feat : solve maximum-subarray

Author: ekgns33

maximum-subarray/ekgns33.java

@@ -0,0 +1,41 @@
+/*
+input : array of integer
+output : largest sum of subarray
+constraints : 
+1) is the input array not empty?
+yes. at least one el
+2) range of integers
+[-10^4, 10^4]
+3) maximum lenght of input
+[10^5]
+>> maximum sum = 10^5 * 10^4 = 10 ^ 9 < INTEGER
+
+sol1) brute force
+nested for loop : O(n^2)
+tc : O(n^2), sc : O(1)
+
+sol2) dp?
+Subarray elements are continuous in the original array, so we can use dp.
+let dp[i] represent the largest sum of a subarray where the ith element is the last element of the subarray.
+
+if dp[i-1] + curval  < cur val : take curval
+if dp[i-1] + cur val >= curval :  take dp[i-1] + curval
+tc : O(n) sc : O(n)
+ */
+class Solution {
+  public int maxSubArray(int[] nums) {
+    int n = nums.length;
+    int[] dp = new int[n];
+    int maxSum = nums[0];
+    dp[0] = nums[0];
+    for(int i = 1; i < n; i++) {
+      if(dp[i-1] + nums[i] < nums[i]) {
+        dp[i] = nums[i];
+      } else {
+        dp[i] = nums[i] + dp[i-1];
+      }
+      maxSum = Math.max(maxSum, dp[i]);
+    }
+    return maxSum;
+  }
+}