## 1326. Minimum Number of Taps to Open to Water a Garden

There is a one-dimensional garden on the x-axis. The garden starts at the point `0`

and ends at the point `n`

. (i.e The length of the garden is `n`

).

There are `n + 1`

taps located at points `[0, 1, ..., n]`

in the garden.

Given an integer `n`

and an integer array `ranges`

of length `n + 1`

where `ranges[i]`

(0-indexed) means the `i-th`

tap can water the area `[i - ranges[i], i + ranges[i]]`

if it was open.

Return *the minimum number of taps* that should be open to water the whole garden, If the garden cannot be watered return **-1**.

**Example 1:**

Input:n = 5, ranges = [3,4,1,1,0,0]Output:1Explanation:The tap at point 0 can cover the interval [-3,3] The tap at point 1 can cover the interval [-3,5] The tap at point 2 can cover the interval [1,3] The tap at point 3 can cover the interval [2,4] The tap at point 4 can cover the interval [4,4] The tap at point 5 can cover the interval [5,5] Opening Only the second tap will water the whole garden [0,5]

**Example 2:**

Input:n = 3, ranges = [0,0,0,0]Output:-1Explanation:Even if you activate all the four taps you cannot water the whole garden.

**Example 3:**

Input:n = 7, ranges = [1,2,1,0,2,1,0,1]Output:3

**Example 4:**

Input:n = 8, ranges = [4,0,0,0,0,0,0,0,4]Output:2

**Example 5:**

Input:n = 8, ranges = [4,0,0,0,4,0,0,0,4]Output:1

**Constraints:**

`1 <= n <= 10^4`

`ranges.length == n + 1`

`0 <= ranges[i] <= 100`

## Rust Solution

```
struct Solution;
impl Solution {
fn min_taps(n: i32, ranges: Vec<i32>) -> i32 {
let n = n as usize;
let mut jumps = vec![0; n + 1];
for i in 0..=n {
let d = ranges[i];
let l = 0.max(i as i32 - d) as usize;
let r = n.min(i + d as usize);
jumps[l] = jumps[l].max(r - l);
}
let mut end = 0;
let mut reach = 0;
let mut res = 0;
for i in 0..n {
if i > reach {
return -1;
}
reach = reach.max(i + jumps[i]);
if i == end {
res += 1;
end = reach;
}
}
if reach >= n as usize {
res
} else {
-1
}
}
}
#[test]
fn test() {
let n = 5;
let ranges = vec![3, 4, 1, 1, 0, 0];
let res = 1;
assert_eq!(Solution::min_taps(n, ranges), res);
let n = 3;
let ranges = vec![0, 0, 0, 0];
let res = -1;
assert_eq!(Solution::min_taps(n, ranges), res);
let n = 7;
let ranges = vec![1, 2, 1, 0, 2, 1, 0, 1];
let res = 3;
assert_eq!(Solution::min_taps(n, ranges), res);
let n = 8;
let ranges = vec![4, 0, 0, 0, 0, 0, 0, 0, 4];
let res = 2;
assert_eq!(Solution::min_taps(n, ranges), res);
}
```

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