Feat: 53. Maximum Subarray

Author: HC-kang

maximum-subarray/HC-kang.ts

@@ -0,0 +1,93 @@
+/**
+ * https://leetcode.com/problems/maximum-subarray
+ * Kadane's Algorithm
+ * T.C. O(n)
+ * S.C. O(1)
+ */
+function maxSubArray(nums: number[]): number {
+  let maxSum = nums[0];
+
+  for (let i = 1; i < nums.length; i++) {
+    nums[i] = Math.max(nums[i], nums[i] + nums[i - 1]);
+    maxSum = Math.max(maxSum, nums[i]);
+  }
+
+  return maxSum;
+}
+
+/**
+ * Divide and Conquer version
+ * T.C. O(n log n)
+ * S.C. O(log n) - call stack
+ */
+function maxSubArray(nums: number[]): number {
+  function maxSubArrayHelper(
+    nums: number[],
+    left: number,
+    right: number
+  ): number {
+    if (left === right) return nums[left];
+
+    const mid = (left + right) >> 1;
+    const leftMax = maxSubArrayHelper(nums, left, mid);
+    const rightMax = maxSubArrayHelper(nums, mid + 1, right);
+    let leftSum = -Infinity;
+    let rightSum = -Infinity;
+    let sum = 0;
+
+    for (let i = mid; i >= left; i--) {
+      sum += nums[i];
+      leftSum = Math.max(leftSum, sum);
+    }
+
+    sum = 0;
+    for (let i = mid + 1; i <= right; i++) {
+      sum += nums[i];
+      rightSum = Math.max(rightSum, sum);
+    }
+
+    return Math.max(leftMax, rightMax, leftSum + rightSum);
+  }
+
+  return maxSubArrayHelper(nums, 0, nums.length - 1);
+}
+
+/**
+ * Iterative version
+ * T.C. O(n log n)
+ * S.C. O(log n) - call stack
+ */
+function maxSubArray(nums: number[]): number {
+  const stack = [[0, nums.length - 1]];
+  let maxSum = nums[0];
+
+  while (stack.length) {
+    const [left, right] = stack.pop()!;
+    if (left === right) {
+      maxSum = Math.max(maxSum, nums[left]);
+      continue;
+    }
+
+    const mid = (left + right) >> 1;
+    stack.push([left, mid], [mid + 1, right]);
+
+    let leftSum = -Infinity;
+    let rightSum = -Infinity;
+    let sum = 0;
+
+    for (let i = mid; i >= left; i--) {
+      sum += nums[i];
+      leftSum = Math.max(leftSum, sum);
+    }
+
+    sum = 0;
+    for (let i = mid + 1; i <= right; i++) {
+      sum += nums[i];
+      rightSum = Math.max(rightSum, sum);
+    }
+
+    maxSum = Math.max(maxSum, leftSum + rightSum);
+  }
+
+  return maxSum;
+}