Tuesday, November 17, 2015

LinkedIn: Can I Win

    In "the 100 game," two players take turns adding, to a running 
    total, any integer from 1..10. The player who first causes the running 
    total to reach or exceed 100 wins. 
    What if we change the game so that players cannot re-use integers? 
    For example, if two players might take turns drawing from a common pool of numbers 
    of 1..15 without replacement until they reach a total >= 100. This problem is 
    to write a program that determines which player would win with ideal play. 

    Write a procedure, "Boolean canIWin(int maxChoosableInteger, int desiredTotal)", 
    which returns true if the first player to move can force a win with optimal play. 

    Your priority should be programmer efficiency; don't focus on minimizing 
    either space or time complexity. 

The crux of the problem is if the largest number remaining is greater than the target remaining, then the player is sure to win.

Code (Java):
public class Solution {

    Boolean canIWin(int maxChoosableInteger, int desiredTotal) {
        if (maxChoosableInteger <= 0 || desiredTotal <= 0) {
            return false;
        List<Integer> pool = new ArrayList<>();
        for (int i = 1; i <= maxChoosableInteger; i++) {
        return canIWinHelper(pool, desiredTotal);

    private boolean canIWinHelper(List<Integer> pool, int desiredTotal) {
        if (pool.get(pool.size() - 1) >= desiredTotal) {
            return true;
        for (int i = 0; i < pool.size(); i++) {
            int removed = pool.remove(i);
            boolean win = !canIWinHelper(pool, desiredTotal - removed);
            pool.add(i, removed);
            if (win) {
                return true;
        return false;
    public static void main(String[] args) {
        int max = 10;
        int total = 11;
        Solution solution = new Solution();
        boolean ans = solution.canIWin(max, total);

1 comment:

  1. The code doesn't pass many tests at https://leetcode.com/problems/can-i-win/