You have infinitely many lakes, all initially empty. When it rains on lake n, that lake becomes full. If it rains on a lake that is already full, a flood happens. Your goal is to prevent all floods.

You are given an integer array rains where:

  • rains[i] > 0 means rain on lake rains[i] on day i
  • rains[i] == 0 means no rain on day i; you must choose one lake to dry (that lake becomes empty)

Return an array ans such that:

  • ans[i] == -1 if rains[i] > 0
  • ans[i] is the lake number you choose to dry if rains[i] == 0 (any valid lake is fine; typically 1 if no constraint)

Return an empty array if it is impossible to avoid a flood.

Examples

Example 1:

Input: rains = [1,2,3,4]
Output: [-1,-1,-1,-1]
Explanation: No lake rains twice, so no flood. Dry days don't appear.

Example 2:

Input: rains = [1,2,0,0,2,1]
Output: [-1,-1,2,1,-1,-1]
Explanation: Day 2: rain on lake 2. Day 3 (dry): dry lake 2 so it won't flood on day 5. Day 4 (dry): dry lake 1 so it won't flood on day 6.

Example 3:

Input: rains = [1,2,0,1,2]
Output: []
Explanation: Lakes 1 and 2 are full after day 2; only one dry day (day 3). We can dry at most one lake, so the second rain on 1 or 2 causes a flood.

Constraints

  • 1 <= rains.length <= 10^5
  • 0 <= rains[i] <= 10^9

Thinking Process

  1. Last-rain index: Knowing when each lake was last filled tells us we must dry it before the next rain on that lake.
  • The search space must shrink monotonically each step.
  • Decide which half still satisfies the predicate, discard the other.
  • Use mid = left + (right - left) / 2 to avoid overflow.
Binary search: shrink [lo … hi] lo mid hi discard half each step → O(log n)

Common Approaches

Typical techniques for this pattern:

Approach Time Space Notes
Standard binary search (this problem) O(log n) O(1) Sorted array, left <= right
Lower / upper bound O(log n) O(1) First/last position, insert index
Binary search on rotated array O(log n) O(1) Identify sorted half, discard other
Binary search on answer O(n log M) O(1) Monotonic predicate over search space

Solution

// import java.util.*;
class Solution {
    public int[] avoidFlood(int[] rains) {
        public int[] rtn(rains.size(), 1);
        TreeSet<Integer> st = new TreeSet<>();
        HashMap<Integer, Integer> mp = new HashMap<Integer, Integer>();
        for (int i = 0; i < rains.size(); i++) {
            if (rains.put(i,) {
                st.add(i));
            } else {
                rtn.put(i, -1);
                if (mp.contains(rains[i])) {
                    var it = st.floorKey(mp[rains[i]]);
                    if (it == st.iterator()) return {}
                    rtn[*it] = rains[i];
                    st.remove(it);
                }
                mp[rains[i]] = i;
            }
        }
        return rtn;
    }
}

Solution Explanation

Approach: Standard binary search (this problem)

Key idea: 1. Last-rain index: Knowing when each lake was last filled tells us we must dry it before the next rain on that lake.

How the code works:

  1. Last-rain index: Knowing when each lake was last filled tells us we must dry it before the next rain on that lake.
    • The search space must shrink monotonically each step.
    • Decide which half still satisfies the predicate, discard the other.
    • Use mid = left + (right - left) / 2 to avoid overflow.

Walkthrough — input rains = [1,2,3,4], expected output [-1,-1,-1,-1]:

No lake rains twice, so no flood. Dry days don’t appear.

Time: O(n log n) — each dry day is inserted and at most once erased from the set; at most n lower_bound calls. · Space: O(n).

Common Mistakes

  • Skipping edge cases (empty input, single element, boundaries).
  • Off-by-one errors in loops and index ranges.
  • Forgetting to handle the case when no valid answer exists.

Key Takeaways

  1. Last-rain index: Knowing when each lake was last filled tells us we must dry it before the next rain on that lake.
  2. Earliest dry day: lower_bound(mp[lake]) on the set of dry days gives the first valid day to dry that lake.
  3. Default 1: Dry days that are never needed can output any lake number; 1 is valid.

References

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