From e7d4f50b766be809373a465767dfe3e05ac2ad37 Mon Sep 17 00:00:00 2001
From: Haidong Ji
Date: Wed, 26 Dec 2018 20:27:48 -0600
Subject: Knapsack maximize gold done!

Interesting signal 11 segmentation fault problem. Once I changed the 2D
array to 2D vector, it worked:
//	int value[W + 1][j + 1];
	vector< vector<int> > value(W + 1, vector<int>(j + 1));---
 PlaygroundCpp/Sources/Playground.cpp | 79 +++++++++++++-----------------------
 1 file changed, 29 insertions(+), 50 deletions(-)

diff --git a/PlaygroundCpp/Sources/Playground.cpp b/PlaygroundCpp/Sources/Playground.cpp
index e402792..50297b2 100644
--- a/PlaygroundCpp/Sources/Playground.cpp
+++ b/PlaygroundCpp/Sources/Playground.cpp
@@ -1,67 +1,46 @@
 #include <iostream>
-#include <algorithm>
 #include <vector>
 //#include <gtest/gtest.h>
 
 using std::vector;
 
-int lcs3(vector<int> &a, vector<int> &b, vector<int> &c) {
-	int l = c.size();
-	int m = b.size();
-	int n = a.size();
-	int D[n + 1][m + 1][l + 1];
-	for (int k = 0; k < l + 1; k++) {
-		for (int j = 0; j < m + 1; j++) {
-			for (int i = 0; i < n + 1; i++) {
-				if (i == 0 || j == 0 || k == 0) {
-					D[i][j][k] = 0;
-					continue;
-				}
-				if (a[i - 1] == b[j - 1] && b[j - 1] == c[k - 1]) {
-					D[i][j][k] = D[i - 1][j - 1][k - 1] + 1;
-				} else {
-					D[i][j][k] = std::max(D[i - 1][j][k],
-							std::max(D[i][j - 1][k], D[i][j][k - 1]));
+int optimalWeight(int W, vector<int> &w2) {
+	int j = w2.size();
+//	int value[W + 1][j + 1];
+	vector< vector<int> > value(W + 1, vector<int>(j + 1));
+
+	for (int i = 0; i < j + 1; i++) {
+		for (int w = 0; w < W + 1; w++) {
+			if (i == 0 || w == 0) {
+				value[w][i] = 0;
+				continue;
+			}
+			value[w][i] = value[w][i - 1];
+			if (w2[i - 1] <= w) {
+				int val = value[w - w2[i - 1]][i - 1] + w2[i - 1];
+				if (value[w][i] < val) {
+					value[w][i] = val;
 				}
 			}
 		}
+
 	}
-	return D[n][m][l];
+	return value[W][j];
 }
 
-//TEST(LCS3, t1) {
-//	vector<int> a = { 1, 2, 3 };
-//	vector<int> b = { 2, 1, 3 };
-//	vector<int> c = { 1, 3, 5 };
-//	ASSERT_EQ(2, lcs3(a, b, c));
-//}
-//
-//TEST(LCS3, t2) {
-//	vector<int> a = { 8, 3, 2, 1, 7 };
-//	vector<int> b = { 8, 2, 1, 3, 8, 10, 7 };
-//	vector<int> c = { 6, 8, 3, 1, 4, 7 };
-//	ASSERT_EQ(3, lcs3(a, b, c));
+//TEST(Knapsack, t1) {
+//	vector<int> w = { 1, 4, 8 };
+//	int W = 10;
+//	ASSERT_EQ(9, optimalWeight(W, w));
 //}
 
 int main() {
-	size_t an;
-	std::cin >> an;
-	vector<int> a(an);
-	for (size_t i = 0; i < an; i++) {
-		std::cin >> a[i];
-	}
-	size_t bn;
-	std::cin >> bn;
-	vector<int> b(bn);
-	for (size_t i = 0; i < bn; i++) {
-		std::cin >> b[i];
-	}
-	size_t cn;
-	std::cin >> cn;
-	vector<int> c(cn);
-	for (size_t i = 0; i < cn; i++) {
-		std::cin >> c[i];
-	}
-	std::cout << lcs3(a, b, c) << std::endl;
+  int n, W;
+  std::cin >> W >> n;
+  vector<int> w(n);
+  for (int i = 0; i < n; i++) {
+    std::cin >> w[i];
+  }
+  std::cout << optimalWeight(W, w) << '\n';
 }
 
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