feat: solve container with most water

container-with-most-water/GangBean.java

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+class Solution {
+    public int maxArea(int[] height) {
+        /**
+        1. understanding
+        - with two pair of line, each can contain "min(line1,line2) * (distance)" mount of water
+        - find maximum amount of water can contain
+        2. strategy
+        - brute force
+            - for each pair of lines, calculate amount and update maximum amount.
+            - it can takes O(N), where N is the count of lines.
+            - N is 10^5 at most, so it can takes 10^10, which can takes about 10 seconds
+        - you need to swap out unnecessary calculation
+        - so, let's find a unnecessary calculation in this problem.
+        3. complexity
+        - time: O(N)
+        - space: O(1)
+        */
+        int l = 0;
+        int r = height.length - 1;
+        int maxAmount = amountOf(height, l, r); // Math.min(height[l], height[r], r-l);
+        while (l < r) { // O(N)
+            maxAmount = Math.max(maxAmount, amountOf(height, l, r));
+            if (height[l] < height[r]) {
+                l++;
+            } else if (height[l] > height[r]) {
+                r--;
+            } else {
+                int nextLeftAmount = amountOf(height, l+1, r);
+                int nextRightAmount = amountOf(height, l, r-1);
+                if (nextLeftAmount < nextRightAmount) {
+                    r--;
+                } else {
+                    l++;
+                }
+            }
+        }
+
+        return maxAmount;
+    }
+
+    private int amountOf(int[] height, int left, int right) {
+        return (Math.min(height[left], height[right]) * (right - left));
+    }
+}
+