previous element to it and next element are greater than it
+  
+  while(min <= max) {
+    
+    // case where we went through entire search space and ended up with elements equal
+    if(arr[min] <= arr[max]) return arr[min]; 
+  
+    var mid = (min + max) >> 1 ; // bitshift one is same as Math.floor and handles overflow
+    
+    // modulo len because if len is the last element we want to look at the first element and vice versus
+    var next = (mid + 1) % len;
+    var prev = (mid + len - 1) % len;
+    
+    // our pivot is less than the element before and after it. we found our pivot so we can return
+    if(arr[mid] <= arr[prev] && arr[mid] <= arr[next] ) {
+      return arr[mid];
+    } else if (arr[mid] <= arr[max]){
+      max = mid + 1;
+    } else if (arr[mid] >= arr[min]){
+      min = mid + 1;
+    } 
+    
+  }
+  
+}
+
+module.exports = {
+  linear: smallestNum,
+  binary_search: bSearchSmallestNum
+};

javascript/test/interview_questions/find_smallest_num_test.js

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+var assert = require('assert');
+var findSmallestFns = require('../../interview_questions/find_smallest_num.js');
+
+Object.keys(findSmallestFns).forEach(function(key) {
+
+  var findSmallest = findSmallestFns[key];
+
+  describe(key + ' Find Smallest Number is sorted rotated array Question', function() {
+    
+    it('works with an empty array', function() {
+      assert.deepEqual ( findSmallest([]) , false);
+    });
+
+    it('works with a 2 element array', function() {
+      assert.deepEqual ( findSmallest([2,1]) , 1);
+    });
+
+    it('works with a n element array', function() {
+      assert.deepEqual ( findSmallest([3,4,5,6,1,2]) , 1);
+    });
+
+  });
+
+});