UVA1025-A Spy in the Metro(動態規劃)

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Problem UVA1025-A Spy in the MetroAccept: 713  Submit: 6160
Time Limit: 3000 mSec Problem Description

 

 

Input

 

 

 OutputFor each test case, print a line containing the case number (starting with 1) and an integer representing the total waiting time in the stations for a best schedule, or the word ‘impossible’ in case Maria is unable to make the appointment. Use the format of the sample output.  Sample Input4
55
5 10 15
4
0 5 10 20
4
0 5 10 15
4
18
1 2 3
5
0 3 6 10 12
6
0 3 5 7 12 15
2
30
20
1
20
7
1 3 5 7 11 13 17
0  Sample Output

Case Number 1: 5

Case Number 2: 0

Case Number 3: impossible

 

題解：很明顯的動態規劃，dp[i][j]表示i時刻在j網站還需要的最短等待時間，總共就三種選擇，狀態轉移方程很簡單，邊界一直是我寫動態規劃題比較頭疼的地方，不過這個題還比較簡單，t時刻在n網站自然是0，在其他網站就是INF（為了不會從這些狀態轉移過去）。

 

 1 #include <bits/stdc++.h> 2  3 using namespace std; 4  5 const int maxt = 200 + 10, maxn = 50 + 5; 6 const int INF = 0x3f3f3f3f; 7  8 int read() { 9     int q = 0; char ch = ‘ ‘;10     while (ch<‘0‘ || ch>‘9‘) ch = getchar();11     while (‘0‘ <= ch && ch <= ‘9‘) {12         q = q * 10 + ch - ‘0‘;13         ch = getchar();14     }15     return q;16 }17 18 int n, t, m1, m2;19 int ti[maxn];20 int dp[maxt][maxn];21 bool have_train[maxt][maxn][2];22 23 void init() {24     memset(have_train, false, sizeof(have_train));25     for (int i = 1; i <= n - 1; i++) {26         dp[t][i] = INF;27     }28     dp[t][n] = 0;29 }30 31 int T = 1;32 33 int main()34 {35     //freopen("input.txt", "r", stdin);36     while (scanf("%d", &n) && n) {37         t = read();38         init();39         for (int i = 1; i < n; i++) {40             ti[i] = read();41         }42         ti[n] = ti[0] = INF;43         m1 = read();44         int d;45         for (int i = 0; i < m1; i++) {46             d = read();47             int cnt = 1;48             for (int j = 1; j <= n; j++) {49                 have_train[d][cnt][0] = true;50                 //printf("d:%d cnt:%d\n", d, cnt);51                 cnt++;52                 d += ti[j];53             }54         }55         //printf("\n");56 57         m2 = read();58         for (int i = 0; i < m2; i++) {59             d = read();60             int cnt = n;61             for (int j = n; j >= 1; j--) {62                 have_train[d][cnt][1] = true;63                 //printf("d:%d cnt:%d\n", d, cnt);64                 cnt--;65                 d += ti[j - 1];66             }67         }68 69         for (int i = t - 1; i >= 0; i--) {70             for (int j = 1; j <= n; j++) {71                 dp[i][j] = dp[i + 1][j] + 1;72                 if (i + ti[j] <= t && have_train[i][j][0]) {73                     dp[i][j] = min(dp[i][j], dp[i + ti[j]][j + 1]);74                 }75 76                 if (i + ti[j - 1] <= t && have_train[i][j][1]) {77                     dp[i][j] = min(dp[i][j], dp[i + ti[j - 1]][j - 1]);78                 }79             }80         }81 82         printf("Case Number %d: ", T++);83         if (dp[0][1] >= INF) {84             printf("impossible\n");85         }86         else {87             printf("%d\n", dp[0][1]);88         }89     }90     return 0;91 }

 

UVA1025-A Spy in the Metro(動態規劃)