- Write a program to find ceiling of a number in a sorted array.
- Algorithm to find the smallest number greater than or equal to X in a sorted integer array.

Given a sorted integer array and an integer X. We have to **find the smallest number greater than or equal to X** in input array.

Sorted array : [1 3 5 6 8 10 11 14 15 20].

**Ceiling**: Ceiling of a number X is the smallest number greater than or equal to X in sorted array. If X is present in array then X is the ceiling otherwise smallest number greater than X.- Ceiling of 9 is 10
- Ceiling of 14 is 14

Let inputArray be the given sorted array of size N.

**Linear search : O(n)**

**Algorithm to find ceiling of a number using linear search**

- If X is smaller than smallest element of inputArray(inputArray[0]). Then smallest element is ceiling element of X.
- If X is larger than largest element of inputArray(inputArray[N-1]), then no ceiling element exist for X.
- Traverse inputArray from index 0 to N-1 and find an index i where inputArray[i] < X && inputArray[i+1] >= X
- Return inputArray[i+1] as it is the first element greater than or equal to X.

## C program to find ceiling of a number in sorted array using linear search.

#include <stdio.h> /* This function prints the ceiling of K in sorted array */ void printCeilingElement(int *array, int size, int K){ int i; /* If K is smaller that smallest element of array, then smallest element is the ceiling of K*/ if(K <= array[0]) printf("%d ", array[0]); /* If K is larger than the largest element of array, then No ceiling element of K exist in array */ if(K > array[size-1]) printf("No Ceiling Element"); /* Traverse input array and search for appropriate position of K in sorted array */ for(i = 0; i< size; i++){ if(K == array[i]) printf("%d", array[i]); if(array[i] < K && array[i+1] > K) printf("%d", array[i+1]); } } int main(){ int array[10] = {1, 3, 5, 6, 8, 10, 11, 14, 15, 20}; printCeilingElement(array, 10, 12); return 0; }Output

14

**By using customized binary search : O(LogN)**

**Algorithm to find smallest number greater than given number X.**

- If X is smaller than smallest element of inputArray(inputArray[0]). Then smallest element is ceiling element of X.
- If X is larger than largest element of inputArray(inputArray[N-1]), then no ceiling element exist for X.
- Now do customized binary search.
- If X is larger than array[mid], then check if array[mid+1] is > X or recursively search in right sub array.
- If X is smaller than array[mid], then check if array[mid-1] is < X or recursively search in left sub array

## C program to find ceiling of a number in sorted array

#include <stdio.h> /* This function returns the index of ceiling of K in sorted array */ int getCeilingIndex(int *array, int left, int right, int K) { int mid; /* If K is smaller that smallest element of array, then smallest element is the ceiling of K*/ if(K <= array[left]) return left; /* If K is larger than the largest element of array, then No ceiling element of K exist in array */ if(K > array[right]) return -1; mid = (left + right)/2; /* CUSTUMIZED BINARY SEARCH */ /* If K is equal to middle element, then return mid */ if(array[mid] == K) return mid; /* If K is larger than array[mid], then check if array[mid+1] is > K or recursively search in right sub array */ else if(array[mid] < K){ if(mid + 1 <= right && K <= array[mid+1]) return mid + 1; else return getCeilingIndex(array, mid+1, right, K); } /* If K is smaller than array[mid], then check if array[mid-1] is < K or recursively search in right sub array */ else { if(mid - 1 >= left && K > array[mid-1]) return mid; else return getCeilingIndex(array, left, mid - 1, K); } } int main(){ int array[10] = {1, 3, 5, 6, 8, 10, 11, 14, 15, 20}; int index = getCeilingIndex(array, 0, 9, 12); if(index == -1){ printf("No Ceiling Element found in Array"); } else { printf("Ceiling Element : %d", array[index]); } return 0; }Output

14