35. Search Insert Position 

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class Solution {
    public int searchInsert(int[] nums, int target) {
        int left = 0, right = nums.length - 1; // [left, right]
        while (left <= right) {
            int mid = (left + right) >>> 1;
            if (target > nums[mid]) {
                left = mid + 1; // 此处不断推进 left 索引能保证最后 left 停留的位置能够合法放置 target
            } else if (target < nums[mid]) {
                right = mid - 1; // 此处不用 mid 是防止死循环，虽然 right 把正确的值排除了，但是最后返回的 left
            } else {
                return mid;
            }
        }

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

Binary Search

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class Solution {
    public int searchInsert(int[] nums, int target) {
        int left = 0, right = nums.length; // [left, right)
        while (left < right) {
            int mid = (left + right) >>> 1;
            if (nums[mid] < target) {
                left = mid + 1;
            } else {
                right = mid;
            }
        }

        // now: left equals to right
        return left;
    }
}

References

35. Search Insert Position
剑指 Offer II 068. 查找插入位置