# 983. Minimum Cost For Tickets

## Description

You have planned some train traveling one year in advance. The days of the year in which you will travel are given as an integer array days. Each day is an integer from 1 to 365.

Train tickets are sold in three different ways:

• a 1-day pass is sold for costs[0] dollars,
• a 7-day pass is sold for costs[1] dollars, and
• a 30-day pass is sold for costs[2] dollars.

The passes allow that many days of consecutive travel.

• For example, if we get a 7-day pass on day 2, then we can travel for 7 days: 2, 3, 4, 5, 6, 7, and 8.

Return the minimum number of dollars you need to travel every day in the given list of days.

Example 1:

Input: days = [1,4,6,7,8,20], costs = [2,7,15]
Output: 11
Explanation: For example, here is one way to buy passes that lets you travel your travel plan:
On day 1, you bought a 1-day pass for costs[0] = 2, which covered day 1.
On day 3, you bought a 7-day pass for costs[1] = 7, which covered days 3, 4, ..., 9.
On day 20, you bought a 1-day pass for costs[0] = 2, which covered day 20.
In total, you spent 11 and covered all the days of your travel.


Example 2:

Input: days = [1,2,3,4,5,6,7,8,9,10,30,31], costs = [2,7,15]
Output: 17
Explanation: For example, here is one way to buy passes that lets you travel your travel plan:
On day 1, you bought a 30-day pass for costs[2] = 15 which covered days 1, 2, ..., 30.
On day 31, you bought a 1-day pass for costs[0] = 2 which covered day 31.
In total, you spent 17 and covered all the days of your travel.


Constraints:

• 1 <= days.length <= 365
• 1 <= days[i] <= 365
• days is in strictly increasing order.
• costs.length == 3
• 1 <= costs[i] <= 1000

## Solutions

• class Solution {
private static final int[] T = new int[] {1, 7, 30};
private int[] costs;
private int[] days;
private int[] f;
private int n;

public int mincostTickets(int[] days, int[] costs) {
n = days.length;
f = new int[n];
this.costs = costs;
this.days = days;
Arrays.fill(f, -1);
return dfs(0);
}

private int dfs(int i) {
if (i >= n) {
return 0;
}
if (f[i] != -1) {
return f[i];
}
int res = Integer.MAX_VALUE;

for (int k = 0; k < 3; ++k) {
int j = lowerBound(days, days[i] + T[k]);
res = Math.min(res, costs[k] + dfs(j));
}
f[i] = res;
return res;
}

private int lowerBound(int[] days, int x) {
int left = 0, right = days.length;
while (left < right) {
int mid = (left + right) >> 1;
if (days[mid] >= x) {
right = mid;
} else {
left = mid + 1;
}
}
return left;
}
}

• class Solution {
public:
vector<int> t = {1, 7, 30};
vector<int> days;
vector<int> costs;
vector<int> f;
int n;

int mincostTickets(vector<int>& days, vector<int>& costs) {
n = days.size();
this->days = days;
this->costs = costs;
f.assign(n, -1);
return dfs(0);
}

int dfs(int i) {
if (i >= n) return 0;
if (f[i] != -1) return f[i];
int res = INT_MAX;
for (int k = 0; k < 3; ++k) {
int j = lower_bound(days.begin(), days.end(), days[i] + t[k]) - days.begin();
res = min(res, costs[k] + dfs(j));
}
f[i] = res;
return res;
}
};

• class Solution:
def mincostTickets(self, days: List[int], costs: List[int]) -> int:
@cache
def dfs(i):
if i >= len(days):
return 0
res = inf
for c, d in zip(costs, [1, 7, 30]):
j = bisect_left(days, days[i] + d)
res = min(res, c + dfs(j))
return res

return dfs(0)


• func mincostTickets(days []int, costs []int) int {
t := []int{1, 7, 30}
n := len(days)
f := make([]int, n)
for i := range f {
f[i] = -1
}
var dfs func(i int) int
dfs = func(i int) int {
if i >= n {
return 0
}
if f[i] != -1 {
return f[i]
}
res := 0x3f3f3f3f
for k, c := range costs {
j := lowerBound(days, days[i]+t[k])
res = min(res, c+dfs(j))
}
f[i] = res
return res
}
return dfs(0)
}

func lowerBound(arr []int, x int) int {
left, right := 0, len(arr)
for left < right {
mid := (left + right) >> 1
if arr[mid] >= x {
right = mid
} else {
left = mid + 1
}
}
return left
}

• function mincostTickets(days: number[], costs: number[]): number {
const n = days.length,
m = days[n - 1] + 1;
const [a, b, c] = costs;
let dp = new Array(m).fill(0);
for (let i = 1; i < m; i++) {
let x = days.includes(i) ? dp[i - 1] + a : dp[i - 1];
let y = (i > 7 ? dp[i - 7] : dp[0]) + b;
let z = (i > 30 ? dp[i - 30] : dp[0]) + c;
dp[i] = Math.min(x, y, z);
}
return dp[m - 1];
}