I solved https://projecteuler.net/problem=18 with the concept of DP!!

Euler18.swift

var cashe :Dictionary<String, Int> = [:]

func search (list: [[Int]], i:Int, j:Int) -> Int {
    if cashe["\(i):\(j)"] != nil {
        return cashe["\(i):\(j)"]!
    }
    if i > 14{
        return 0
    }
    else {
        let ans1 = list[i][j] + search(list, i: i+1, j: j)
        let ans2 = list[i][j] + search(list, i: i+1, j: j+1)
        let answer = max(ans1, ans2)
        cashe["\(i):\(j)"] = answer
        return answer
    }
}


var list = [
    [75],
    [95, 64],
    [17, 47, 82],
    [18, 35, 87, 10],
    [20, 04, 82, 47, 65],
    [19, 01, 23, 75, 03, 34],
    [88, 02, 77, 73, 07, 63, 67],
    [99, 65, 04, 28, 06, 16, 70, 92],
    [41, 41, 26, 56, 83, 40, 80, 70, 33],
    [41, 48, 72, 33, 47, 32, 37, 16, 94, 29],
    [53, 71, 44, 65, 25, 43, 91, 52, 97, 51, 14],
    [70, 11, 33, 28, 77, 73, 17, 78, 39, 68, 17, 57],
    [91, 71, 52, 38, 17, 14, 91, 43, 58, 50, 27, 29, 48],
    [63, 66, 04, 68, 89, 53, 67, 30, 73, 16, 69, 87, 40, 31],
    [04, 62, 98, 27, 23, 09, 70, 98, 73, 93, 38, 53, 60, 04, 23]
]

print(search(list, i: 0, j: 0))