Python中二维数组子部分的总和

Question

Here is a task description: I have 2d array NxM, N, M<1000, and there are K(K<100000) sets of coordinates(x1, x2, y1, y2). I need to sum all the elements in rectangle(x1, x2, y1, y2).
My code works but I need make it faster cause the largest tests dont work in required time.

Here it is:

def build_y(cx, fx, lx, cy, fy, ly):
    if fy == ly:
        if fx == lx:
            t[cx][cy] = a[fx][fy]
        else:
            t[cx][cy] = t[cx*2][cy] + t[cx*2+1][cy];
    else:
        my = int((fy + ly) / 2)
        build_y (cx, fx, lx, cy*2, fy, my)
        build_y (cx, fx, lx, cy*2+1, my+1, ly)
        t[cx][cy] = t[cx][cy*2] + t[cx][cy*2+1]

def build_x(cx, fx, lx):
    if fx != lx:
        mx = int((fx + lx) / 2)
        build_x (cx*2, fx, mx)
        build_x (cx*2+1, mx+1, lx)
    build_y (cx, fx, lx, 1, 0, m-1)

def sum_y (cx, cy, tfy, tly, fy, ly):
    if fy > ly:
        return 0
    if fy == tfy and tly == ly:
        return t[cx][cy]
    tmy = int((tfy + tly) / 2)
    return sum_y(cx, cy*2, tfy, tmy, fy, min(ly, tmy)) + sum_y(cx, cy*2+1, tmy+1, tly, max(fy, tmy+1), ly)
def sum_x(cx, tfx, tlx, fx, lx, fy, ly):
    if fx > lx:
        return 0
    if fx == tfx and tlx == lx:
        return sum_y(cx, 1, 0, m-1, fy, ly)
    tmx = int((tfx + tlx) / 2)
    return sum_x(cx*2, tfx, tmx, fx, min(lx, tmx), fy, ly) + sum_x(cx*2+1, tmx+1, tlx, max(fx, tmx+1), lx, fy, ly)
fin = open('input.txt', 'r').read().split()
n = int(fin[0])
m = int(fin[1])
k = int(fin[2])
a = []
b = []
t = [0]*3*n
for i in range(3*n):
    t[i] = [0]*3*m
for i in range(n):
    a.append([int(j) for j in fin[3+i*m:3+i*m+m]])
build_x(1, 0, n-1)
for i in range(k):
    b.append([int(j) for j in fin [3+n*m+4*i:3+n*m+4*i+4]])
for i in range(k):
    print(sum_x(1, 0, n-1, b[i][0]-1, b[i][2]-1, b[i][1]-1, b[i][3]-1))

Answer 1

use numpy and rewrite all the lists as numpy arrays, for example t[cx][cy] = a[fx][fy] becomes t[cx,cy] = a[fx,fy] after you have initialized t, a as numpy arrays. You can simply get a factor 100 of speed-up. In fact, the numpy operations are much faster than list operations, so if you have a lot of them the use of numpy is very suitable.