第三章

面试题16

    /**
     * 面试题16 求数值的整数次方
     * 注意：非法输入的处理
     *
     * @param base
     * @param exponent
     * @return
     */
    public double power(double base, int exponent) throws Exception {
        if (base == 0.0 && exponent < 0) throw new Exception("base=0 and exponent<0"); //deal with invalid input
        if (exponent == 0) return 1;//exponent=0
        int absExp = Math.abs(exponent);//get the abs of exponent
        double result = powerCore(base, absExp);//power
        if (exponent < 0) result = 1.0 / result;//deal with exponent<0
        return result;
    }

    private double powerCore(double base, int absExp) {
        if(absExp==0) return 1;
        if(absExp==1)return base;
        double result = powerCore(base,absExp>>1);
        result *=result;
        if((absExp&0x01)!=0) result*=base;
        return result;

    }

    /*
    private double powerCore(double base, int absExp) {
        //使用动态规划的方法
        double prevResult = base;//previous result
        int num = 1;
        while ((num = num<<1) <= absExp) {
            prevResult = prevResult * prevResult;
        }
        for(int i=0;i<absExp-(num>>1);i++){
            prevResult *= base;
        }
        return prevResult;
    }
     */


    public static void main(String[] args) {
        Solution solution = new Solution();
        try {
            System.out.println(solution.power(2,7));
        } catch (Exception e) {
            e.printStackTrace();
        }
    }

面试题17

    /**
     * 面试题17 打印1到最大的n位数
     * 注意：大数问题，用数组来模拟大数的加减
     *
     * @param n
     */
    public void printMaxDigits(int n) {
        //invalid input
        if (n <= 0) return;
        int[] arr = new int[n + 1];
        while (increatment(arr)) {
            StringBuilder str = new StringBuilder(n);
            int index = n;
            while (arr[index] == 0) index--;
            for (int i = index; i >= 1; i--) {
                str.append(arr[i]);
            }
            System.out.println(str);
        }
    }

    /**
     * 全排列的思想
     *
     * @param n
     */
    public void printMaxDigits2(int n) {
        if (n <= 0) return;
        int[] arr = new int[n]; //模仿大数的数组
        for (int i = 0; i <= 9; i++) {
            arr[0] = i;
            printPermutation(arr, n, 0);
        }
    }

    /**
     * 打印数组arr,长度是n,已经确定i前索引对应的值的全排列
     * @param arr
     * @param n
     * @param index
     */
    private void printPermutation(int[] arr, int n, int index) {
        if(index == arr.length -1){
            System.out.println(Arrays.toString(arr));
            return;
        }
        for (int i = 0; i <= 9; i++) {
            arr[index+1] = i;
            printPermutation(arr, n, index+1);
        }
    }

    /**
     * 模拟大数的自增1
     *
     * @param arr
     * @return 能自增时返回true，达到最大值时返回false
     */
    private boolean increatment(int[] arr) {
        boolean suc = true;
        boolean flag = true;
        for (int i = 1; i <= arr.length - 1; i++) {
            if (flag) { //低位有进位
                arr[i]++;
                if (arr[i] == 10) {//向高位进位
                    arr[i] = 0;
                    flag = true;
                    if (i == arr.length - 1)//最高位进位
                        suc = false;
                } else flag = false;//向高位无进位
            } else break;
        }
        return suc;
    }

    public static void main(String[] args) {
        Solution solution = new Solution();
        solution.printMaxDigits2(2);
    }