C Program to Find Ceiling of a Number in Sorted Array

  • 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
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