約瑟夫環（約瑟夫問題）求最後出列的人數

約瑟夫環（約瑟夫問題）是一個數學的應用問題：已知n我的（以編號1，2，3...n分別表示）圍坐在一張圓桌周圍。從編號爲k的人開始報數，數到m的那我的出列；他的下一我的又從1開始報數，數到m的那我的又出列；依此規律重複下去，直到圓桌周圍的人所有出列。如5我的，從編號爲1的人開始報數，數到3的人出列，最後出列的人的編號爲4。

編寫一個函數，總人數爲50，從編號爲1的人開始報數，數到3的人出列，計算出最後出列的人的編號。

NSUInteger printLastDequeuedNumberInRoundTable(NSUInteger allMembersCount, NSUInteger dequeueNumber) {
    NSMutableDictionary<NSNumber *, NSString *> *dictM = @{}.mutableCopy;
    NSUInteger startIdx = 1;//first idx is 1 in round table issue
    //all members always dequeued finally
    while (dictM.allKeys.count != allMembersCount) {
        //members always sing from `1..dequeueNumber`
        for (NSUInteger i = 1; i <= dequeueNumber; i++) {
            //member at startIdx dequeued
            if (dictM[@(startIdx)]) {
                //ignore this, step next
                i--;
            } else {
                if (i == dequeueNumber) {
                    //record every `round table number` when last member who sing `dequeueNumber`
                    dictM[@(startIdx)] = @"dequeued";
                    if (dictM.allKeys.count == allMembersCount) {
                        NSUInteger lastNum = (startIdx - 1)%allMembersCount + 1;
                        NSLog(@"last member at number %ld dequeued", lastNum);
                        return lastNum;
                    } else {
                        NSLog(@"member at number %ld dequeued", (startIdx - 1)%allMembersCount + 1);
                    }
                }
            }
            ++startIdx;
            //the index in round table member varied from 1 to allMembersCount
            startIdx = (startIdx - 1)%allMembersCount + 1;
        }
    }
    return NSNotFound;
}
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結果

NSUInteger lastNumber = printLastDequeuedNumberInRoundTable(50, 3);
lastNumber = 11;
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