Search the index
You are given with an array of integer and the length of array. Now u have to find an index i such that a(i)=i.
[AMAZON] Vertical sum of nodes
Given a Binary Tree, find vertical sum of the nodes that are in same vertical line. Print all sums through different vertical lines. Examples: 1 / \ 2 3 / \ / \ 4 5 6 7 The tree has 5 vertical lines Vertical-Line-1 has only one node 4 => vertical sum is 4 Vertical-Line-2: has only one node 2=> vertical sum is 2 Vertical-Line-3: has three nodes: 1,5,6 => vertical sum is 1+5+6 = 12 Vertical-Line-4: has only one node 3 => vertical sum is 3 Vertical-Line-5: has only one node 7 => vertical sum is 7 So expected output is 4, 2, 12, 3 and 7
This can be done in O(logN) time and O(1) space by using a slightly modified binary search.
ReplyDeleteConsider a new array Y such that Y[i] = X[i] - i
Array X : -3 -1 0 3 5 7
index : 0 1 2 3 4 5
Array Y : -3 -2 -2 0 1 2
Since the elements in X are in increasing order, the elements in the new array Y will be in non-decreasing order. So a binary search for 0 in Y will give the answer.
But creating Y will take O(N) space and O(N) time. So instead of creating the new array you just modify the binary search such that a reference to Y[i] is replaced by X[i] - i.
Code :
int FindIndex_Value(int a[],int low,int high){
int mid = (low+high)/2;
if( a[mid] == mid )
return mid;
if(a[mid]< mid)
return FindIndex_Value(a,low,mid-1);
else
return FindIndex_Value(a,mid+1,high);
}