67 lines
2.2 KiB
C
67 lines
2.2 KiB
C
/**
|
|
* File: binary_search_edge.c
|
|
* Created Time: 2023-09-09
|
|
* Author: Gonglja (glj0@outlook.com)
|
|
*/
|
|
|
|
#include "../utils/common.h"
|
|
|
|
/* Binary search for insertion point (with duplicate elements) */
|
|
int binarySearchInsertion(int *nums, int numSize, int target) {
|
|
int i = 0, j = numSize - 1; // Initialize double closed interval [0, n-1]
|
|
while (i <= j) {
|
|
int m = i + (j - i) / 2; // Calculate midpoint index m
|
|
if (nums[m] < target) {
|
|
i = m + 1; // Target is in interval [m+1, j]
|
|
} else {
|
|
j = m - 1; // First element less than target is in interval [i, m-1]
|
|
}
|
|
}
|
|
// Return insertion point i
|
|
return i;
|
|
}
|
|
|
|
/* Binary search for the leftmost target */
|
|
int binarySearchLeftEdge(int *nums, int numSize, int target) {
|
|
// Equivalent to finding the insertion point of target
|
|
int i = binarySearchInsertion(nums, numSize, target);
|
|
// Did not find target, thus return -1
|
|
if (i == numSize || nums[i] != target) {
|
|
return -1;
|
|
}
|
|
// Found target, return index i
|
|
return i;
|
|
}
|
|
|
|
/* Binary search for the rightmost target */
|
|
int binarySearchRightEdge(int *nums, int numSize, int target) {
|
|
// Convert to finding the leftmost target + 1
|
|
int i = binarySearchInsertion(nums, numSize, target + 1);
|
|
// j points to the rightmost target, i points to the first element greater than target
|
|
int j = i - 1;
|
|
// Did not find target, thus return -1
|
|
if (j == -1 || nums[j] != target) {
|
|
return -1;
|
|
}
|
|
// Found target, return index j
|
|
return j;
|
|
}
|
|
|
|
/* Driver Code */
|
|
int main() {
|
|
// Array with duplicate elements
|
|
int nums[] = {1, 3, 6, 6, 6, 6, 6, 10, 12, 15};
|
|
printf("\nArray nums =");
|
|
printArray(nums, sizeof(nums) / sizeof(nums[0]));
|
|
|
|
// Binary search for left and right boundaries
|
|
int targets[] = {6, 7};
|
|
for (int i = 0; i < sizeof(targets) / sizeof(targets[0]); i++) {
|
|
int index = binarySearchLeftEdge(nums, sizeof(nums) / sizeof(nums[0]), targets[i]);
|
|
printf("Index of the leftmost element %d = %d\n", targets[i], index);
|
|
index = binarySearchRightEdge(nums, sizeof(nums) / sizeof(nums[0]), targets[i]);
|
|
printf("Index of the rightmost element %d = %d\n", targets[i], index);
|
|
}
|
|
|
|
return 0;
|
|
} |