new question added

Author: arorarahul

README.md

@@ -182,6 +182,7 @@ For eg storing the minimum so far in another stack so that each time when a numb
 - [Given a max heap, apply different heap operations (find max, delete max,increase key, insert key, decrease key.)](/heaps/question2.c)
 - [Write a program for heap sort](/heaps/question3.c)
 - [Find a max element in a min-heap](/heaps/question4.c)
+- [Build a min-heap and write algo to delete an arbitrary element](/heaps/question5.c)
 
 ## Some important concepts to solve algos better
 

heaps/question5.c

@@ -0,0 +1,106 @@
+/*
+Build a min-heap and write algo to delete an arbitrary element
+
+
+Time complexity: O(n) 
+because finding that element will take O(n) time linear search and deleting will take O(logn) time
+Total in O(n)
+Space complexity: O(1)
+*/
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+
+void swap(int *a, int *b){
+	int temp = *a;
+	*a = *b;
+	*b = temp;
+}
+
+void minHeapify(int *arr,int i, int size){
+	int left = 2*i+1,right=2*i+2,smallest, heapSize = size;
+	if(left < heapSize-1 && arr[i] < arr[left]){
+		smallest = i;
+	}else{
+		smallest = left;
+	}
+	if(right < heapSize-1 && arr[right] < arr[smallest]){
+		smallest = right;
+	}
+	if(smallest < heapSize - 1 && smallest !=i){
+		swap(&arr[smallest],&arr[i]);
+		minHeapify(arr,smallest,size);
+	}
+}
+
+void buildMinHeap(int *arr, int size){
+	int index = floor(size/2);
+	printf("value of index is...%d\n", index);
+	for(int i=index; i>=0;i--){
+		minHeapify(arr,i,size);
+	}
+}
+
+void display(int *arr,int size){
+	for(int i=0;i<size;i++){
+		printf("%d\t", arr[i]);
+	}
+	printf("\n");
+}
+
+int deleteElement(int *arr, int index, int *size){
+	if(*size < 1){
+		return -1;
+	}
+	int result = arr[index];
+	int temp = arr[index];
+	arr[index]=arr[*size-1];
+	arr[*size-1]=temp;
+	*size = *size-1;
+	minHeapify(arr,index,*size);
+	return result;
+}
+
+int findIndex(int *arr, int size, int value){
+	for(int i=0;i<size;i++){
+		if(arr[i]==value){
+			return i;
+		}
+	}
+	return -1;
+}
+
+int main(){
+	int *arr, size, elm, result;
+	printf("enter the size of the min-heap\n");
+	scanf("%d",&size);
+	arr = (int *)malloc(sizeof(int)*size);
+
+	for(int i=0; i<size;i++){
+		printf("enter %d th element\n", i);
+		scanf("%d",&arr[i]);
+	}
+
+	buildMinHeap(arr,size);
+	display(arr, size);
+
+	while(1){
+		printf("enter the element to be deleted\n");
+		scanf("%d",&elm);
+		int index  = findIndex(arr,size,elm);
+		if(index >= 0){
+			result = deleteElement(arr,index,&size);
+			if(result < 0){
+				printf("underflow\n");
+			}else{
+				printf("%d was removed\n", result);
+			}
+			printf("updated heap is..\n");
+			display(arr,size);
+		}else{
+			printf("element not found\n");
+		}
+	}
+	return 0;
+}

nextquestions.md

@@ -40,4 +40,5 @@ TODO:
 - double linked list implementation for question7 stacks and queues to be done
 - question 8, 9 implementation for stacks and queues to be done
 - Program to find then the stock should be sold in order to gain max profit
-- insert key in heap question2 to be done
+- insert key in heap question2 to be done
+- building min/max heap for duplicate elements