New Problem Soluiton "Split Array Largest Sum"

README.md

@@ -12,6 +12,7 @@ LeetCode
 |414|[Third Maximum Number](https://leetcode.com/problems/third-maximum-number/) | [C++](./algorithms/cpp/thirdMaximumNumber/ThirdMaximumNumber.cpp)|Easy|
 |413|[Arithmetic Slices](https://leetcode.com/problems/arithmetic-slices/) | [C++](./algorithms/cpp/arithmeticSlices/ArithmeticSlices.cpp)|Medium|
 |412|[Fizz Buzz](https://leetcode.com/problems/fizz-buzz/) | [C++](./algorithms/cpp/fizzBuzz/FizzBuzz.cpp)|Easy|
+|410|[Split Array Largest Sum](https://leetcode.com/problems/split-array-largest-sum/) | [C++](./algorithms/cpp/splitArrayLargestSum/SplitArrayLargestSum.cpp)|Hard|
 |409|[Longest Palindrome](https://leetcode.com/problems/longest-palindrome/) | [C++](./algorithms/cpp/longestPalindrome/LongestPalindrome.cpp)|Easy|
 |406|[Queue Reconstruction by Height](https://leetcode.com/problems/queue-reconstruction-by-height/) | [C++](./algorithms/cpp/queueReconstructionByHeight/QueueReconstructionByHeight.cpp)|Medium|
 |405|[Convert a Number to Hexadecimal](https://leetcode.com/problems/convert-a-number-to-hexadecimal/) | [C++](./algorithms/cpp/convertANumberToHexadecimal/ConvertANumberToHexadecimal.cpp)|Easy|

algorithms/cpp/splitArrayLargestSum/SplitArrayLargestSum.cpp

@@ -0,0 +1,69 @@
+// Source : https://leetcode.com/problems/split-array-largest-sum/
+// Author : Hao Chen
+// Date   : 2016-11-13
+
+/*************************************************************************************** 
+ *
+ * Given an array which consists of non-negative integers and an integer m, you can 
+ * split the array into m non-empty continuous subarrays. Write an algorithm to 
+ * minimize the largest sum among these m subarrays.
+ * 
+ * Note:
+ * Given m satisfies the following constraint: 1 ≤ m ≤  length(nums) ≤ 14,000.
+ * 
+ * Examples: 
+ * 
+ * Input:
+ * nums = [7,2,5,10,8]
+ * m = 2
+ * 
+ * Output:
+ * 18
+ * 
+ * Explanation:
+ * There are four ways to split nums into two subarrays.
+ * The best way is to split it into [7,2,5] and [10,8],
+ * where the largest sum among the two subarrays is only 18.
+ ***************************************************************************************/
+
+class Solution {
+public:
+    // Idea
+    //   1) The max of the result is the sum of the whole array.
+    //   2) The min of the result is the max num among the array.
+    //   3) Then, we use Binary Search to find the resullt between the `min` and  the `max`
+    
+    int splitArray(vector<int>& nums, int m) {
+        int min = 0, max = 0;
+        for (int n : nums) {
+            min = std::max(min, n);
+            max += n;
+        }
+        while (min < max) {
+            int mid = min + (max - min) / 2;
+            if (hasSmallerSum(nums, m, mid)) max = mid;
+            else min = mid + 1;
+        }
+        return min;
+    }
+    
+    
+    // Using a specific `sum` to check wheter we can get `smaller sum`
+    // The idea here as below:
+    //   find all of possible `sub array` whose sum greater than `sum`
+    //   1) if the number of `sub array` >  m, whcih means the actual result is greater than `sum`
+    //   2) if the number of `sub array` <= m, whcih means we can have `smaller sum`
+    //
+    bool hasSmallerSum(vector<int>& nums, int m, int sum) {
+        int cnt = 1, curSum = 0;
+        for (int n : nums) {
+            curSum += n;
+            if (curSum > sum) {
+                curSum = n;
+                cnt++;
+                if (cnt > m) return false;
+            }
+        }
+        return true;
+    }
+};