new question added

Author: arorarahul

README.md

@@ -456,6 +456,7 @@ use KMP
 - [Given a string of digits, find the length of the longest substring of a string, such that the length of the substring is '2k' digits and sum of left k digits is equal to the sum of right k digits](/dynamic-programming/question31.c)
 - [Given a rod of length 'n' inches and an array of prices that contains prices of all pieces of size smaller than n, find the max value obtainable by cutting the rod and selling the pieces](/dynamic-programming/question32.c)
 - [Fibonacci series](/dynamic-programming/question33.c)
+- [Max product sub array](/dynamic-programming/question34.c)
 
 ### Graphs
 

dynamic-programming/question2.c

@@ -33,7 +33,7 @@ int compareStrings(char *str1, char *str2, int len1, int len2){
 		for(j=0;j<=len2;j++){
 			if(i==0 || j==0){
 				m[i][j] = 0;
-			}else if(str1[i] == str2[j]){
+			}else if(str1[i-1] == str2[j-1]){
 				m[i][j] = 1 + m[i-1][j-1];
 			}else{
 				m[i][j] = max(m[i-1][j],m[i][j-1]);
@@ -54,4 +54,60 @@ int main(){
 
   	printf("length is %d\n", len);
 	return 0;
+}
+
+
+//METHOD2 using recursion
+#include <stdio.h>
+#include <stdlib.h>
+#define MAX 200
+
+int table[MAX][MAX];
+
+int max(int a, int b){
+	// printf("finding max between %d, %d \n",a,b);
+	return a>b?a:b;
+}
+
+int lcs(int start1, int start2, char *str1, char *str2, int len1, int len2){
+	if(start1 == len1 || start2 == len2){
+		return 0;
+	}
+	if(table[start1][start2] == -1){
+		if(str1[start1] == str2[start2]){
+			table[start1][start2] =  1 + lcs(start1+1,start2+1,str1, str2, len1, len2);
+		}else{
+			int a = lcs(start1+1,start2,str1,str2,len1,len2);
+			int b = lcs(start1,start2+1,str1,str2,len1,len2);
+			table[start1][start2] =  max(a,b);		
+		}
+	}
+	return table[start1][start2];
+}
+
+void init(){
+	int i,j;
+	for(i=0;i<MAX;i++){
+		for(j=0;j<MAX;j++){
+			table[i][j] = -1;
+		}
+	}
+
+}
+
+int main(){
+	int cases;
+	scanf("%d", &cases);
+	int i;
+	for(i=0;i<cases;i++){
+		int len1, len2;
+		scanf("%d %d", &len1, &len2);
+		char str1[len1+1],str2[len2+1];
+		scanf("%s",str1);
+		scanf("%s",str2);
+		init();
+		int me = lcs(0,0,str1,str2, len1, len2);
+		printf("%d\n", me);
+	}
+	return 0;
 }

dynamic-programming/question33.c

@@ -82,4 +82,6 @@ int main(){
 	printf("answer is %d\n", fib(n));
 
 	return 0;
-}
+}
+
+

dynamic-programming/question34.c

@@ -0,0 +1,87 @@
+/*
+
+Find the max product sub array
+
+METHOD:
+Here we traverse the array from both the sides, handling corner cases.
+Also the algorithm takes into account the number of negative numbers
+
+This is not a DP question.
+
+Another method listed at GFG
+http://www.geeksforgeeks.org/maximum-product-subarray/
+
+
+
+*/
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <limits.h>
+
+void maxProductSubArray(int *arr, int size){
+	int i;
+	int countNegatives = 0;
+	for(i=0;i<size;i++){
+		if(arr[i] < 0){
+			countNegatives++;
+		}
+	}
+	int lastCountNegativesValues = countNegatives;
+
+	int curr = 1, max = INT_MIN;
+
+	for(i=0;i<size;i++){
+		curr = curr*arr[i];
+
+		if(curr > max){
+			max = curr;
+		}
+
+		if(arr[i] < 0){
+			countNegatives--;
+		}
+
+		if((curr < 0 && countNegatives <= 0) || (curr == 0)){
+			curr = 1;
+		}
+	}
+
+	curr = 1;
+	countNegatives = lastCountNegativesValues;
+
+	for(i=size-1;i>=0;i--){
+		curr = curr*arr[i];
+		if(curr > max){
+			max = curr;
+		}
+
+		if(arr[i] < 0){
+			countNegatives--;
+		}
+
+		if((curr < 0 && countNegatives <= 0) || (curr == 0)){
+			curr = 1;
+		}
+	}
+
+	printf("%d\n", max);
+}	
+
+int main(){
+	int cases;
+	scanf("%d",&cases);
+	int i;
+	for(i=0;i<cases;i++){
+		int size;
+		scanf("%d",&size);
+		int j;
+		int arr[size];
+		for(j=0;j<size;j++){
+			scanf("%d",&arr[j]);
+		}
+		maxProductSubArray(arr, size);
+
+	}
+	return 0;
+}

