## Description

Koko loves to eat bananas. There are N piles of bananas, the i-th pile has piles[i] bananas. The guards have gone and will come back in H hours.

Koko can decide her bananas-per-hour eating speed of K. Each hour, she chooses some pile of bananas, and eats K bananas from that pile. If the pile has less than K bananas, she eats all of them instead, and won’t eat any more bananas during this hour.

Koko likes to eat slowly, but still wants to finish eating all the bananas before the guards come back.

Return the minimum integer K such that she can eat all the bananas within H hours.

Example 1: Input: piles = [3,6,7,11], H = 8 Output: 4

Example 2: Input: piles = [30,11,23,4,20], H = 5 Output: 30

Example 3: Input: piles = [30,11,23,4,20], H = 6 Output: 23

Note:

1 <= piles.length <= 10^4 piles.length <= H <= 10^9 1 <= piles[i] <= 10^9

## Solution

Use binary search, this problem is the fourth kind of question in our binary search problem set in this summary. When we want to find a target that meets certain conditions in a large or limited solution space, we should think of if we can use binary search, eg. Find square root of a number.

## Code

```
class Solution {
public:
int minEatingSpeed(vector<int>& piles, int H) {
int left = 1;
int right = maxPile(piles); /*❶*/
while(left < right) { /*❷*/
int mid = left + (right - left)/2;
if(canEat(piles, mid, H)) {
right = mid;
}else{
left = mid + 1;
}
}
return left; /*❸*/
}
int maxPile(vector<int>& piles) {
int max = 0;
for(auto pile : piles) {
if(max < pile) {
max = pile;
}
}
return max;
}
bool canEat(vector<int>& piles, int mid, int H) {
int count = 0;
for(auto pile : piles) {
count += (pile-1)/mid + 1;
}
return count <= H;
}
};
```

❶ Get the limited solution space, or we could just a very large space.

❷, ❸ This is the template used in this thread

## Insight

- We can think of this question as is there a lower bound of H that meets the requirement. So when we want to find a lower bound of the target, use this template. and the index left is the lower bound position.
- After realize this is a template for looking for lower bound, please think of the reason why
**left < right**and**right = mid**. These two key attributes are important.