390. Elimination Game

Description

You have a list arr of all integers in the range [1, n] sorted in a strictly increasing order. Apply the following algorithm on arr:

  • Starting from left to right, remove the first number and every other number afterward until you reach the end of the list.
  • Repeat the previous step again, but this time from right to left, remove the rightmost number and every other number from the remaining numbers.
  • Keep repeating the steps again, alternating left to right and right to left, until a single number remains.

Given the integer n, return the last number that remains in arr.

 

Example 1:

Input: n = 9
Output: 6
Explanation:
arr = [1, 2, 3, 4, 5, 6, 7, 8, 9]
arr = [2, 4, 6, 8]
arr = [2, 6]
arr = [6]

Example 2:

Input: n = 1
Output: 1

 

Constraints:

  • 1 <= n <= 109

Solutions

Solution 1

Python Code
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class Solution:
    def lastRemaining(self, n: int) -> int:
        a1, an = 1, n
        i, step, cnt = 0, 1, n
        while cnt > 1:
            if i % 2:
                an -= step
                if cnt % 2:
                    a1 += step
            else:
                a1 += step
                if cnt % 2:
                    an -= step
            cnt >>= 1
            step <<= 1
            i += 1
        return a1

Java Code
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class Solution {
    public int lastRemaining(int n) {
        int a1 = 1, an = n, step = 1;
        for (int i = 0, cnt = n; cnt > 1; cnt >>= 1, step <<= 1, ++i) {
            if (i % 2 == 1) {
                an -= step;
                if (cnt % 2 == 1) {
                    a1 += step;
                }
            } else {
                a1 += step;
                if (cnt % 2 == 1) {
                    an -= step;
                }
            }
        }
        return a1;
    }
}

C++ Code
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class Solution {
public:
    int lastRemaining(int n) {
        int a1 = 1, an = n, step = 1;
        for (int i = 0, cnt = n; cnt > 1; cnt >>= 1, step <<= 1, ++i) {
            if (i % 2) {
                an -= step;
                if (cnt % 2) a1 += step;
            } else {
                a1 += step;
                if (cnt % 2) an -= step;
            }
        }
        return a1;
    }
};

Go Code
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func lastRemaining(n int) int {
	a1, an, step := 1, n, 1
	for i, cnt := 0, n; cnt > 1; cnt, step, i = cnt>>1, step<<1, i+1 {
		if i%2 == 1 {
			an -= step
			if cnt%2 == 1 {
				a1 += step
			}
		} else {
			a1 += step
			if cnt%2 == 1 {
				an -= step
			}
		}
	}
	return a1
}