34. Find First and Last Position of Element in Sorted Array 

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class Solution {
    public int[] searchRange(int[] nums, int target) {
        int startIndex = findStartIndex(nums, target);
        if (startIndex == -1) {
            return new int[]{-1, -1};
        } else {
            return new int[]{startIndex, findEndIndex(nums, target)};
        }
    }

    private int findEndIndex(int[] nums, int target) {
        int left = 0, right = nums.length - 1; // [left, right]
        while (left <= right) {
            int mid = (left + right) >>> 1;
            if (nums[mid] < target) {
                left = mid + 1;
            } else if (nums[mid] > target) {
                right = mid - 1;
            } else {
                left = mid + 1;
            }
        }

        // now: right, left
        if (right == -1 || nums[right] != target) {
            return -1;
        }

        return right;
    }

    private int findStartIndex(int[] nums, int target) {
        int left = 0, right = nums.length - 1; // [left, right]
        while (left <= right) {
            int mid = (left + right) >>> 1;
            if (nums[mid] < target) {
                left = mid + 1;
            } else if (nums[mid] > target) {
                right = mid - 1;
            } else {
                right = mid - 1;
            }
        }

        // now: right, left
        if (left == nums.length || nums[left] != target) {
            return -1;
        }

        return left;
    }
}

Binary Search

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class Solution {
    public int[] searchRange(int[] nums, int target) {
        int firstIndex = findFirstIndex(nums, target);
        if (firstIndex >= nums.length || nums[firstIndex] != target) {
            return new int[]{-1, -1};
        }

        int nextValueIndex = findFirstIndex(nums, target + 1);
        return new int[]{firstIndex, nextValueIndex - 1};
    }

    private int findFirstIndex(int[] nums, int target) {
        int left = 0, right = nums.length - 1;
        while (left <= right) { // 注意此处需要使用小于等于，保证数组中所有元素参与比较，否则 [1] 这样的数组无法进入循环，[2, 2] 这样的数组在搜索 3 时 left 会停留在最后一个索引上，导致结果错误
            int mid = (left + right) >>> 1;
            if (nums[mid] < target) {
                left = mid + 1;
            } else if (nums[mid] > target) {
                right = mid - 1;
            } else {
                right = mid - 1; // 注意此处即使搜索到了目标值也要继续搜索，因为我们的搜索目标是第一个位置，而不是搜索到任意一个就返回
            }
        }

        // now: right, left
        return left;
    }
}

注意此题是搜索第一个和最后一个位置而不是搜索插入位置，所以需要比较最后停留的位置的值是否为目标值。

References

34. Find First and Last Position of Element in Sorted Array