UVALive - 2031 Dance Dance Revolution 三維dp

UVALive - 2031 Dance Dance Revolution 三維dp

題目大意：有一個胖子在玩跳舞機，剛開始的位置在(0,0)，跳舞機有四個方向鍵，上左下右分別對應1,2,3,4.現在有以下規則
1.如果從0位置移動到任意四個位置，消耗能量2
2.如果從非0位置跳到相鄰的位置，如1跳到2或4，消耗能量3
3.如果從非0位置跳到對面的位置，如2跳到4，消耗能量4
4.如果跳同一個位置，消耗能量1
5.兩只腳不能在同一個位置

解題思路：這題其實很水，直接暴力就可以解決了，討論所有情況，用dp[i][j][k]表示跳第k個數字，左腳在i這個位置，右腳在j這個位置時所消耗的能量，接著分類討論

1.如果其中一只腳在0上的情況
2.其中一只腳踩的數字和當前要跳的數字一樣
3.兩只腳踩的數字和當前的數字不一樣

三種情況，分別在細分即可，具體看代碼

#include
#include
#include
using namespace std;
#define maxn 50010
#define INF 0x3f3f3f3f
int dp[5][5][maxn];
int seq[maxn];
int strength[2] = {4,3};
int n;

int solve() {
    memset(dp, 0x3f, sizeof(dp));
    dp[0][seq[0]][0] = dp[seq[0]][0][0] = 2;

    for(int i = 1; i < n; i++) {
        for(int j = 0; j < 5; j++) {
            if(dp[j][seq[i-1]][i-1] != INF) {

                if(j == 0) {
                    if(seq[i] != seq[i-1])
                        dp[seq[i]][seq[i-1]][i] = dp[j][seq[i-1]][i-1] + 2;

                    if(seq[i] == seq[i-1])
                        dp[j][seq[i-1]][i] = dp[j][seq[i-1]][i-1] + 1;
                    else
                        dp[j][seq[i]][i] = dp[j][seq[i-1]][i-1] + strength[(seq[i-1] + seq[i]) % 2];    
                }
                else if(j == seq[i] || seq[i-1] == seq[i]) 
                    dp[j][seq[i-1]][i] = min(dp[j][seq[i-1]][i],dp[j][seq[i-1]][i-1] + 1);
                else {
                    dp[seq[i]][seq[i-1]][i] = min(dp[j][seq[i-1]][i-1] + strength[(j + seq[i]) % 2], dp[seq[i]][seq[i-1]][i]);
                    dp[j][seq[i]][i] = min(dp[j][seq[i-1]][i-1] + strength[(seq[i-1] + seq[i] ) % 2], dp[j][seq[i]][i]);
                }
            }

            if(dp[seq[i-1]][j][i-1] != INF) {
                if(j == 0) {
                    if(seq[i] != seq[i-1])
                        dp[seq[i]][seq[i-1]][i] = dp[seq[i-1]][j][i-1] + 2;

                    if(seq[i] == seq[i-1])
                        dp[seq[i-1]][j][i] = dp[seq[i-1]][j][i-1] + 1;
                    else
                        dp[seq[i]][j][i] = dp[seq[i-1]][j][i-1] + strength[(seq[i-1] + seq[i]) % 2];    
                }

                if(j == seq[i] || seq[i-1] == seq[i]) 
                    dp[seq[i-1]][j][i] = min(dp[seq[i-1]][j][i],dp[seq[i-1]][j][i-1] + 1);
                else {
                    dp[seq[i]][seq[i-1]][i] = min(dp[seq[i-1]][j][i-1] + strength[(j + seq[i]) % 2], dp[seq[i]][seq[i-1]][i]);
                    dp[seq[i]][j][i] = min(dp[seq[i-1]][j][i-1] + strength[(seq[i-1] + seq[i] ) % 2], dp[seq[i]][j][i]);
                }
            }
        }
    }
    int ans = INF;
    for(int i = 0; i < 5; i++)
        ans = min(min(ans, dp[seq[n-1]][i][n-1]), dp[i][seq[n-1]][n-1]);

    return ans;
}

int main() {
    n = 0;
    while(scanf("%d", &seq[n]) != EOF && seq[n++]) {
        while(scanf("%d", &seq[n]) && seq[n])
            n++;    
        printf("%d\n", solve());
        n = 0;
    }
    return 0;
}

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