CodeChef - The Ball And Cups - Finding the number in a shuffled array

https://www.codechef.com/problems/TAVISUAL

All submissions for this problem are available.

At the end of a busy day, The Chef and his assistants play a game together. The game is not just for fun but also used to decide who will have to clean the kitchen. The Chef is a Game Master, so his concern is how to manage the game but not how to win the game like his assistants do.

The game requires players to find the only ball under one of the N cups after their positions are changed in a special way. At the beginning of the game, The Chef places N cups in a row and put a ball under the C-th cup from the left (the cups are numbered from 1 to N). All players can see the initial position of the ball. Then Chef performs Q flip operations. Each flip operation is defined by two integers L and R such that 1 ≤ L ≤ R ≤ N and consists in reversing the segment [L, R] of cups. Namely, Chef swaps L-th and R-th cups, (L+1)-th and (R−1)-th cups, and so on. After performing all the operations Chef asks his assistants to choose a cup that they think the ball is under it. Who can guess the position of the ball will win the game, and of course, the others will have to clean the kitchen.

The Chef doesn't want to check all the N cups at the end of the game. He notes down the value of C and the pairs (L, R) and asked you, the mastered programmer, to determine the cup that contains the ball.

Input

The first line of the input contains a single integer T, denoting the number of test cases. The description of Ttest cases follows. The first line of each test case contains three space-separated integers N, C and Q, denoting the total number of cups, the initial position of the ball and the number of flip operations Chef will perform. Each of the following Q lines contains two space-separated integers L and R, denoting the ends of the segment of the current flip operation.

Output

For each test case output on a separate line the final position of the ball.

Constraints

• 1 ≤ T ≤ 10
• 1 ≤ N ≤ 100000 (10⁵)
• 1 ≤ C ≤ N
• 1 ≤ Q ≤ 10000 (10⁴)
• 1 ≤ L ≤ R ≤ N

Example

Input:
1
5 2 3
1 4
3 5
1 5

Output:
1

http://letuscode.in/index.php/2015/12/11/finding-number-shuffled-array/

Given an array [1, 2, 3,…N], we apply a series of reversal operations on different range of indices [L,R].
How to find out the position of a number after these operations are applied?

For example consider an array of 5 numbers [1, 2, 3, 4, 5] and the number 2.

Reverse elements between 1, and 3, the array becomes [3, 2, 1, 4, 5]
Reverse elements between 3, and 5, the array becomes [3, 2, 5, 4, 1]
Reverse elements between 2, and 5, the array becomes [3, 1, 4, 5, 2]

So the final position of 2 is 5.

If we want to track just one number, we need not perform reversal operations everytime. This process takes O(n^2) time in worst case.

As we perform the reversal operations, we just need to track what is the new position of target number.

How do we track the position?
Consider the positions L = left, R= right, C = current
After we reverse the elements between L, R, C will be placed x steps before R

C – L = R – X
X = R + L – C
The new position of C will be (R+L-C)
The position of C will not be altered if we are reversing the part which includes C.

#include <iostream>

#include <vector>

#include <algorithm>

using namespace std;

int main()

{

  int t;

  cin >> t;

  while(t--)

  {

    int n,c,q;

    cin >> n >> c >> q;

    int i;

    vector<int> nums(n);

    for( i = 0; i < n; i++ )

    {

      nums[i] = i+1;

    }

    for( i = 0; i < q; i++ )

    {

      int l,r;

      cin >> l >> r;

      if( c >= l && c <= r )

      c = l+r-c;

    }

    cout << c << endl;

  }

  return 0;