Similar to the relationship between marginal and joint distribution in form, we put forward a novel approximate greedy algorithm for Robot Coin Collection Problem. By reducing the coin distribution in the matrix to the marginal distribution, we can perform the greedy selection on the marginal distribution and locate the sub-matrix most likely to pick up the most coins. Moreover, we can obtain the approximate solution by recursion. The space complexity can be reduced to O(m+n) under the condition that the time complexity is guaranteed to be O(mn) without increasing the original problem conditions. Meanwhile, in the worse case, twice the maximum number of coins picked up by our method is more than that of the optimal solution. If we extend the dimension of the matrix to x-dimension, x ≥ 2, the space complexity can be reduced to O(mx-1) while the time complexity is still O(mx).