Merge pull request matthewsamuel95#293 from BlackVS/iss258

Max Sum Increasing Subsequence .py and .cpp solutions

Author: matthewsamuel95

DP/Maximum Sum Increasing Subsequence/MaximumSumIncreasingSubsequence.cpp

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+// sol.cpp : Defines the entry point for the console application.
+//
+
+//#include "stdafx.h"
+#include <bits/stdc++.h>
+/* Dynamic Programming solution to construct Maximum Sum Increasing Subsequence */
+
+#include <cmath>
+#include <cstdio>
+#include <fstream>
+#include <string>
+#include <iostream>
+#include <vector>
+#include <utility>
+#include <algorithm>
+using namespace std;
+
+
+typedef vector<int> VI;
+
+// Function to construct Maximum Sum Increasing Subsequence
+VI calcMaxSumIS(VI arr)
+{
+	int n = arr.size();
+
+	// L[i] stores the Maximum Sum Increasing Subsequence that ends with arr[i]
+	vector<VI> L(n);
+
+	// msis[i] stores the Maximum Sum of Increasing Subsequence that
+	// ends with arr[i]
+	VI msis(n);
+
+	// L[0] is equal to arr[0]
+	L[0].push_back(arr[0]);
+	msis[0] = arr[0];
+
+	// start from index 1
+	for (int i = 1; i < n; i++)
+	{
+		// for every j less than i
+		for (int j = 0; j < i; j++)
+		{
+			// L[i] = {MaxSum(L[j])} + arr[i] where j < i and arr[j] < arr[i]
+			if ((arr[i] > arr[j]) && (msis[i] < msis[j]))
+			{
+				L[i] = L[j];
+				msis[i] = msis[j];
+			}
+		}
+		// L[i] ends with arr[i]
+		L[i].push_back(arr[i]);
+		msis[i] += arr[i];
+
+		// L[i] now stores Maximum Sum Increasing Subsequence of arr[0..i]
+		// that ends with arr[i]
+	}
+
+	int maxIndex = 0;
+	int max = msis[0];
+
+	// find max
+	for (int i = 1; i < n; i++)
+		if (msis[i] > max)
+		{
+			max = msis[i];
+			maxIndex = i;
+		}
+
+	// max will contain result
+	return L[maxIndex];
+}
+
+int main() {
+	ifstream infile("test1.txt");
+	if (infile)
+	{
+		VI arr;
+		string s;
+		int a;
+		while(true) {
+			try {
+				getline(infile,s);
+				a = stoi(s);
+			}
+			catch (...) {
+				break;
+			}
+			arr.push_back(a);
+		}
+		auto res= calcMaxSumIS(arr);
+		for (auto r : res)
+			cout << r << " ";
+		cout << endl;
+	}
+}

DP/Maximum Sum Increasing Subsequence/MaximumSumIncreasingSubsequence.py

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+#!/bin/python3
+import sys
+from copy import copy
+
+fstd="test2"
+sys.stdin = open('%s.txt' % fstd, 'r')
+input = sys.stdin.readline
+
+# DP based Python  
+# implementation of Maximum Sum  
+# Increasing Subsequence (MSIS) 
+# problem 
+  
+# constructMaxSumIS() returns the tupple:
+# ( max sum of increasing subsequence, found subsequence )
+def constructMaxSumIS(arr): 
+    N = len(arr)
+    
+    # L[i] stores the Maximum Sum Increasing Subsequence that ends with arr[i]
+    L=[ [] for _ in range(N) ]
+    # L[0] is equal to arr[0]
+    L[0].append(arr[0])
+    
+    # msis[i] stores the Maximum Sum of Increasing Subsequence that
+    # ends with arr[i]
+    msis = [0]*N 
+    # Initialize msis values 
+    msis[0]=arr[0]
+  
+    # Compute maximum sum  
+    # values in bottom up manner 
+    for i in range(1, N): 
+        for j in range(i): 
+            if (arr[i] > arr[j]) and (msis[i] < msis[j]): 
+                msis[i] = msis[j]
+                L[i] = copy(L[j])
+        L[i].append(arr[i])
+        msis[i]+=arr[i]
+
+    # Find max 
+    maxIndex=max(range(N), key=lambda i:msis[i])
+    return (msis[maxIndex],L[maxIndex])
+
+if __name__ == "__main__":
+    print("Input sequence:")
+    A=[]
+    while(True):
+        line=input().strip()
+        try:
+            num=int(line)
+        except ValueError:
+            break
+        A.append(num)
+    print(A)
+    res=constructMaxSumIS(A)
+    print("Max sum is {}".format(res[0]))
+    print("Found sequence is: {} ".format(res[1]))
+   

DP/Maximum Sum Increasing Subsequence/test1.txt

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+1
+101
+2
+3
+100
+4
+5
+
+
+Result: 1, 2, 3, 100

DP/Maximum Sum Increasing Subsequence/test2.txt

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+1
+101
+2
+3
+100
+4
+5
+10
+20
+15
+40
+20
+90
+100
+10
+40
+50
+60
+
+Result: 1 2 3 4 5 10 20 40 90 100