Solve "Find the Duplicate Number" problem in an array of n+1 integers?

Short answer: public int FindDuplicate(int[] nums) { int slow = nums[0], fast = nums[0]; do { slow = nums[slow]; fast = nums[nums[fast]]; } while (slow != fast); fast = nums[0]; while (slow != fast) { slow = nums[slow]; fast = nums[fast]; } return slow; } Explanation: Floyd’s Tortoise and Hare cycle detection, treating values as pointers.

Example code

public int FindDuplicate(int[] nums) {
int slow = nums[0], fast = nums[0]; do { slow = nums[slow];
fast = nums[nums[fast]];
} while (slow != fast);
fast = nums[0]; while (slow != fast) { slow = nums[slow];
fast = nums[fast];
}
return slow;
} Explanation: Floyd’s Tortoise and Hare cycle detection, treating values as pointers.

Real-world example (ShopNest)

In coding rounds, state complexity aloud, write a clear ShopNest-flavored example (orders, carts), then handle edge cases (empty list, null, overflow).

Say this in the interview

1. Define — one clear sentence (the short answer above).
2. Example — relate it to a project like ShopNest or your real work.
3. Trade-off — when you would not use it.