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140 lines (116 loc) · 3.62 KB
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package array;
public class BinarySearch {
// 最简单的二分查找算法：针对有序无重复元素数组
// 迭代
public static int binarySearch(int[] array, int target) {
if (array == null) return -1;
int lo = 0;
int hi = array.length-1; // 始终在[lo, hi]范围内查找target
while (lo <= hi) {
int mid = lo + ((hi - lo) >> 1); // 这里若是 (lo + hi) / 2 有可能造成整型溢出
if (array[mid] > target) {
hi = mid - 1;
} else if (array[mid] < target) {
lo = mid + 1;
} else {
return mid;
}
}
return -1;
}
// 递归
public static int binarySearchRecur(int[] array, int target) {
if (array == null) return -1;
return bs(array, target, 0, array.length-1);
}
private static int bs(int[] array, int target, int lo, int hi) {
if (lo <= hi) {
int mid = lo + ((hi - lo) >> 1);
if (array[mid] > target) {
return bs(array, target, lo, mid-1);
} else if (array[mid] < target) {
return bs(array, target, mid+1, hi);
} else {
return mid;
}
}
return -1;
}
// 二分查找变形问题
// 1. 查找第一个值等于给定值的元素
public static int bsFirst(int[] array, int target) {
int lo = 0;
int hi = array.length - 1;
while (lo <= hi) {
int mid = lo + ((hi - lo) >> 1);
if (array[mid] > target) {
hi = mid - 1;
} else if (array[mid] < target) {
lo = mid + 1;
} else {
if (mid == lo || array[mid-1] != array[mid]) {
return mid;
} else {
hi = mid - 1;
}
}
}
return -1;
}
// 2. 查找最后一个值等于给定值的元素
public static int bsLast(int[] array, int target) {
int lo = 0;
int hi = array.length - 1;
while (lo <= hi) {
int mid = lo + ((hi - lo) >> 1);
if (array[mid] > target) {
hi = mid - 1;
} else if (array[mid] < target) {
lo = mid + 1;
} else {
if (mid == hi || array[mid] != array[mid+1]) {
return mid;
} else {
lo = mid + 1;
}
}
}
return -1;
}
// 3. 查找第一个大于等于给定值的元素
public static int bsFistGE(int[] array, int target) {
int lo = 0;
int hi = array.length - 1;
while (lo <= hi) {
int mid = lo + ((hi - lo) >> 1);
if (array[mid] >= target) {
if (mid == 0 || array[mid-1] < target) {
return mid;
} else {
hi = mid - 1;
}
} else {
lo = mid + 1;
}
}
return -1;
}
// 4. 查找最后一个小于等于给定值的元素
public static int bsLastLE(int[] array, int target) {
int lo = 0;
int hi = array.length - 1;
while (lo <= hi) {
int mid = lo + ((hi - lo) >> 1);
if (array[mid] <= target) {
if (mid == hi || array[mid+1] > target) {
return mid;
} else {
lo = mid + 1;
}
} else {
hi = mid - 1;
}
}
return -1;
}
}