Find duplicate integer in time O(n logn) and space O(n)

Sat, 02 Jun 2018 21:46:22 +0000

Here’s how you can find a duplicate integer in a list of integers (read array) in space O(n) and time O(nlogn). This will only return the first duplicate integer in the array.

Note: This only applies for a list of integers 1..n. This won’t work otherwise.

function findDuplicate(arr) {
 var floor = 1;
 var ceiling = arr.length - 1;

 while (floor < ceiling) {
 var midpoint = Math.floor(floor + (ceiling - floor) / 2);
 var lowerRangeFloor = floor;
 var lowerRangeCeiling = midpoint;
 var upperRangeFloor = midpoint + 1;
 var upperRangeCeiling = ceiling;

 var distinctPossibleIntegersInLowerRange =
 lowerRangeCeiling - lowerRangeFloor + 1;
 var itemsInLowerRange = 0;
 arr.forEach(function (item) {
 if (item >= lowerRangeFloor && item <= lowerRangeCeiling) {
 itemsInLowerRange += 1;
 }
 });
 if (itemsInLowerRange > distinctPossibleIntegersInLowerRange) {
 floor = lowerRangeFloor;
 ceiling = lowerRangeCeiling;
 } else {
 floor = upperRangeFloor;
 ceiling = upperRangeCeiling;
 }
 }
 return floor;
}

// Example use case
let arr = [1, 2, 3, 4, 5, 4, 6, 3, 4, 6];
console.log(findDuplicate(arr)); // 3

Snippet on Elliot Sachs

Find duplicate integer in time O(n logn) and space O(n)