约瑟夫环（约瑟夫问题）求最后出列的人数

约瑟夫环（约瑟夫问题）是一个数学的应用问题：已知n个人（以编号1，2，3...n分别表示）围坐在一张圆桌周围。从编号为k的人开始报数，数到m的那个人出列；他的下一个人又从1开始报数，数到m的那个人又出列；依此规律重复下去，直到圆桌周围的人全部出列。如5个人，从编号为1的人开始报数，数到3的人出列，最后出列的人的编号为4。

编写一个函数，总人数为50，从编号为1的人开始报数，数到3的人出列，计算出最后出列的人的编号。

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