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DREAMGRID 的 Music Game Problem Analysis

DREAMGRID recently finished a music game called "Live Love," and he received a sequence of notes consisting of "PERFECT" and "NON-PERFECT" results. The score of the song is determined by the maximum number of continuous "PERFECT" results in the sequence, known as the max-combo.

Problem Analysis

The sequence's score is the length of the longest consecutive "PERFECT" streak. The challenge is to determine the minimum and maximum possible scores given the total number of "PERFECT" results and the sequence length.

Key Insights

Solution Code

#include 
   
    #include 
    
     #include 
     
      #include 
      
       using namespace std;int main() {    int t, n, m;    vector
       
         a(30, 0);    scanf("%d", &t);    while (t--) {        scanf("%d%d", &n, &m);        // Calculate maximum possible score        int maxx = m;        if (m == 0) {            maxx = 0;        } else if (n == m) {            maxx = n;        } else {            maxx = m;        }        // Calculate minimum possible score        int minn = 1;        if (m == 0) {            minn = 0;        } else {            int gaps = n - m;            if (gaps == 0) {                minn = m;            } else if (gaps <= m - 1) {                minn = 1;            } else {                minn = (m + gaps - 1) / gaps;            }        }        cout << maxx << " " << minn << endl;    }    return 0;}
       
      
     
    
   

XOR Clique Problem Analysis

The problem requires finding the maximum subset of a given sequence where the XOR of any two elements is less than the smaller of the two.

Key Insights

Solution Code

#include 
   
    #include 
    
     #include 
     
      #include 
      
       using namespace std;int main() {    int t, n;    vector
       
         nums;    scanf("%d", &t);    while (t--) {        scanf("%d", &n);        nums.clear();        while (n--) {            int x = 0;            int y = 0;            while (nums.size() < 30) {                x++;                if ((x & 1) == 1) {                    y |= (1 << (x - 1));                }                x >>= 1;            }            nums.push_back(y);        }        int max_group = 0;        if (!nums.empty()) {            int count[30] = {0};            for (int num : nums) {                int bits = 0;                while (num) {                    bits++;                    num >>= 1;                }                count[bits]++;                max_group = max(max_group, count[bits]);            }        }        cout << max_group << endl;    }    return 0;}
       
      
     
    
   

Summary of Results

• DREAMGRID Problem: For each test case, compute the maximum and minimum possible scores based on the sequence length and number of "PERFECT" results.
• XOR Clique Problem: Determine the maximum subset size where the XOR of any two elements is less than the smaller element, achieved by grouping numbers by their binary lengths.