@@ -39,27 +39,120 @@ coins = 3*1*5 + 3*5*8 + 1*3*8 + 1*8*1 = 167</pre>
3939 <li><code>0 <= nums[i] <= 100</code></li>
4040</ul >
4141
42-
4342## 解法
4443
4544<!-- 这里可写通用的实现逻辑 -->
4645
46+ 区间 DP。
47+
48+ - 状态表示：` dp[i][j] ` 表示戳破区间 ` (i, j) ` 内所有气球获得的最大硬币数。
49+ - 状态计算：枚举开区间 ` (i, j) ` 中以气球 k 作为最后戳破的气球。那么 ` dp[i][j] = max(dp[i][k] + dp[k][j] + nums[i] * nums[k] * nums[j]), k ∈ [i + 1, j) ` 。
50+
51+ 以区间长度 l 从小到大开始处理每个状态值。
52+
4753<!-- tabs:start -->
4854
4955### ** Python3**
5056
5157<!-- 这里可写当前语言的特殊实现逻辑 -->
5258
5359``` python
54-
60+ class Solution :
61+ def maxCoins (self nums : List[int ]) -> int :
62+ nums = [1 ] + nums + [1 ]
63+ n = len (nums)
64+ dp = [[0 ] * n for _ in range (n)]
65+ for l in range (2 , n):
66+ for i in range (n - l):
67+ j = i + l
68+ for k in range (i + 1 , j):
69+ dp[i][j] = max (dp[i][j], dp[i][k] + dp[k][j] + nums[i] * nums[k] * nums[j])
70+ return dp[0 ][- 1 ]
5571```
5672
5773### ** Java**
5874
5975<!-- 这里可写当前语言的特殊实现逻辑 -->
6076
6177``` java
78+ class Solution {
79+ public int maxCoins (int [] nums ) {
80+ int [] vals = new int [nums. length + 2 ];
81+ vals[0 ] = 1 ;
82+ vals[vals. length - 1 ] = 1 ;
83+ System . arraycopy(nums, 0 , vals, 1 , nums. length);
84+ int n = vals. length;
85+ int [][] dp = new int [n][n];
86+ for (int l = 2 ; l < n; ++ l) {
87+ for (int i = 0 ; i + l < n; ++ i) {
88+ int j = i + l;
89+ for (int k = i + 1 ; k < j; ++ k) {
90+ dp[i][j] = Math . max(dp[i][j], dp[i][k] + dp[k][j] + vals[i] * vals[k] * vals[j]);
91+ }
92+ }
93+ }
94+ return dp[0 ][n - 1 ];
95+ }
96+ }
97+ ```
98+
99+ ### ** C++**
100+
101+ ``` cpp
102+ class Solution {
103+ public:
104+ int maxCoins(vector<int >& nums) {
105+ nums.insert(nums.begin(), 1);
106+ nums.push_back(1);
107+ int n = nums.size();
108+ vector<vector<int >> dp(n, vector<int >(n));
109+ for (int l = 2; l < n; ++l)
110+ {
111+ for (int i = 0; i + l < n; ++i)
112+ {
113+ int j = i + l;
114+ for (int k = i + 1; k < j; ++k)
115+ {
116+ dp[ i] [ j ] = max(dp[ i] [ j ] , dp[ i] [ k ] + dp[ k] [ j ] + nums[ i] * nums[ k] * nums[ j] );
117+ }
118+ }
119+ }
120+ return dp[ 0] [ n - 1 ] ;
121+ }
122+ };
123+ ```
62124
125+ ### **Go**
126+
127+ ```go
128+ func maxCoins(nums []int) int {
129+ vals := make([]int, len(nums)+2)
130+ for i := 0; i < len(nums); i++ {
131+ vals[i+1] = nums[i]
132+ }
133+ n := len(vals)
134+ vals[0], vals[n-1] = 1, 1
135+ dp := make([][]int, n)
136+ for i := 0; i < n; i++ {
137+ dp[i] = make([]int, n)
138+ }
139+ for l := 2; l < n; l++ {
140+ for i := 0; i+l < n; i++ {
141+ j := i + l
142+ for k := i + 1; k < j; k++ {
143+ dp[i][j] = max(dp[i][j], dp[i][k]+dp[k][j]+vals[i]*vals[k]*vals[j])
144+ }
145+ }
146+ }
147+ return dp[0][n-1]
148+ }
149+
150+ func max(a, b int) int {
151+ if a > b {
152+ return a
153+ }
154+ return b
155+ }
63156```
64157
65158### ** ...**
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