Determine the Winner of a Bowling Game — Easy Problem & Solution

Problem statement

Two players bowl. player1[i] and player2[i] are the pins each knocked down in turn i.

A turn's points are doubled if the player knocked down all 10 pins in either of the two previous turns; otherwise the points equal the pins.

Return 1 if player 1 wins, 2 if player 2 wins, and 0 on a tie.

Example 1

Input: player1 = [4,10,7,9], player2 = [6,5,2,3]
Output: 1
Explanation: Player 1 scores 4 + 10 + 14 + 18 = 46 against 16.

Example 2

Input: player1 = [3,5,7,6], player2 = [8,10,10,2]
Output: 2

Example 3

Input: player1 = [2,3], player2 = [4,1]
Output: 0
Explanation: Both total 5.

Constraints

• n == player1.length == player2.length
• 1 <= n <= 1000
• 0 <= player1[i], player2[i] <= 10

How to solve Determine the Winner of a Bowling Game

A direct simulation. For each turn, look back at most two turns for a strike; if one is there, the turn's points double.

Approach

1. For each player, sweep the turns keeping a running total.
2. At turn i, double the points when p[i-1] == 10 or p[i-2] == 10 (guarding the bounds).
3. Compare the totals and report 1, 2 or 0.

Why it works

The rule refers only to the raw pins in the previous turns, not to the doubled points, so no propagation is needed and one left-to-right pass is exact. The two players never interact, so scoring them separately is correct.

Complexity

• Time — O(n)
• Space — O(1)

Pitfalls

• The doubling looks at the pins, not the already-doubled score of a previous turn.
• Both previous turns count, so it is an or over two look-backs, not just the immediately preceding one.
• The first two turns need bounds guards.

Reference solution

Python

from typing import List

def isWinner(player1: List[int], player2: List[int]) -> int:
    def score(p: List[int]) -> int:
        s = 0
        for i, v in enumerate(p):
            bonus = (i >= 1 and p[i - 1] == 10) or (i >= 2 and p[i - 2] == 10)
            s += 2 * v if bonus else v
        return s

    a, b = score(player1), score(player2)
    if a > b:
        return 1
    if b > a:
        return 2
    return 0

JavaScript

var isWinner = function(player1, player2) {
    var score = function(p) {
        var s = 0;
        for (var i = 0; i < p.length; i++) {
            var bonus = (i >= 1 && p[i - 1] === 10) || (i >= 2 && p[i - 2] === 10);
            s += bonus ? 2 * p[i] : p[i];
        }
        return s;
    };
    var a = score(player1), b = score(player2);
    if (a > b) return 1;
    if (b > a) return 2;
    return 0;
};

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