Problem
You are given an integer array nums
. Two players are playing a game with this array: player 1 and player 2.
Player 1 and player 2 take turns, with player 1 starting first. Both players start the game with a score of 0
. At each turn, the player takes one of the numbers from either end of the array (i.e., nums[0]
or nums[nums.length - 1]
) which reduces the size of the array by 1
. The player adds the chosen number to their score. The game ends when there are no more elements in the array.
Return true
if Player 1 can win the game. If the scores of both players are equal, then player 1 is still the winner, and you should also return true
. You may assume that both players are playing optimally.
Example 1:
Input: nums = [1,5,2]
Output: false
Explanation: Initially, player 1 can choose between 1 and 2.
If he chooses 2 (or 1), then player 2 can choose from 1 (or 2) and 5. If player 2 chooses 5, then player 1 will be left with 1 (or 2).
So, final score of player 1 is 1 + 2 = 3, and player 2 is 5.
Hence, player 1 will never be the winner and you need to return false.
Example 2:
Input: nums = [1,5,233,7]
Output: true
Explanation: Player 1 first chooses 1. Then player 2 has to choose between 5 and 7. No matter which number player 2 choose, player 1 can choose 233.
Finally, player 1 has more score (234) than player 2 (12), so you need to return True representing player1 can win.
Constraints:
1 <= nums.length <= 20
0 <= nums[i] <= 107
Solution
/**
* @param {number[]} nums
* @return {boolean}
*/
var PredictTheWinner = function(nums) {
return maxDiff(nums, 0, nums.length - 1) >= 0;
};
var maxDiff = function(nums, left, right) {
if (left === right) return nums[left];
return Math.max(
nums[left] - maxDiff(nums, left + 1, right),
nums[right] - maxDiff(nums, left, right - 1),
);
};
Explain:
nope.
Complexity:
- Time complexity : O(n ^ 2).
- Space complexity : O(n ^ 2).