Leetcode:Largest Number詳細題解

題目

Given a list of non negative integers, arrange them such that they form the largest number.git

For example, given [3, 30, 34, 5, 9], the largest formed number is 9534330.算法

Note: The result may be very large, so you need to return a string instead of an integer.ide

 

原題連接: https://oj.leetcode.com/problems/largest-number/函數

 

算法分析

case1(通常狀況):

[3, 30, 34, 5, 9] -> (9 -> 5 -> 34 -> 3 -> 30) -> 9534330spa

 

直觀想法按位從高到底排序設計

能夠很容易獲得9->5的順序,然而接下來問題來了,位相等的狀況怎麼辦?code

考慮3,30,34(數字組1)orm

簡單考慮[3, 30],顯然3->30要比30->3的值更大,即3>30的個位0;blog

再考慮[3, 34],(34->3) > (3->34),即34的個位4>3;排序

最後[30, 34],34 > 30;

因此數字組1的排序爲34->3->30;

最終結果爲9->5->34->3->30

 

case2(不止一位相等,多位高位相等的狀況):

[824, 8247] -> (824 -> 8247) -> 8248247

 

逐一從高位到低位比較,那麼第二個數字的最低位7應該與第一個數字的哪位比較呢?決定這兩數順序的不外乎,824->8247,8247->824這兩種狀況,直觀上7應與第一個數字的第一位8比較,因爲7<8,因此824->8247

 

case3 (不止一位相等,多位高位相等的狀況):

[824, 82483] -> (82483 -> 824) -> 82483824

 

case4(重複數字):

[33, 333] -> 33333

通常考慮假設待比較的數字爲a1a2, b1b2b3,a1b1…均爲位;在重複數字的狀況下

a1 a2

 ||   ||

b1 b2 b3

且b3 == a1,b1 == a2,此時能夠獲得b1 == a1 == a2 == b2 == b3,即全等,所以最大的比較次數爲數字1的位數加數字2的位數 - 1次,該例子的狀況爲4次。

 

題目陷阱

case1(有數字爲0):

[1, 2, 3, 4, 5, 6, 7, 8, 9, 0]

 

case2(數字均爲0):

[0, 0]

 

算法設計

Integer類,將int按位存儲,next取出下一位方法;

 1 class Integer {
 2 public:    
 3     Integer(int i);
 4 
 5     int getCount() { return count; }
 6 
 7     int next() {
 8         if (!tmp_count) {
 9             tmp_count = count;
10         }
11         return digits[--tmp_count];
12     }
13 
14 private:
15     int _i;
16     int count;
17     int tmp_count;
18     int digits[10];
19 };
20 
21 Integer::Integer(int i):count(0),tmp_count(0) {
22         // there has a great trap when i == 0
23     if (i) {
24         while (i) {
25             digits[count++] = i % 10;
26             i /= 10;
27         }
28     } else {
29         ++count;
30         digits[0] = 0;
31     }
32     tmp_count = count;
33 }    

 

比較函數cmp,按位從高到低循環比較,等於最大比較次數後退出;

 1 bool cmp(const int& a, const int& b) {
 2     Integer ia(a);
 3     Integer ib(b);
 4 
 5     int maxCmpCount = ia.getCount() + ib.getCount() - 1;
 6     int curCmpCount = 0;
 7 
 8     while (curCmpCount < maxCmpCount) {
 9          int bita = ia.next();
10         int bitb = ib.next();
11         
12         if (bita > bitb) {
13             return true;
14         }
15 
16         if (bita < bitb) {
17             return false;
18         }
19 
20         ++curCmpCount;
21     }
22 
23     return false;
24 }

 

完整代碼(Runtime:9ms)

 1 #include <string>
 2 #include <vector>
 3 #include <cstdio>
 4 
 5 class Integer {
 6 public:    
 7     Integer(int i);
 8 
 9     int getCount() { return count; }
10 
11     int next() {
12         if (!tmp_count) {
13             tmp_count = count;
14         }
15         return digits[--tmp_count];
16     }
17 
18 private:
19     int _i;
20     int count;
21     int tmp_count;
22     int digits[10];
23 };
24 
25 Integer::Integer(int i):count(0),tmp_count(0) { // there has a great trap when i == 0
26     if (i) {
27         while (i) {
28             digits[count++] = i % 10;
29             i /= 10;
30         }
31     } else {
32         ++count;
33         digits[0] = 0;
34     }
35     tmp_count = count;
36 }
37 
38 bool cmp(const int& a, const int& b) {
39     Integer ia(a);
40     Integer ib(b);
41 
42     int maxCmpCount = ia.getCount() + ib.getCount() - 1;
43     int curCmpCount = 0;
44 
45     while (curCmpCount < maxCmpCount) {
46          int bita = ia.next();
47         int bitb = ib.next();
48         
49         if (bita > bitb) {
50             return true;
51         }
52 
53         if (bita < bitb) {
54             return false;
55         }
56 
57         ++curCmpCount;
58     }
59 
60     return false;
61 }
62 
63 class Solution {
64 public:
65     std::string largestNumber(std::vector<int> &num) {
66         // there is a trap when nums is all zero
67         bool allZero = true;
68         for (auto itr = num.begin(); allZero && itr != num.end(); ++itr) {
69             if (*itr != 0) {
70                 allZero = false;
71             }
72         }
73 
74         if (allZero) {
75             return std::string("0");
76         }
77 
78         std::sort(num.begin(), num.end(), cmp);
79         std::string rel;
80         char tmp[10];
81         for (auto itr = num.begin(); itr != num.end(); ++itr) {
82             sprintf(tmp, "%d", *itr);
83             rel += tmp;
84         }
85         return rel;
86     }
87 };
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