dynamic-programming/question8.c

@@ -63,3 +63,63 @@ int main(){
 	maxSumSubArr(arr, size);
 	return 0;
 }
+
+//this will handle negative cases as well because in that case the answer will be the max number in the
+//array. Also this can be done by simply comparing the negative value of curr with max and then seeing
+//is the assignment should be done and later assigning 0 to curr
+#include <stdio.h>
+#include <stdlib.h>
+
+void maxSumSubArray(int *arr, int size){
+	int i;
+	int max = arr[0];
+	int curr = arr[0];
+	int end = 0;
+
+	if(curr < 0){
+		curr = 0;
+	}
+
+	for(i=1;i<size;i++){
+		curr += arr[i];
+		
+		if(max < curr){
+			max = curr;
+			end = i;
+		}	
+
+		if(curr < 0){
+			curr = 0;
+		}
+	}
+
+	printf("max is %d\n", max);
+	printf("end is %d\n", end);
+
+	int temp = end;
+	int sum = 0, start;
+	while(temp >=0){
+		sum += arr[temp];
+		if(sum == max){
+			start = temp;
+			break;
+		}
+		temp--;
+	}
+
+	for(i=start;i<=end;i++){
+		printf("%d ", arr[i]);
+	}
+
+}
+
+int main(){
+
+	int arr[] = {-2,-3,-4,-1,-2,-1,-5,-3};
+
+	int size = sizeof(arr)/sizeof(arr[0]);
+
+	maxSumSubArray(arr, size);
+
+	return 0;
+}

test1.c

@@ -1,34 +1,70 @@
 #include <stdio.h>
 #include <stdlib.h>
+#include <limits.h>
 
-struct node{
-	int data;
-	struct node *left;
-	struct node *right;
-}*root = NULL, *root2 = NULL;
+void maxProductSubArray(int *arr, int size){
+	int i;
+	int countNegatives = 0;
+	for(i=0;i<size;i++){
+		if(arr[i] < 0){
+			countNegatives++;
+		}
+	}
+	int lastCountNegativesValues = countNegatives;
 
-struct node *newNode(int data){
-	struct node *temp = (struct node *)malloc(sizeof(struct node));
-	temp->data = data;
-	temp->left = temp->right = NULL;
-	return temp;
-}
+	int curr = 1, max = INT_MIN;
 
-struct node *mirror(struct node *root, struct node *root2){
-	
-}
+	for(i=0;i<size;i++){
+		curr = curr*arr[i];
 
-int main(){
+		if(curr > max){
+			max = curr;
+		}
+
+		if(arr[i] < 0){
+			countNegatives--;
+		}
+
+		if((curr < 0 && countNegatives <= 0) || (curr == 0)){
+			curr = 1;
+		}
+	}
+
+	curr = 1;
+	countNegatives = lastCountNegativesValues;
 
-	root = newNode(10);
-	root->left = newNode(20);
-	root->left->left = newNode(30);
-	root->left->right = newNode(40);
-	root->right = newNode(50);
-	root->right->left = newNode(50);
-	root->right->right = newNode(50);
+	for(i=size-1;i>=0;i--){
+		curr = curr*arr[i];
+		if(curr > max){
+			max = curr;
+		}
 
-	root2 = mirror(root, root2);
+		if(arr[i] < 0){
+			countNegatives--;
+		}
+
+		if((curr < 0 && countNegatives <= 0) || (curr == 0)){
+			curr = 1;
+		}
+	}
+
+	printf("%d\n", max);
+}	
+
+int main(){
+	int cases;
+	scanf("%d",&cases);
+	int i;
+	for(i=0;i<cases;i++){
+		int size;
+		scanf("%d",&size);
+		int j;
+		int arr[size];
+		for(j=0;j<size;j++){
+			scanf("%d",&arr[j]);
+		}
+		maxProductSubArray(arr, size);
 
+	}
 	return 0;
 }