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  • HDU 5492 Find a path

    Find a path

    Time Limit: 1000ms
    Memory Limit: 32768KB
    This problem will be judged on HDU. Original ID: 5492
    64-bit integer IO format: %I64d      Java class name: Main

    Frog fell into a maze. This maze is a rectangle containing N rows and M columns. Each grid in this maze contains a number, which is called the magic value. Frog now stays at grid (1, 1), and he wants to go to grid (N, M). For each step, he can go to either the grid right to his current location or the grid below his location. Formally, he can move from grid (x, y) to (x + 1, y) or (x, y +1), if the grid he wants to go exists.
    Frog is a perfectionist, so he'd like to find the most beautiful path. He defines the beauty of a path in the following way. Let’s denote the magic values along a path from (1, 1) to (n, m) as $A_1,A_2,…A_{N+M−1}$, and $A_{avg}$ is the average value of all $A_i$. The beauty of the path is (N+M–1) multiplies the variance of the values:$(N+M−1)sum_{i=1}^{N+M−1}(A_i−A_{avg})^2$
    In Frog's opinion, the smaller, the better. A path with smaller beauty value is more beautiful. He asks you to help him find the most beautiful path.


    Input
    The first line of input contains a number T indicating the number of test cases $(Tleq 50).$
    Each test case starts with a line containing two integers N and M $(1leq N,Mleq 30)$. Each of the next N lines contains M non-negative integers, indicating the magic values. The magic values are no greater than 30.


    Output
    For each test case, output a single line consisting of “Case #X: Y”. X is the test case number starting from 1. Y is the minimum beauty value.


    Sample Input
    1
    2 2
    1 2
    3 4


    Sample Output
    Case #1: 14


    Source
    2015 ACM/ICPC Asia Regional Hefei Online

    解题:动态规划,最小方差路

    $dp[i][j][k]表示在(i,j)格子中sum{A_i}为k的时候最小的sum{A_i^2}$

     1 #include <bits/stdc++.h>
     2 using namespace std;
     3 const int INF = 0x3f3f3f3f;
     4 const int maxn = 35;
     5 int mp[maxn][maxn],dp[maxn][maxn][1810];
     6 int main(){
     7     int kase,n,m,cs = 1;
     8     scanf("%d",&kase);
     9     while(kase--){
    10         scanf("%d%d",&n,&m);
    11         for(int i = 1; i <= n; ++i)
    12             for(int j = 1; j <= m; ++j)
    13                 scanf("%d",mp[i] + j);
    14         memset(dp,0x3f,sizeof dp);
    15         dp[1][0][0] = dp[0][1][0] = 0;
    16         for(int i = 1; i <= n; ++i){
    17             for(int j = 1; j <= m; ++j){
    18                 for(int k = 0; k <= 1800; ++k){
    19                     if(dp[i-1][j][k] != INF)
    20                         dp[i][j][k + mp[i][j]] = min(dp[i][j][k + mp[i][j]],dp[i-1][j][k] + mp[i][j]*mp[i][j]);
    21                     if(dp[i][j-1][k] != INF)
    22                         dp[i][j][k + mp[i][j]] = min(dp[i][j][k + mp[i][j]],dp[i][j-1][k] + mp[i][j]*mp[i][j]);
    23                 }
    24             }
    25         }
    26         int ret = INF;
    27         for(int i = 0; i <= 1800; ++i)
    28             if(dp[n][m][i] < INF) ret = min(ret,(n + m - 1)*dp[n][m][i] - i*i);
    29         printf("Case #%d: %d
    ",cs++,ret);
    30     }
    31     return 0;
    32 }
    View Code
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  • 原文地址:https://www.cnblogs.com/crackpotisback/p/4868265.html
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