By SaddisticDude, history, 5 weeks ago, Hi I came across this problem which I later found exactly on leetcode,

A series of highways connect n cities numbered from 0 to n — 1. You are given a 2D integer array highways where highways[i] = [city1i, city2i, tolli] indicates that there is a highway that connects city1i and city2i, allowing a car to go from city1i to city2i and vice versa for a cost of tolli.

You are also given an integer discounts which represents the number of discounts you have. You can use a discount to travel across the ith highway for a cost of tolli / 2 (integer division). Each discount may only be used once, and you can only use at most one discount per highway.

Return the minimum total cost to go from city 0 to city n — 1, or -1 if it is not possible to go from city 0 to city n — 1

You can find more explanation here here

I know this can be solved by using Djikstra but I was curious whether it can be solved using dfs + memoization(top down DP)

Tried to implement a solution but its failing on 72/76 test case.

class Solution {
public:
const int inf = 1e9;
vector<vector<int>>dp;
vector<bool>vis;
int n;
int dfs(int u, int discounts){
if(u==n-1)
return 0;

if(dp[u][discounts]!=-1){
return dp[u][discounts];
}

vis[u] = true;

int ans = inf;
if(vis[v])
continue;
ans = min(ans, w + dfs(v, discounts));
if(discounts>0){
ans = min(ans,  (w/2) + dfs(v, discounts-1));
}
}
vis[u] = false;
return dp[u][discounts] = ans;
}
int minimumCost(int nn, vector<vector<int>>& highways, int discounts) {
n = nn;
dp.assign(n, vector<int>(discounts+1, -1));
vis.assign(n, false);

for(auto& edges:highways){
auto [u,v,w] = tuple(edges, edges, edges);
}

int ans = dfs(0, discounts);

if(ans<inf)
return ans;
return -1;
}
};


Can anyone help to understand the flaw in my solution or propose their own solution? dp, Comments (4)
 » Auto comment: topic has been updated by SaddisticDude (previous revision, new revision, compare).
 » What are the bounds? Are the bounds large enough to make the problem's answer not fit in integer?
 » Provide properly understandable statement
 » 5 weeks ago, # | ← Rev. 2 →   I couldn't find any problem in your solution either :( Maybe seeing the test case can give some hint. (I don't have leetcode premium so I can't check that out myself)For people having no leetcode premium: Question LinkEdit1: Just a suggestion when your code is long you can use spoiler tag to hide it. Check under Markdown general formatting: https://codeforces.cc/blog/entry/104522