There are n pieces arranged in a line, and each piece is colored either by 'A' or by 'B'. You are given a string colors of length n where colors[i] is the color of the ith piece.
Alice and Bob are playing a game where they take alternating turns removing pieces from the line. In this game, Alice moves first.
- Alice is only allowed to remove a piece colored
'A'if both its neighbors are also colored'A'. She is not allowed to remove pieces that are colored'B'. - Bob is only allowed to remove a piece colored
'B'if both its neighbors are also colored'B'. He is not allowed to remove pieces that are colored'A'. - Alice and Bob cannot remove pieces from the edge of the line.
- If a player cannot make a move on their turn, that player loses and the other player wins.
Assuming Alice and Bob play optimally, return true if Alice wins, or return false if Bob wins.
Example 1:
Input: colors = "AAABABB" Output: true Explanation: AAABABB -> AABABB Alice moves first. She removes the second 'A' from the left since that is the only 'A' whose neighbors are both 'A'. Now it's Bob's turn. Bob cannot make a move on his turn since there are no 'B's whose neighbors are both 'B'. Thus, Alice wins, so return true.
Example 2:
Input: colors = "AA" Output: false Explanation: Alice has her turn first. There are only two 'A's and both are on the edge of the line, so she cannot move on her turn. Thus, Bob wins, so return false.
Example 3:
Input: colors = "ABBBBBBBAAA" Output: false Explanation: ABBBBBBBAAA -> ABBBBBBBAA Alice moves first. Her only option is to remove the second to last 'A' from the right. ABBBBBBBAA -> ABBBBBBAA Next is Bob's turn. He has many options for which 'B' piece to remove. He can pick any. On Alice's second turn, she has no more pieces that she can remove. Thus, Bob wins, so return false.
Constraints:
1 <= colors.length <= 105colorsconsists of only the letters'A'and'B'
Companies: JPMorgan, Walmart Labs, MathWorks
Related Topics:
Math, String, Greedy, Game Theory
Similar Questions:
Hints:
- Does the number of moves a player can make depend on what the other player does? No
- How many moves can Alice make if colors == "AAAAAA"
- If a group of n consecutive pieces has the same color, the player can take n - 2 of those pieces if n is greater than or equal to 3
Each continuous segment of A or B of length cnt has cnt - 2 pieces avaiable for the players to pick. We sum these cnt - 2s up and Alice wins if her sum is greater.
// OJ: https://leetcode.com/problems/remove-colored-pieces-if-both-neighbors-are-the-same-color/
// Author: github.com/lzl124631x
// Time: O(N)
// Space: O(1)
class Solution {
public:
bool winnerOfGame(string s) {
int sum[2] = {};
for (int i = 0, N = s.size(); i < N;) {
int c = s[i], cnt = 0;
while (i < N && c == s[i]) ++i, ++cnt;
sum[c - 'A'] += max(0, cnt - 2);
}
return sum[0] > sum[1];
}
};