Count Pairs Whose Sum is Less than Target
Given a <strong>0-indexed</strong> integer array <code>nums</code> of length <code>n</code> and an integer <code>target</code>, return <em>the number of pairs</em> <code>(i, j)</code> <em>where</em> <code>0 &lt;= i &lt; j &lt; n</code> <em>and</em> <code>nums[i] + nums[j] &lt; target</code>.

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [-1,1,2,3,1], target = 2
<strong>Output:</strong> 3
<strong>Explanation:</strong> There are 3 pairs of indices that satisfy the conditions in the statement:
- (0, 1) since 0 &lt; 1 and nums[0] + nums[1] = 0 &lt; target
- (0, 2) since 0 &lt; 2 and nums[0] + nums[2] = 1 &lt; target 
- (0, 4) since 0 &lt; 4 and nums[0] + nums[4] = 0 &lt; target
Note that (0, 3) is not counted since nums[0] + nums[3] is not strictly less than the target.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [-6,2,5,-2,-7,-1,3], target = -2
<strong>Output:</strong> 10
<strong>Explanation:</strong> There are 10 pairs of indices that satisfy the conditions in the statement:
- (0, 1) since 0 &lt; 1 and nums[0] + nums[1] = -4 &lt; target
- (0, 3) since 0 &lt; 3 and nums[0] + nums[3] = -8 &lt; target
- (0, 4) since 0 &lt; 4 and nums[0] + nums[4] = -13 &lt; target
- (0, 5) since 0 &lt; 5 and nums[0] + nums[5] = -7 &lt; target
- (0, 6) since 0 &lt; 6 and nums[0] + nums[6] = -3 &lt; target
- (1, 4) since 1 &lt; 4 and nums[1] + nums[4] = -5 &lt; target
- (3, 4) since 3 &lt; 4 and nums[3] + nums[4] = -9 &lt; target
- (3, 5) since 3 &lt; 5 and nums[3] + nums[5] = -3 &lt; target
- (4, 5) since 4 &lt; 5 and nums[4] + nums[5] = -8 &lt; target
- (4, 6) since 4 &lt; 6 and nums[4] + nums[6] = -4 &lt; target
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length == n &lt;= 50</code></li>
	<li><code>-50 &lt;= nums[i], target &lt;= 50</code></li>
</ul>
Array; Two Pointers; Binary Search; Sorting
class Solution {
    public int countPairs(List<Integer> nums, int target) {
        Collections.sort(nums);
        int ans = 0;
        for (int j = 0; j < nums.size(); ++j) {
            int x = nums.get(j);
            int i = search(nums, target - x, j);
            ans += i;
        }
        return ans;
    }

    private int search(List<Integer> nums, int x, int r) {
        int l = 0;
        while (l < r) {
            int mid = (l + r) >> 1;
            if (nums.get(mid) >= x) {
                r = mid;
            } else {
                l = mid + 1;
            }
        }
        return l;
    }
}