maximum-subarray

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Algorithms

Given an integer array <code>nums</code>, find the subarray with the largest sum, and return its sum.

&nbsp;
Example 1:

<pre>
Input: nums = [-2,1,-3,4,-1,2,1,-5,4]
Output: 6
Explanation: The subarray [4,-1,2,1] has the largest sum 6.
</pre>

Example 2:

<pre>
Input: nums = [1]
Output: 1
Explanation: The subarray [1] has the largest sum 1.
</pre>

Example 3:

<pre>
Input: nums = [5,4,-1,7,8]
Output: 23
Explanation: The subarray [5,4,-1,7,8] has the largest sum 23.
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= nums.length &lt;= 105</code></li>
	<li><code>-104 &lt;= nums[i] &lt;= 104</code></li>
</ul>

&nbsp;
Follow up: If you have figured out the <code>O(n)</code> solution, try coding another solution using the divide and conquer approach, which is more subtle.

maxSubArray

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Array

Divide and Conquer

Dynamic Programming

&#32473;&#20320;&#19968;&#20010;&#25972;&#25968;&#25968;&#32452; <code>nums</code> &#65292;&#35831;&#20320;&#25214;&#20986;&#19968;&#20010;&#20855;&#26377;&#26368;&#22823;&#21644;&#30340;&#36830;&#32493;&#23376;&#25968;&#32452;&#65288;&#23376;&#25968;&#32452;&#26368;&#23569;&#21253;&#21547;&#19968;&#20010;&#20803;&#32032;&#65289;&#65292;&#36820;&#22238;&#20854;&#26368;&#22823;&#21644;&#12290;

&#23376;&#25968;&#32452; &#26159;&#25968;&#32452;&#20013;&#30340;&#19968;&#20010;&#36830;&#32493;&#37096;&#20998;&#12290;

&nbsp;

&#31034;&#20363; 1&#65306;

<pre>
&#36755;&#20837;&#65306;nums = [-2,1,-3,4,-1,2,1,-5,4]
&#36755;&#20986;&#65306;6
&#35299;&#37322;&#65306;&#36830;&#32493;&#23376;&#25968;&#32452;&nbsp;[4,-1,2,1] &#30340;&#21644;&#26368;&#22823;&#65292;&#20026;&nbsp;6 &#12290;
</pre>

&#31034;&#20363; 2&#65306;

<pre>
&#36755;&#20837;&#65306;nums = [1]
&#36755;&#20986;&#65306;1
</pre>

&#31034;&#20363; 3&#65306;

<pre>
&#36755;&#20837;&#65306;nums = [5,4,-1,7,8]
&#36755;&#20986;&#65306;23
</pre>

&nbsp;

&#25552;&#31034;&#65306;

<ul>
	<li><code>1 &lt;= nums.length &lt;= 105</code></li>
	<li><code>-104 &lt;= nums[i] &lt;= 104</code></li>
</ul>

&nbsp;

&#36827;&#38454;&#65306;&#22914;&#26524;&#20320;&#24050;&#32463;&#23454;&#29616;&#22797;&#26434;&#24230;&#20026; <code>O(n)</code> &#30340;&#35299;&#27861;&#65292;&#23581;&#35797;&#20351;&#29992;&#26356;&#20026;&#31934;&#22937;&#30340; &#20998;&#27835;&#27861; &#27714;&#35299;&#12290;

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