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g1901_2000.s1927_sum_game.readme.md Maven / Gradle / Ivy

1927\. Sum Game

Medium

Alice and Bob take turns playing a game, with **Alice starting first**.

You are given a string `num` of **even length** consisting of digits and `'?'` characters. On each turn, a player will do the following if there is still at least one `'?'` in `num`:

1.  Choose an index `i` where `num[i] == '?'`.
2.  Replace `num[i]` with any digit between `'0'` and `'9'`.

The game ends when there are no more `'?'` characters in `num`.

For Bob to win, the sum of the digits in the first half of `num` must be **equal** to the sum of the digits in the second half. For Alice to win, the sums must **not be equal**.

*   For example, if the game ended with `num = "243801"`, then Bob wins because `2+4+3 = 8+0+1`. If the game ended with `num = "243803"`, then Alice wins because `2+4+3 != 8+0+3`.

Assuming Alice and Bob play **optimally**, return `true` _if Alice will win and_ `false` _if Bob will win_.

**Example 1:**

**Input:** num = "5023"

**Output:** false

**Explanation:** There are no moves to be made. The sum of the first half is equal to the sum of the second half: 5 + 0 = 2 + 3.

**Example 2:**

**Input:** num = "25??"

**Output:** true

**Explanation:** Alice can replace one of the '?'s with '9' and it will be impossible for Bob to make the sums equal.

**Example 3:**

**Input:** num = "?3295???"

**Output:** false

**Explanation:** It can be proven that Bob will always win. One possible outcome is: 

- Alice replaces the first '?' with '9'. num = "93295???". 

- Bob replaces one of the '?' in the right half with '9'. num = "932959??". 

- Alice replaces one of the '?' in the right half with '2'. num = "9329592?".

- Bob replaces the last '?' in the right half with '7'. num = "93295927". 
  
Bob wins because 9 + 3 + 2 + 9 = 5 + 9 + 2 + 7.

**Constraints:**

*   2 <= num.length <= 105
*   `num.length` is **even**.
*   `num` consists of only digits and `'?'`.