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/**

* Given an array of scores that are non-negative integers. Player 1 picks one

* of the numbers from either end of the array followed by the player 2 and

* then player 1 and so on. Each time a player picks a number, that number will

* not be available for the next player. This continues until all the scores

* have been chosen. The player with the maximum score wins.

*

* Given an array of scores, predict whether player 1 is the winner. You can

* assume each player plays to maximize his score.

*

* Example 1:

* Input: [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: [1, 5, 233, 7]

* Output: True

* Explanation: Player 1 first chooses 1. Then player 2 have 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.

*

* Note:

* 1 <= length of the array <= 20.

* Any scores in the given array are non-negative integers and will not exceed

* 10,000,000.

* If the scores of both players are equal, then player 1 is still the winner.

*/

public class PredictTheWinner486 {

public boolean PredictTheWinner(int[] nums) {

if (nums.length <= 1) return true;

int sum = 0;

for (int n: nums) sum += n;

int player1 = helper(nums, 0, 0, nums.length - 1, true);

return player1 >= (sum - player1);

}

private int helper(int[] nums, int p1, int left, int right, boolean turn1) {

if (left == right) return p1 + (turn1 ? nums[left] : 0);

if (turn1) {

p1 += nums[left];

int a = helper(nums, p1, left+1, right, false);

p1 -= nums[left];

p1 += nums[right];

int b = helper(nums, p1, left, right-1, false);

p1 -= nums[right];

return Math.max(a, b);

} else {

int a = helper(nums, p1, left+1, right, true);

int b = helper(nums, p1, left, right-1, true);

return Math.min(a, b);

}

}

public boolean PredictTheWinner2(int[] nums) {

if (nums.length <= 1) return true;

int sum = 0;

for (int n: nums) sum += n;

int player1 = helper(nums, 0, nums.length - 1, true);

return player1 >= (sum - player1);

}

private int helper(int[] nums, int left, int right, boolean turn1) {

if (left == right) return turn1 ? nums[left] : 0;

if (turn1) {

int a = nums[left] + helper(nums, left+1, right, false);

int b = nums[right] + helper(nums, left, right-1, false);

return Math.max(a, b);

} else {

int a = helper(nums, left+1, right, true);

int b = helper(nums, left, right-1, true);

return Math.min(a, b);

}

}

public boolean PredictTheWinner3(int[] nums) {

if (nums.length <= 1) return true;

int sum = 0;

for (int n: nums) sum += n;

int[][][] mem = new int[2][nums.length][nums.length];

int player1 = helper(nums, 0, nums.length - 1, true, mem);

return player1 >= (sum - player1);

}

private int helper(int[] nums, int left, int right, boolean turn1, int[][][] mem) {

if (left == right) return turn1 ? nums[left] : 0;

if (turn1) {

if (mem[0][left][right] > 0) return mem[0][left][right];

int a = nums[left] + helper(nums, left+1, right, false, mem);

int b = nums[right] + helper(nums, left, right-1, false, mem);

mem[0][left][right] = Math.max(a, b);

return Math.max(a, b);

} else {

if (mem[1][left][right] > 0) return mem[1][left][right];

int a = helper(nums, left+1, right, true, mem);

int b = helper(nums, left, right-1, true, mem);

mem[1][left][right] = Math.min(a, b);

return Math.min(a, b);

}

}

/**

* https://leetcode.com/problems/predict-the-winner/solution/

*/

public boolean PredictTheWinner4(int[] nums) {

Integer[][] memo = new Integer[nums.length][nums.length];

return winner(nums, 0, nums.length - 1, memo) >= 0;

}

public int winner(int[] nums, int s, int e, Integer[][] memo) {

if (s == e)

return nums[s];

if (memo[s][e] != null)

return memo[s][e];

int a = nums[s] - winner(nums, s + 1, e, memo);

int b = nums[e] - winner(nums, s, e - 1, memo);

memo[s][e] = Math.max(a, b);

return memo[s][e];

}

/**

* https://leetcode.com/problems/predict-the-winner/solution/

*/

public boolean PredictTheWinner5(int[] nums) {

int[][] dp = new int[nums.length + 1][nums.length];

for (int s = nums.length; s >= 0; s--) {

for (int e = s + 1; e < nums.length; e++) {

int a = nums[s] - dp[s + 1][e];

int b = nums[e] - dp[s][e - 1];

dp[s][e] = Math.max(a, b);

}

}

return dp[0][nums.length - 1] >= 0;

}

/**

* https://leetcode.com/problems/predict-the-winner/solution/

*/

public boolean PredictTheWinner6(int[] nums) {

int[] dp = new int[nums.length];

for (int s = nums.length; s >= 0; s--) {

for (int e = s + 1; e < nums.length; e++) {

int a = nums[s] - dp[e];

int b = nums[e] - dp[e - 1];

dp[e] = Math.max(a, b);

}

}

return dp[nums.length - 1] >= 0;

}

}