Description
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:
- Choose an index
iwherenum[i] == '?'. - 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 because2+4+3 = 8+0+1. If the game ended withnum = "243803", then Alice wins because2+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 <= 105num.lengthis even.numconsists of only digits and'?'.
Solutions
Attempt at better performance. There's a mathematical optimization possible here, but I didn't try hard enough to get it.
Language: javascript(2026-08-23 08:58)DONE
CPU Performance35.71%
Memory Performance35.71%
/**
* @param {string} num
* @return {boolean}
*/
var sumGame = function(num) {
const n = num.length;
const halfLen = n / 2;
const sum = [0, 0];
const quest = [0, 0];
for (let i = 0; i < n; i++) {
const pos = i < halfLen ? 0 : 1;
if (num[i] !== '?') {
sum[pos] += num.charCodeAt(i) - 48;
continue;
}
if (quest[pos] === 0) {
quest[pos]++;
continue;
}
sum[pos] += 9;
quest[pos]--;
}
if (quest[0] !== quest[1]) {
return true;
}
return sum[0] !== sum[1];
};