# 1652. Defuse Bombs: Simple Prefix and Use Problems

## Topic description

This is on LeetCode 1652. Defuse the Bomb , the difficulty is easy.

Tag : "simulation", "prefix sum"

You have a bomb to defuse and time is running out! Your agent will give you a circular array code of length n and a key k.

To get the correct password, you need to replace every number. All numbers will be replaced at the same time.

• If $k > 0$, replace the ith number with the sum of the next k numbers.
• If $k < 0$, replace the ith digit with the sum of the previous k digits.
• If $k = 0$, replace the i-th digit with 0.

Since code is cyclic, the next element of code[n-1] is code[0] and the previous element of code[0] is code[n-1] .

Given the loop array code and integer key k, please return the decrypted result to defuse the bomb!

Example 1:

enter: code = [5,7,1,4], k = 3

output:[12,10,16,13]

Explanation: Each number is replaced by the sum of the next 3 numbers. The decrypted password is [7+1+4, 1+4+5, 4+5+7, 5+7+1]. Notice that the arrays are concatenated circularly.

Example 2:

enter: code = [1,2,3,4], k = 0

output:[0,0,0,0]

Explanation: when k When 0, all numbers are replaced by 0.

Example 3:

enter: code = [2,4,9,3], k = -2

output:[12,5,6,13]

Explanation: The decrypted password is [3+9, 2+3, 4+2, 9+4] . Notice that the arrays are concatenated circularly. if k is negative, then the sum is the number before .

hint:

• $n = code.length$
• $1 <= nĀ <= 100$
• $1 <= code[i] <= 100$
• $-(n - 1) <= k <= n - 1$

## prefix sum

According to the meaning of the question code is a circular array, we can build a prefix sum array of length $2 \times n$ (for convenience, we make the prefix and array subscripts start from $1$), and use the prefix sum array to construct the answer.

For each $ans[i - 1]$where $i$ranges from $[1, n]$, we determine Which paragraph is taken from the prefix and array based on the positive and negative k values:

• If there is $k < 0$: you need to take the number of $-k$before the position $i$to prevent the lower crossing mark, first move the position $i$backwards by $n$offsets (i.e., position $i + n$), then you know the corresponding interval $[i + n + k, i + n - 1]$, corresponding interval and $sum[i + n - 1] - sum[i + n + k - 1]$
• If there is $k > 0$: the number of $k$after the position $i$is required, corresponding to the prefix and array subscript $[i + 1, i + k]$, corresponding to the interval sum of $sum[i + k] - sum[i]$

Java code:

class Solution {
public int[] decrypt(int[] code, int k) {
int n = code.length;
int[] ans = new int[n];
if (k == 0) return ans;
int[] sum = new int[n * 2 + 10];
for (int i = 1; i <= 2 * n; i++) sum[i] += sum[i - 1] + code[(i - 1) % n];
for (int i = 1; i <= n; i++) {
if (k < 0) ans[i - 1] = sum[i + n - 1] - sum[i + n + k - 1];
else ans[i - 1] = sum[i + k] - sum[i];
}
return ans;
}
}

TypeScript code:

function decrypt(code: number[], k: number): number[] {
const n = code.length
const ans = new Array<number>(n).fill(0)
if (k == 0) return ans
const sum = new Array<number>(2 * n + 10).fill(0)
for (let i = 1; i <= 2 * n; i++) sum[i] = sum[i - 1] + code[(i - 1) % n]
for (let i = 1; i <= n; i++) {
if (k < 0) ans[i - 1] = sum[i + n - 1] - sum[i + n + k - 1]
else ans[i - 1] = sum[i + k] - sum[i]
}
return ans
};

Python code:

class Solution:
def decrypt(self, code: List[int], k: int) -> List[int]:
n = len(code)
ans = [0] * n
if k == 0:
return ans
sum = [0] * (2 * n + 10)
for i in range(1, 2 * n + 1):
sum[i] = sum[i - 1] + code[(i - 1) % n]
for i in range(1, n + 1):
if k < 0:
ans[i - 1] = sum[i + n - 1] - sum[i + n + k - 1]
else:
ans[i - 1] = sum[i + k] - sum[i]
return ans
• Time complexity: $O(n)$
• Space complexity: $O(n)$

## at last

This is No.1652 of our "Brush through LeetCode" series, starting in 2021/01/01. There are 1916 titles on LeetCode as of the start date, some of which are all lock titles. We will start with all Finished the topics with the lock.

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