Given n people standing in a circle where 1st is having sword, find the luckiest person in the circle, if from 1st soldier who is having a sword each have to kill the next soldier and handover the sword to next soldier, in turn the soldier will kill the adjacent soldier and handover the sword to next soldier such that one soldier remain in this war who is not killed by anyone.

Prerequisite : Puzzle 81 | 100 people in a circle with gun puzzle

Examples :

Input : 5

Output : 3

Explanation :

N = 5

Soldier 1 2 3 4 5 (5 soldiers)

In first go 1 3 5 (remains) as 2 and 4 killed by 1 and 3.

In second go 3 as 5 killed 1 and 3rd kill 5 soldier 3 remains alive.Input : 100

Output : 73

Explanation :

N = 10

Soldiers 1 2 3 4 5 6 7 8 9 10 (10 soldiers)

In first 1 3 5 7 9 as 2 4 6 8 10 were killed by 1 3 5 7 and 9.

In second 1 5 9 as 9 kill 1 and in turn 5 kill 9th soldier.

In third 5 5th soldiers remain alive

**Approach :** The idea is to use circular linked list. A circular linked list is made based on number of soldier N. As rule state you have to kill your adjacent soldier and handover the sword to the next soldier who in turn kill his adjacent soldier and handover sword to the next soldier. So in circular linked list the adjacent soldier are killed and the remaining soldier fights against each other in a circular way and a single soldier survive who is not killed by anyone.

`// CPP code to find the luckiest person ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Node structure ` `struct` `Node { ` ` ` `int` `data; ` ` ` `struct` `Node* next; ` `}; ` ` ` `Node *newNode(` `int` `data) ` `{ ` ` ` `Node *node = ` `new` `Node; ` ` ` `node->data = data; ` ` ` `node->next = NULL; ` ` ` `return` `node; ` `} ` ` ` `// Function to find the luckiest person ` `int` `alivesol(` `int` `Num) ` `{ ` ` ` `if` `(Num == 1) ` ` ` `return` `1; ` ` ` ` ` `// Create a single node circular ` ` ` `// linked list. ` ` ` `Node *last = newNode(1); ` ` ` `last->next = last; ` ` ` ` ` `for` `(` `int` `i = 2; i <= Num; i++) { ` ` ` `Node *temp = newNode(i); ` ` ` `temp->next = last->next; ` ` ` `last->next = temp; ` ` ` `last = temp; ` ` ` `} ` ` ` ` ` `// Starting from first soldier. ` ` ` `Node *curr = last->next; ` ` ` ` ` `// condition for evaluating the existence ` ` ` `// of single soldier who is not killed. ` ` ` `Node *temp; ` ` ` `while` `(curr->next != curr) { ` ` ` `temp = curr; ` ` ` `curr = curr->next; ` ` ` `temp->next = curr->next; ` ` ` ` ` `// deleting soldier from the circular ` ` ` `// list who is killed in the fight. ` ` ` `delete` `curr; ` ` ` `temp = temp->next; ` ` ` `curr = temp; ` ` ` `} ` ` ` ` ` `// Returning the Luckiest soldier who ` ` ` `// remains alive. ` ` ` `int` `res = temp->data; ` ` ` `delete` `temp; ` ` ` ` ` `return` `res; ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `int` `N = 100; ` ` ` `cout << alivesol(N) << endl; ` ` ` `return` `0; ` `} ` |

*chevron_right*

*filter_none*

**Output:**

73

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