From 9d6bc8ef30b7677ec23a39f397ebd414f434e5e2 Mon Sep 17 00:00:00 2001
From: Chen Xu <xckomorebi@icloud.com>
Date: Wed, 7 Sep 2022 03:41:08 -0400
Subject: [PATCH] Day 22 - DP III

---
 DPIII.java | 24 +++++++++++++++++++++++-
 1 file changed, 23 insertions(+), 1 deletion(-)

diff --git a/DPIII.java b/DPIII.java
index 641dbeb..379b84e 100644
--- a/DPIII.java
+++ b/DPIII.java
@@ -261,6 +261,28 @@ public int largest2(int[][] matrix) {
      * sum. Return the sum of the submatrix.
      */
     public int largest3(int[][] matrix) {
-        return 0;
+        int H = matrix.length;
+        int W = matrix[0].length;
+
+        int[][] dp = new int[H + 1][W];
+
+        for (int i = 0; i < H; i++) {
+            for (int j = 0; j < W; j++) {
+                dp[i + 1][j] = dp[i][j] + matrix[i][j];
+            }
+        }
+
+        int max = Integer.MIN_VALUE;
+        for (int i = 0; i < H; i++) {
+            for (int j = i + 1; j < H + 1; j++) {
+                int cur = 0;
+                for (int k = 0; k < W; k++) {
+                    cur += dp[j][k] - dp[i][k];
+                    max = Math.max(cur, max);
+                    cur = Math.max(0, cur);
+                }
+            }
+        }
+        return max;
     }
 }