Algorithm Analysis

We will implement a recursive function with memoization.

Algorithm Implementation

Declare a two-dimensional array for memoizing the function values: dp[x][y] = f(x, y).

long long dp[51][51];

Implementation of the recursive function with memoization.

long long f(int x, int y)
{
    if (x <= 0 || y <= 0) return 0;
    if (dp[x][y] != -1) return dp[x][y];
    if (x <= y) return dp[x][y] = f(x-1,y-2) + f(x-2,y-1) + 2;
    return dp[x][y] = f(x-2,y-2) + 1;
}

The main part of the program. Read the input data. Initialize the dp array cells with the value -1. Call the function f(x, y) and print its value.

scanf("%d %d",&x,&y);
memset(dp,-1,sizeof(dp));
printf("%lld\n",f(x,y));